2026
Benavoli, Alessio; Binder, Felix C.
Quantum Wiener architecture for quantum reservoir computing Journal Article
In: Phys. Rev. A, vol. 114, iss. 1, pp. 012433, 2026.
Links | BibTeX | Tags: quantum computation
@article{benavoli2026d,
title = {Quantum Wiener architecture for quantum reservoir computing},
author = {Alessio Benavoli and Felix C. Binder},
url = {https://link.aps.org/doi/10.1103/ktt8-l2tw},
doi = {10.1103/ktt8-l2tw},
year = {2026},
date = {2026-07-01},
urldate = {2026-07-01},
journal = {Phys. Rev. A},
volume = {114},
issue = {1},
pages = {012433},
publisher = {American Physical Society},
keywords = {quantum computation},
pubstate = {published},
tppubtype = {article}
}
Murphy, Fiona; Benavoli, Alessio
Constraint- and Score-Based Nonlinear Granger Causality Discovery with Kernels Journal Article
In: Machine Learning, vol. 115, no. 7, pp. 150, 2026, ISSN: 1573-0565.
Abstract | Links | BibTeX | Tags: causality, Gaussian Process
@article{Murphy2026,
title = {Constraint- and Score-Based Nonlinear Granger Causality Discovery with Kernels},
author = {Fiona Murphy and Alessio Benavoli},
url = {https://doi.org/10.1007/s10994-026-07093-z},
doi = {10.1007/s10994-026-07093-z},
issn = {1573-0565},
year = {2026},
date = {2026-01-01},
urldate = {2026-01-01},
journal = {Machine Learning},
volume = {115},
number = {7},
pages = {150},
abstract = {Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality (GC) approaches can be theoretically unified under the framework of Kernel Principal Component Regression (KPCR), and introduce a method based on this unification, demonstrating that this approach can improve causal identification. Additionally, we introduce a Gaussian Process score-based model with Smooth Information Criterion penalisation on the marginal likelihood, and demonstrate improved performance over existing state of the art time-series nonlinear causal discovery methods. Furthermore, we propose a contemporaneous causal identification algorithm, fully based on GC, using the proposed score-based GP_SIC method, and compare its performance to a state of the art contemporaneous time series causal discovery algorithm.},
keywords = {causality, Gaussian Process},
pubstate = {published},
tppubtype = {article}
}
Kernel-based methods are used in the context of Granger Causality to enable the identification of nonlinear causal relationships between time series variables. In this paper, we show that two state of the art kernel-based Granger Causality (GC) approaches can be theoretically unified under the framework of Kernel Principal Component Regression (KPCR), and introduce a method based on this unification, demonstrating that this approach can improve causal identification. Additionally, we introduce a Gaussian Process score-based model with Smooth Information Criterion penalisation on the marginal likelihood, and demonstrate improved performance over existing state of the art time-series nonlinear causal discovery methods. Furthermore, we propose a contemporaneous causal identification algorithm, fully based on GC, using the proposed score-based GP_SIC method, and compare its performance to a state of the art contemporaneous time series causal discovery algorithm.
Benavoli, Alessio; Azzimonti, Dario
A tutorial on learning from preferences and choices with Gaussian processes Journal Article
In: Foundations and Trends in Machine Learning, vol. 19, no. 1, pp. 1-120, 2026, ISSN: 1935-8237.
Abstract | Links | BibTeX | Tags:
@article{10.1108/FTMAL-03-2025-0124,
title = {A tutorial on learning from preferences and choices with Gaussian processes},
author = {Alessio Benavoli and Dario Azzimonti},
url = {https://arxiv.org/abs/2403.11782},
doi = {10.1108/FTMAL-03-2025-0124},
issn = {1935-8237},
year = {2026},
date = {2026-01-01},
urldate = {2026-01-01},
journal = {Foundations and Trends in Machine Learning},
volume = {19},
number = {1},
pages = {1-120},
abstract = {Preference modelling lies at the intersection of economics, decision theory, machine learning and statistics. By understanding individuals’ preferences and how they make choices, we can build products that closely match their expectations, paving the way for more efficient and personalised applications across a wide range of domains. The objective of this tutorial is to present a cohesive and comprehensive framework for preference learning with Gaussian processes (GPs), demonstrating how to seamlessly incorporate rationality principles (from economics and decision theory) into the learning process. By suitably tailoring the likelihood function, this framework enables the construction of preference learning models that encompass random utility models, limits of discernment, and scenarios with multiple conflicting utilities for both object- and label-preference. This tutorial starts by reviewing the mathematical concept of preference, its properties and the representation via utility functions. We then organise preferential data into three types: object preferences, label preferences and choices. We present five GP-models for object preferences showing in which situations each one is better adapted. For label preferences we present three models based on different noise assumptions. Finally for choice data we present a model for rational choice functions and one for pseudo-rational choice functions. The last part of the tutorial presents five applications of GP-based preference learning. This tutorial builds upon established research while simultaneously introducing some novel GP-based models to address specific gaps in the existing literature.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Preference modelling lies at the intersection of economics, decision theory, machine learning and statistics. By understanding individuals’ preferences and how they make choices, we can build products that closely match their expectations, paving the way for more efficient and personalised applications across a wide range of domains. The objective of this tutorial is to present a cohesive and comprehensive framework for preference learning with Gaussian processes (GPs), demonstrating how to seamlessly incorporate rationality principles (from economics and decision theory) into the learning process. By suitably tailoring the likelihood function, this framework enables the construction of preference learning models that encompass random utility models, limits of discernment, and scenarios with multiple conflicting utilities for both object- and label-preference. This tutorial starts by reviewing the mathematical concept of preference, its properties and the representation via utility functions. We then organise preferential data into three types: object preferences, label preferences and choices. We present five GP-models for object preferences showing in which situations each one is better adapted. For label preferences we present three models based on different noise assumptions. Finally for choice data we present a model for rational choice functions and one for pseudo-rational choice functions. The last part of the tutorial presents five applications of GP-based preference learning. This tutorial builds upon established research while simultaneously introducing some novel GP-based models to address specific gaps in the existing literature.
2025
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Why AI Safety Requires Uncertainty, Incomplete Preferences, and Non-Archimedean Utilities Miscellaneous
2025.
Abstract | Links | BibTeX | Tags: AI safety
@misc{benavoli2025aisafetyrequiresuncertainty,
title = {Why AI Safety Requires Uncertainty, Incomplete Preferences, and Non-Archimedean Utilities},
author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
url = {https://arxiv.org/abs/2512.23508},
year = {2025},
date = {2025-12-30},
urldate = {2025-01-01},
abstract = {How can we ensure that AI systems are aligned with human values and remain safe? We can study this problem through the frameworks of the AI assistance and the AI shutdown games. The AI assistance problem concerns designing an AI agent that helps a human to maximise their utility function(s). However, only the human knows these function(s); the AI assistant must learn them. The shutdown problem instead concerns designing AI agents that: shut down when a shutdown button is pressed; neither try to prevent nor cause the pressing of the shutdown button; and otherwise accomplish their task competently. In this paper, we show that addressing these challenges requires AI agents that can reason under uncertainty and handle both incomplete and non-Archimedean preferences.},
keywords = {AI safety},
pubstate = {published},
tppubtype = {misc}
}
How can we ensure that AI systems are aligned with human values and remain safe? We can study this problem through the frameworks of the AI assistance and the AI shutdown games. The AI assistance problem concerns designing an AI agent that helps a human to maximise their utility function(s). However, only the human knows these function(s); the AI assistant must learn them. The shutdown problem instead concerns designing AI agents that: shut down when a shutdown button is pressed; neither try to prevent nor cause the pressing of the shutdown button; and otherwise accomplish their task competently. In this paper, we show that addressing these challenges requires AI agents that can reason under uncertainty and handle both incomplete and non-Archimedean preferences.
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
The AI off-switch problem as a signalling game: bounded rationality and incomparability Proceedings Article
In: Destercke, Sébastien; Erreygers, Alexander; Nendel, Max; Riedel, Frank; Troffaes, Matthias C. M. (Ed.): Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, pp. 1–11, PMLR, 2025.
Abstract | Links | BibTeX | Tags: AI safety
@inproceedings{pmlr-v290-benavoli25a,
title = {The AI off-switch problem as a signalling game: bounded rationality and incomparability},
author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
editor = {Sébastien Destercke and Alexander Erreygers and Max Nendel and Frank Riedel and Matthias C. M. Troffaes},
url = {https://proceedings.mlr.press/v290/benavoli25a.html},
year = {2025},
date = {2025-07-01},
urldate = {2025-07-01},
booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications},
volume = {290},
pages = {1--11},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
abstract = {The off-switch problem is a critical challenge in AI control: if an AI system resists being switched off, it poses a significant risk. In this paper, we model the off-switch problem as a signalling game, where a human decision-maker communicates its preferences about some underlying decision problem to an AI agent, which then selects actions to maximise the human’s utility. We assume that the human is a bounded rational agent and explore various bounded rationality mechanisms. Using real machine learning models, we reprove prior results and demonstrate that a necessary condition for an AI system to refrain from disabling its off-switch is its uncertainty about the human’s utility. We also analyse how message costs influence optimal strategies and extend the analysis to scenarios involving incomparability.},
keywords = {AI safety},
pubstate = {published},
tppubtype = {inproceedings}
}
The off-switch problem is a critical challenge in AI control: if an AI system resists being switched off, it poses a significant risk. In this paper, we model the off-switch problem as a signalling game, where a human decision-maker communicates its preferences about some underlying decision problem to an AI agent, which then selects actions to maximise the human’s utility. We assume that the human is a bounded rational agent and explore various bounded rationality mechanisms. Using real machine learning models, we reprove prior results and demonstrate that a necessary condition for an AI system to refrain from disabling its off-switch is its uncertainty about the human’s utility. We also analyse how message costs influence optimal strategies and extend the analysis to scenarios involving incomparability.
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Connecting classical finite exchangeability to quantum theory and indistinguishability Journal Article
In: International Journal of Approximate Reasoning, pp. 109604, 2025, ISSN: 0888-613X.
Abstract | Links | BibTeX | Tags: bosons, de Finetti, Exchangeability, quantum de Finetti
@article{BENAVOLI2025109604,
title = {Connecting classical finite exchangeability to quantum theory and indistinguishability},
author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
url = {https://arxiv.org/abs/2306.03869},
doi = {https://doi.org/10.1016/j.ijar.2025.109604},
issn = {0888-613X},
year = {2025},
date = {2025-01-01},
urldate = {2025-01-01},
journal = {International Journal of Approximate Reasoning},
pages = {109604},
abstract = {Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti’s theorem provides a representation of infinitely exchangeable sequences of random variables as mixtures of independent and identically distributed variables. The quantum de Finetti theorem extends this result to symmetric quantum states on tensor product Hilbert spaces. It is well known that both theorems do not hold for finitely exchangeable sequences. The aim of this work is to investigate two lesser-known representation theorems, which were developed in classical probability theory to extend de Finetti’s theorem to finitely exchangeable sequences by using quasi-probabilities and quasi-expectations. With the aid of these theorems, we illustrate how a de Finetti-like representation theorem for finitely exchangeable sequences can be formulated through a mathematical representation which is formally equivalent to quantum theory (with boson-symmetric density matrices). We then show a promising application of this connection to the challenge of defining entanglement for indistinguishable bosons.},
keywords = {bosons, de Finetti, Exchangeability, quantum de Finetti},
pubstate = {published},
tppubtype = {article}
}
Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. The classical de Finetti’s theorem provides a representation of infinitely exchangeable sequences of random variables as mixtures of independent and identically distributed variables. The quantum de Finetti theorem extends this result to symmetric quantum states on tensor product Hilbert spaces. It is well known that both theorems do not hold for finitely exchangeable sequences. The aim of this work is to investigate two lesser-known representation theorems, which were developed in classical probability theory to extend de Finetti’s theorem to finitely exchangeable sequences by using quasi-probabilities and quasi-expectations. With the aid of these theorems, we illustrate how a de Finetti-like representation theorem for finitely exchangeable sequences can be formulated through a mathematical representation which is formally equivalent to quantum theory (with boson-symmetric density matrices). We then show a promising application of this connection to the challenge of defining entanglement for indistinguishable bosons.
Murphy, Fiona; Bachiller, Marina Navas; D’Arcy, Deirdre M; Benavoli, Alessio
Gaussian process with dissolution spline kernel for in vitro dissolution testing Journal Article
In: Journal of the Royal Statistical Society Series C: Applied Statistics, pp. qlaf052, 2025, ISSN: 0035-9254.
Abstract | Links | BibTeX | Tags: dissolution, Gaussian Process
@article{Fiona2025,
title = {Gaussian process with dissolution spline kernel for in vitro dissolution testing},
author = {Fiona Murphy and Marina Navas Bachiller and Deirdre M D’Arcy and Alessio Benavoli},
url = {https://doi.org/10.1093/jrsssc/qlaf052},
doi = {10.1093/jrsssc/qlaf052},
issn = {0035-9254},
year = {2025},
date = {2025-01-01},
urldate = {2025-01-01},
journal = {Journal of the Royal Statistical Society Series C: Applied Statistics},
pages = {qlaf052},
abstract = {In vitro dissolution testing is a critical component in the quality control of manufactured drug products. The f2 statistic is the standard for assessing similarity between two dissolution profiles. However, the f2 statistic has known limitations: it lacks an uncertainty estimate, is a discrete-time metric, and is a biased measure, calculating the differences between profiles at discrete time points. To address these limitations, we propose a Gaussian Process (GP) with a dissolution spline kernel for dissolution profile comparison. The dissolution spline kernel is a new spline kernel using piecewise logistic functions as its feature maps, enabling the GP to capture the expected monotonic increase in dissolution curves. This results in better predictions of dissolution curves. This new GP model reduces bias in the f2 calculation by allowing predictions to be interpolated in time between observed values, and provides uncertainty quantification. We assess the model’s performance through simulations and real datasets, demonstrating its improvement over a previous GP-based model introduced for dissolution testing. We also show that the new model can be adapted to include dissolution-specific covariates. Applying the model to real ibuprofen dissolution data under various conditions, we demonstrate its ability to extrapolate curve shapes across different experimental settings.},
keywords = {dissolution, Gaussian Process},
pubstate = {published},
tppubtype = {article}
}
In vitro dissolution testing is a critical component in the quality control of manufactured drug products. The f2 statistic is the standard for assessing similarity between two dissolution profiles. However, the f2 statistic has known limitations: it lacks an uncertainty estimate, is a discrete-time metric, and is a biased measure, calculating the differences between profiles at discrete time points. To address these limitations, we propose a Gaussian Process (GP) with a dissolution spline kernel for dissolution profile comparison. The dissolution spline kernel is a new spline kernel using piecewise logistic functions as its feature maps, enabling the GP to capture the expected monotonic increase in dissolution curves. This results in better predictions of dissolution curves. This new GP model reduces bias in the f2 calculation by allowing predictions to be interpolated in time between observed values, and provides uncertainty quantification. We assess the model’s performance through simulations and real datasets, demonstrating its improvement over a previous GP-based model introduced for dissolution testing. We also show that the new model can be adapted to include dissolution-specific covariates. Applying the model to real ibuprofen dissolution data under various conditions, we demonstrate its ability to extrapolate curve shapes across different experimental settings.
Benavoli, Alessio; Piga, Dario; Forgione, Marco; Zaffalon, Marzo
dynoGP: Deep Gaussian Processes for dynamic system identification Journal Article
In: 2025.
Abstract | Links | BibTeX | Tags: deep learning, Gaussian Process, system identification
@article{benavoli2025a,
title = {dynoGP: Deep Gaussian Processes for dynamic system identification},
author = {Alessio Benavoli and Dario Piga and Marco Forgione and Marzo Zaffalon},
url = {http://arxiv.org/abs/2502.05620},
year = {2025},
date = {2025-01-01},
urldate = {2025-01-01},
abstract = {In this work, we present a novel approach to system identification for dynamical systems, based on a specific class of Deep Gaussian Processes (Deep GPs). These models are constructed by interconnecting linear dynamic GPs (equivalent to stochastic linear time-invariant dynamical systems) and static GPs (to model static nonlinearities). Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution. This offers a more comprehensive framework for system identification that includes uncertainty quantification. Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.},
keywords = {deep learning, Gaussian Process, system identification},
pubstate = {published},
tppubtype = {article}
}
In this work, we present a novel approach to system identification for dynamical systems, based on a specific class of Deep Gaussian Processes (Deep GPs). These models are constructed by interconnecting linear dynamic GPs (equivalent to stochastic linear time-invariant dynamical systems) and static GPs (to model static nonlinearities). Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution. This offers a more comprehensive framework for system identification that includes uncertainty quantification. Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.
2024
Benavoli, Alessio; Azzimonti, Dario
Linearly Constrained Gaussian Processes are SkewGPs: application to Monotonic Preference Learning and Desirability Proceedings Article
In: The 40th Conference on Uncertainty in Artificial Intelligence, 2024.
Abstract | Links | BibTeX | Tags: bayesian nonparametric, Gaussian Process
@inproceedings{benavolilinearly2024,
title = {Linearly Constrained Gaussian Processes are SkewGPs: application to Monotonic Preference Learning and Desirability},
author = {Alessio Benavoli and Dario Azzimonti},
url = {http://alessiobenavoli.com/wp-content/uploads/2024/07/487_linearly_constrained_gaussian_-2024-1.pdf},
year = {2024},
date = {2024-07-16},
urldate = {2024-07-16},
booktitle = {The 40th Conference on Uncertainty in Artificial Intelligence},
abstract = {We show that existing approaches to Linearly Constrained Gaussian Processes (LCGP) for regression, based on imposing constraints on a finite set
of operational points, can be seen as Skew Gaussian Processes (SkewGPs). In particular, focusing
on inequality constraints and building upon a recent unification of regression, classification, and
preference learning through SkewGPs, we extend
LCGP to handle monotonic preference learning
and desirability, crucial for understanding and predicting human decision making. We demonstrate
the efficacy of the proposed model on simulated
and real data.},
keywords = {bayesian nonparametric, Gaussian Process},
pubstate = {published},
tppubtype = {inproceedings}
}
We show that existing approaches to Linearly Constrained Gaussian Processes (LCGP) for regression, based on imposing constraints on a finite set
of operational points, can be seen as Skew Gaussian Processes (SkewGPs). In particular, focusing
on inequality constraints and building upon a recent unification of regression, classification, and
preference learning through SkewGPs, we extend
LCGP to handle monotonic preference learning
and desirability, crucial for understanding and predicting human decision making. We demonstrate
the efficacy of the proposed model on simulated
and real data.
of operational points, can be seen as Skew Gaussian Processes (SkewGPs). In particular, focusing
on inequality constraints and building upon a recent unification of regression, classification, and
preference learning through SkewGPs, we extend
LCGP to handle monotonic preference learning
and desirability, crucial for understanding and predicting human decision making. We demonstrate
the efficacy of the proposed model on simulated
and real data.
Ristic, Branko; Benavoli, Alessio
Credal Valuation Network for Ongoing Threat Assessment Proceedings Article
In: 2024 27th International Conference on Information Fusion (FUSION), pp. 1–7, IEEE 2024.
Abstract | Links | BibTeX | Tags:
@inproceedings{ristic2024credal,
title = {Credal Valuation Network for Ongoing Threat Assessment},
author = {Branko Ristic and Alessio Benavoli},
url = {https://ieeexplore.ieee.org/abstract/document/10706493},
year = {2024},
date = {2024-01-01},
booktitle = {2024 27th International Conference on Information Fusion (FUSION)},
pages = {1--7},
organization = {IEEE},
abstract = {The paper develops a valuation network for sequential assessment of threat under epistemic uncertainty based on theoretical foundations and semantics of imprecise probability theory. The valuations are expressed as credal sets defined by coherent probability intervals on singletons. The combination rule is the generalized Bayes rule introduced by Walley. The model of a single-target threat is based on the classical “capability-intent” paradigm in an air surveillance context. Numerical results illustrate the performance of developed credal valuation network (with imprecise probabilities) against the valuation network with precise probabilistic models.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
The paper develops a valuation network for sequential assessment of threat under epistemic uncertainty based on theoretical foundations and semantics of imprecise probability theory. The valuations are expressed as credal sets defined by coherent probability intervals on singletons. The combination rule is the generalized Bayes rule introduced by Walley. The model of a single-target threat is based on the classical “capability-intent” paradigm in an air surveillance context. Numerical results illustrate the performance of developed credal valuation network (with imprecise probabilities) against the valuation network with precise probabilistic models.
Ristic, Branko; Benavoli, Alessio; Arulampalam, Sanjeev
Bayes’ Rule Using Imprecise Probabilities [Lecture Notes] Journal Article
In: IEEE Signal Processing Magazine, vol. 41, no. 1, pp. 67-71, 2024.
Links | BibTeX | Tags: Uncertainty;Training data;Signal processing;Probabilistic logic;Probability distribution
@article{10502175,
title = {Bayes’ Rule Using Imprecise Probabilities [Lecture Notes]},
author = {Branko Ristic and Alessio Benavoli and Sanjeev Arulampalam},
doi = {10.1109/MSP.2023.3335893},
year = {2024},
date = {2024-01-01},
journal = {IEEE Signal Processing Magazine},
volume = {41},
number = {1},
pages = {67-71},
keywords = {Uncertainty;Training data;Signal processing;Probabilistic logic;Probability distribution},
pubstate = {published},
tppubtype = {article}
}
2023
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Closure operators, classifiers and desirability Proceedings
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:25-36, 2023.
Abstract | Links | BibTeX | Tags: imprecise probability
@proceedings{Benavoli2023e,
title = {Closure operators, classifiers and desirability},
author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
editor = {Enrique Miranda, Ignacio Montes, Erik Quaeghebeur, Barbara Vantaggi},
url = {https://proceedings.mlr.press/v215/benavoli23a/benavoli23a.pdf},
year = {2023},
date = {2023-07-15},
urldate = {2023-07-15},
abstract = {At the core of Bayesian probability theory, or dually desirability theory, lies an assumption of linearity of the scale in which rewards are measured. We revisit two recent papers that extend desirability theory to the nonlinear case by letting the utility scale be represented either by a general closure operator or by a binary general (nonlinear) classifier. By using standard results in logic, we highlight the connection between these two approaches and show that this connection allows us to extend the separating hyper plane theorem (which is at the core of the duality between Bayesian decision theory and desirability theory) to the nonlinear case.},
howpublished = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:25-36},
keywords = {imprecise probability},
pubstate = {published},
tppubtype = {proceedings}
}
At the core of Bayesian probability theory, or dually desirability theory, lies an assumption of linearity of the scale in which rewards are measured. We revisit two recent papers that extend desirability theory to the nonlinear case by letting the utility scale be represented either by a general closure operator or by a binary general (nonlinear) classifier. By using standard results in logic, we highlight the connection between these two approaches and show that this connection allows us to extend the separating hyper plane theorem (which is at the core of the duality between Bayesian decision theory and desirability theory) to the nonlinear case.
Benavoli, Alessio; Azzimonti, Dario; Piga, Dario
Learning Choice Functions with Gaussian Processes Proceedings Article
In: Evans, Robin J.; Shpitser, Ilya (Ed.): Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, pp. 141–151, PMLR, 2023.
Abstract | Links | BibTeX | Tags:
@inproceedings{benavoli2023a,
title = {Learning Choice Functions with Gaussian Processes},
author = {Alessio Benavoli and Dario Azzimonti and Dario Piga},
editor = {Robin J. Evans and Ilya Shpitser},
url = {https://proceedings.mlr.press/v216/benavoli23a.html},
year = {2023},
date = {2023-07-01},
urldate = {2023-07-01},
booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
volume = {216},
pages = {141--151},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
abstract = {In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not be able to select a single most preferred object. To address these situations, we need a choice model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice data. The model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not be able to select a single most preferred object. To address these situations, we need a choice model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice data. The model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.
Kia, Arash; Waterson, James; Bargary, Norma; Rolt, Stuart; Burke, Kevin; Robertson, Jeremy; Garcia, Samuel; Benavoli, Alessio; Bergström, David
Determinants of Intravenous Infusion Longevity and Infusion Failure via a Nonlinear Model Analysis of Smart Pump Event Logs: Retrospective Study Journal Article
In: JMIR AI, vol. 2, pp. e48628, 2023, ISSN: 2817-1705.
Abstract | Links | BibTeX | Tags:
@article{info:doi/10.2196/48628,
title = {Determinants of Intravenous Infusion Longevity and Infusion Failure via a Nonlinear Model Analysis of Smart Pump Event Logs: Retrospective Study},
author = {Arash Kia and James Waterson and Norma Bargary and Stuart Rolt and Kevin Burke and Jeremy Robertson and Samuel Garcia and Alessio Benavoli and David Bergström},
url = {https://doi.org/10.2196/48628},
doi = {10.2196/48628},
issn = {2817-1705},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
journal = {JMIR AI},
volume = {2},
pages = {e48628},
abstract = {Background: Infusion failure may have severe consequences for patients receiving critical, short--half-life infusions. Continued interruptions to infusions can lead to subtherapeutic therapy. Objective: This study aims to identify and rank determinants of the longevity of continuous infusions administered through syringe drivers, using nonlinear predictive models. Additionally, this study aims to evaluate key factors influencing infusion longevity and develop and test a model for predicting the likelihood of achieving successful infusion longevity. Methods: Data were extracted from the event logs of smart pumps containing information on care profiles, medication types and concentrations, occlusion alarm settings, and the final infusion cessation cause. These data were then used to fit 5 nonlinear models and evaluate the best explanatory model. Results: Random forest was the best-fit predictor, with an F1-score of 80.42, compared to 5 other models (mean F1-score 75.06; range 67.48-79.63). When applied to infusion data in an individual syringe driver data set, the predictor model found that the final medication concentration and medication type were of less significance to infusion longevity compared to the rate and care unit. For low-rate infusions, rates ranging from 2 to 2.8 mL/hr performed best for achieving a balance between infusion longevity and fluid load per infusion, with an occlusion versus no-occlusion ratio of 0.553. Rates between 0.8 and 1.2 mL/hr exhibited the poorest performance with a ratio of 1.604. Higher rates, up to 4 mL/hr, performed better in terms of occlusion versus no-occlusion ratios. Conclusions: This study provides clinicians with insights into the specific types of infusion that warrant more intense observation or proactive management of intravenous access; additionally, it can offer valuable information regarding the average duration of uninterrupted infusions that can be expected in these care areas. Optimizing rate settings to improve infusion longevity for continuous infusions, achieved through compounding to create customized concentrations for individual patients, may be possible in light of the study's outcomes. The study also highlights the potential of machine learning nonlinear models in predicting outcomes and life spans of specific therapies delivered via medical devices.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Background: Infusion failure may have severe consequences for patients receiving critical, short--half-life infusions. Continued interruptions to infusions can lead to subtherapeutic therapy. Objective: This study aims to identify and rank determinants of the longevity of continuous infusions administered through syringe drivers, using nonlinear predictive models. Additionally, this study aims to evaluate key factors influencing infusion longevity and develop and test a model for predicting the likelihood of achieving successful infusion longevity. Methods: Data were extracted from the event logs of smart pumps containing information on care profiles, medication types and concentrations, occlusion alarm settings, and the final infusion cessation cause. These data were then used to fit 5 nonlinear models and evaluate the best explanatory model. Results: Random forest was the best-fit predictor, with an F1-score of 80.42, compared to 5 other models (mean F1-score 75.06; range 67.48-79.63). When applied to infusion data in an individual syringe driver data set, the predictor model found that the final medication concentration and medication type were of less significance to infusion longevity compared to the rate and care unit. For low-rate infusions, rates ranging from 2 to 2.8 mL/hr performed best for achieving a balance between infusion longevity and fluid load per infusion, with an occlusion versus no-occlusion ratio of 0.553. Rates between 0.8 and 1.2 mL/hr exhibited the poorest performance with a ratio of 1.604. Higher rates, up to 4 mL/hr, performed better in terms of occlusion versus no-occlusion ratios. Conclusions: This study provides clinicians with insights into the specific types of infusion that warrant more intense observation or proactive management of intravenous access; additionally, it can offer valuable information regarding the average duration of uninterrupted infusions that can be expected in these care areas. Optimizing rate settings to improve infusion longevity for continuous infusions, achieved through compounding to create customized concentrations for individual patients, may be possible in light of the study's outcomes. The study also highlights the potential of machine learning nonlinear models in predicting outcomes and life spans of specific therapies delivered via medical devices.
Ristic, Branko; Benavoli, Alessio; Skvortsov, Alex
Robust target area search using sets of probabilities Journal Article
In: Digital Signal Processing, vol. 142, pp. 104195, 2023, ISSN: 1051-2004.
Abstract | Links | BibTeX | Tags: Autonomous search, Imprecise probabilities, Sensor control, Sequential Bayesian estimation
@article{RISTIC2023104195,
title = {Robust target area search using sets of probabilities},
author = {Branko Ristic and Alessio Benavoli and Alex Skvortsov},
url = {https://www.sciencedirect.com/science/article/pii/S1051200423002907},
doi = {https://doi.org/10.1016/j.dsp.2023.104195},
issn = {1051-2004},
year = {2023},
date = {2023-01-01},
journal = {Digital Signal Processing},
volume = {142},
pages = {104195},
abstract = {Target area search in the standard Bayesian information-theoretic formulation consists of a repetitive cycle of sensing, recursive Bayesian estimation and motion control. The paper formulates the problem of target area search in the framework of imprecise probability theory using probability sets. The rationale is that the measurement model parameters, such as the probability of detection or the probability of false alarm, are rarely known as precise values. Instead, we adopt probability intervals to express beliefs. The paper formulates the Bayes-like state estimation equations as well as the reward function for motion control. The reward function is based on an uncertainty measure which takes into account both randomness and epistemic uncertainty.},
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Target area search in the standard Bayesian information-theoretic formulation consists of a repetitive cycle of sensing, recursive Bayesian estimation and motion control. The paper formulates the problem of target area search in the framework of imprecise probability theory using probability sets. The rationale is that the measurement model parameters, such as the probability of detection or the probability of false alarm, are rarely known as precise values. Instead, we adopt probability intervals to express beliefs. The paper formulates the Bayes-like state estimation equations as well as the reward function for motion control. The reward function is based on an uncertainty measure which takes into account both randomness and epistemic uncertainty.
Benavoli, Alessio; Azzimonti, Dario; Piga, Dario
Bayesian Optimization For Choice Data Proceedings Article
In: 2023 Genetic and Evolutionary Computation Conference Companion (GECCO '23 Companion), July 15--19, 2023, Lisbon, 2023.
Abstract | Links | BibTeX | Tags:
@inproceedings{benavoli2023d,
title = {Bayesian Optimization For Choice Data},
author = {Alessio Benavoli and Dario Azzimonti and Dario Piga},
doi = {10.1145/3583133.3596324},
year = {2023},
date = {2023-01-01},
urldate = {2023-01-01},
booktitle = {2023 Genetic and Evolutionary Computation Conference Companion (GECCO '23 Companion), July 15--19, 2023, Lisbon},
abstract = {In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as ``I pick options A,B,C among this set of five options A,B,C,D,E''. The fact that the option D is rejected means that there is at least one option among the selected ones A,B,C that I strictly prefer over D (but I do not have to specify which one). We assume that there is a latent vector function U for some dimension d which embeds the options into the real vector space of dimension d, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on U and by using a novel likelihood model for choice data, we derive a surrogate model for the latent vector function. We then propose two novel acquisition functions to solve the multi-objective Bayesian optimisation from choice data.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as ``I pick options A,B,C among this set of five options A,B,C,D,E''. The fact that the option D is rejected means that there is at least one option among the selected ones A,B,C that I strictly prefer over D (but I do not have to specify which one). We assume that there is a latent vector function U for some dimension d which embeds the options into the real vector space of dimension d, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on U and by using a novel likelihood model for choice data, we derive a surrogate model for the latent vector function. We then propose two novel acquisition functions to solve the multi-objective Bayesian optimisation from choice data.
Ristic, Branko; Benavoli, Alessio; Arulampalam, Sanjeev
Credal Valuation Networks for Machine Reasoning Under Uncertainty Journal Article
In: IEEE Transactions on Artificial Intelligence, pp. 1-10, 2023.
@article{10050733,
title = {Credal Valuation Networks for Machine Reasoning Under Uncertainty},
author = {Branko Ristic and Alessio Benavoli and Sanjeev Arulampalam},
doi = {10.1109/TAI.2023.3247971},
year = {2023},
date = {2023-01-01},
journal = {IEEE Transactions on Artificial Intelligence},
pages = {1-10},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2022
Schürch, Manuel; Azzimonti, Dario; Benavoli, Alessio; Zaffalon, Marco
Correlated Product of Experts for Sparse Gaussian Process Regression Journal Article
In: Machine Learning, 2022.
Abstract | Links | BibTeX | Tags:
@article{schuch2023correlated,
title = {Correlated Product of Experts for Sparse Gaussian Process Regression},
author = {Manuel Schürch and Dario Azzimonti and Alessio Benavoli and Marco Zaffalon},
doi = {10.1007/s10994-022-06297-3},
year = {2022},
date = {2022-12-31},
urldate = {2022-01-01},
journal = {Machine Learning},
abstract = { Gaussian processes (GPs) are an important tool in machine learning and statistics. However, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past years. In this paper, we focus on GP regression tasks and propose a new approach based on aggregating predictions from several local and correlated experts. Thereby, the degree of correlation between the experts can vary between independent up to fully correlated experts. The individual predictions of the experts are aggregated taking into account their correlation resulting in consistent uncertainty estimates. Our method recovers independent Product of Experts, sparse GP and full GP in the limiting cases. The presented framework can deal with a general kernel function and multiple variables, and has a time and space complexity which is linear in the number of experts and data samples, which makes our approach highly scalable. We demonstrate superior performance, in a time vs. accuracy sense, of our proposed method against state-of-the-art GP approximations for synthetic as well as several real-world datasets with deterministic and stochastic optimization.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Gaussian processes (GPs) are an important tool in machine learning and statistics. However, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past years. In this paper, we focus on GP regression tasks and propose a new approach based on aggregating predictions from several local and correlated experts. Thereby, the degree of correlation between the experts can vary between independent up to fully correlated experts. The individual predictions of the experts are aggregated taking into account their correlation resulting in consistent uncertainty estimates. Our method recovers independent Product of Experts, sparse GP and full GP in the limiting cases. The presented framework can deal with a general kernel function and multiple variables, and has a time and space complexity which is linear in the number of experts and data samples, which makes our approach highly scalable. We demonstrate superior performance, in a time vs. accuracy sense, of our proposed method against state-of-the-art GP approximations for synthetic as well as several real-world datasets with deterministic and stochastic optimization.
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality Technical Report
2022.
Abstract | Links | BibTeX | Tags: Quantum mechanics
@techreport{Benavoli2022,
title = {Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality},
author = {Benavoli , Alessio and Facchini, Alessandro and Zaffalon, Marco},
url = {https://arxiv.org/abs/2203.04124},
year = {2022},
date = {2022-09-05},
abstract = {We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs). This formulation provides a direct interpretation of density matrices as quasi-moment matrices. Using QEOs, we will provide a series of representation theorems, a' la de Finetti, relating a classical probability mass function (satisfying certain symmetries) to a quasi-expectation operator. We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. Although particles indistinguishability is considered a truly "weird" quantum phenomenon, it is not special. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT. Using this connection, we will rederive the first and second quantisation in QT for bosons through the classical statistical concept of exchangeable random variables. Using this approach, we will show how classical reality emerges in QT as the number of identical bosons increases (similar to what happens for finitely exchangeable sequences of rolls of a classical dice).},
keywords = {Quantum mechanics},
pubstate = {published},
tppubtype = {techreport}
}
We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs). This formulation provides a direct interpretation of density matrices as quasi-moment matrices. Using QEOs, we will provide a series of representation theorems, a' la de Finetti, relating a classical probability mass function (satisfying certain symmetries) to a quasi-expectation operator. We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. Although particles indistinguishability is considered a truly "weird" quantum phenomenon, it is not special. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT. Using this connection, we will rederive the first and second quantisation in QT for bosons through the classical statistical concept of exchangeable random variables. Using this approach, we will show how classical reality emerges in QT as the number of identical bosons increases (similar to what happens for finitely exchangeable sequences of rolls of a classical dice).
McGrath, Eanna; Mahony, Nick; Fleming, Neil; Benavoli, Alessio; Donne, Bernard
Prediction of Functional Threshold Power from Graded Exercise Test Data in Highly-Trained Individuals Journal Article
In: International Journal of Exercise Science, vol. 15, no. 4, pp. 747, 2022.
@article{mcgrath2022prediction,
title = {Prediction of Functional Threshold Power from Graded Exercise Test Data in Highly-Trained Individuals},
author = {Eanna McGrath and Nick Mahony and Neil Fleming and Alessio Benavoli and Bernard Donne},
url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9365101/},
year = {2022},
date = {2022-01-01},
journal = {International Journal of Exercise Science},
volume = {15},
number = {4},
pages = {747},
publisher = {Western Kentucky University},
keywords = {},
pubstate = {published},
tppubtype = {article}
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Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Quantum indistinguishability through exchangeability Journal Article
In: International Journal of Approximate Reasoning, vol. 151, pp. 389-412, 2022, ISSN: 0888-613X.
Abstract | Links | BibTeX | Tags: Coherence, Entanglement, Exchangeability, Indistinguishability, Quantum mechanics
@article{BENAVOLI2022389,
title = {Quantum indistinguishability through exchangeability},
author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
url = {https://www.sciencedirect.com/science/article/pii/S0888613X22001621},
doi = {https://doi.org/10.1016/j.ijar.2022.10.003},
issn = {0888-613X},
year = {2022},
date = {2022-01-01},
journal = {International Journal of Approximate Reasoning},
volume = {151},
pages = {389-412},
abstract = {Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrisation postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.},
keywords = {Coherence, Entanglement, Exchangeability, Indistinguishability, Quantum mechanics},
pubstate = {published},
tppubtype = {article}
}
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrisation postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
Casanova, Arianna; Benavoli, Alessio; Zaffalon, Marco
Nonlinear desirability as a linear classification problem Journal Article
In: International Journal of Approximate Reasoning, vol. 152, pp. 1-32, 2022, ISSN: 0888-613X.
Abstract | Links | BibTeX | Tags: Coherence, Convex coherence, Imprecise probabilities, Monetary scale, Piecewise separators
@article{CASANOVA20231,
title = {Nonlinear desirability as a linear classification problem},
author = {Arianna Casanova and Alessio Benavoli and Marco Zaffalon},
url = {https://www.sciencedirect.com/science/article/pii/S0888613X22001670},
doi = {https://doi.org/10.1016/j.ijar.2022.10.008},
issn = {0888-613X},
year = {2022},
date = {2022-01-01},
journal = {International Journal of Approximate Reasoning},
volume = {152},
pages = {1-32},
abstract = {This paper presents an interpretation as classification problem for standard desirability and other instances of nonlinear desirability (convex coherence and positive additive coherence). In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject respects these axioms on the basis of a finite set of acceptable and a finite set of rejectable gambles can be reformulated as a binary classification problem where the family of classifiers used changes with the axioms considered. Moreover, by borrowing ideas from machine learning, we show the possibility of defining a feature mapping, which allows us to reformulate the above nonlinear classification problems as linear ones in higher-dimensional spaces. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to provide a practical tool to check the rationality of an agent.},
keywords = {Coherence, Convex coherence, Imprecise probabilities, Monetary scale, Piecewise separators},
pubstate = {published},
tppubtype = {article}
}
This paper presents an interpretation as classification problem for standard desirability and other instances of nonlinear desirability (convex coherence and positive additive coherence). In particular, we analyze different sets of rationality axioms and, for each one of them, we show that proving that a subject respects these axioms on the basis of a finite set of acceptable and a finite set of rejectable gambles can be reformulated as a binary classification problem where the family of classifiers used changes with the axioms considered. Moreover, by borrowing ideas from machine learning, we show the possibility of defining a feature mapping, which allows us to reformulate the above nonlinear classification problems as linear ones in higher-dimensional spaces. This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to provide a practical tool to check the rationality of an agent.
Almardeny, Yahya; Benavoli, Alessio; Boujnah, Noureddine; Naredo, Enrique
A Reinforcement Learning System for Generating Instantaneous Quality Random Sequences Journal Article
In: IEEE Transactions on Artificial Intelligence, pp. 1-1, 2022.
Links | BibTeX | Tags: reinforcement learning
@article{Yahya2022,
title = {A Reinforcement Learning System for Generating Instantaneous Quality Random Sequences},
author = {Yahya Almardeny and Alessio Benavoli and Noureddine Boujnah and Enrique Naredo},
doi = {10.1109/TAI.2022.3161893},
year = {2022},
date = {2022-01-01},
journal = {IEEE Transactions on Artificial Intelligence},
pages = {1-1},
keywords = {reinforcement learning},
pubstate = {published},
tppubtype = {article}
}
2021
Benavoli, Alessio; Wyse, Jason; White, Arthur
Gaussian Processes to speed up MCMC with automatic exploratory-exploitation effect Proceedings Article
In: ProbProg21, 2021.
Abstract | Links | BibTeX | Tags:
@inproceedings{Benavoli2021b,
title = {Gaussian Processes to speed up MCMC with automatic exploratory-exploitation effect},
author = {Alessio Benavoli and Jason Wyse and Arthur White},
url = {https://arxiv.org/abs/2109.13891},
year = {2021},
date = {2021-10-20},
booktitle = {ProbProg21},
crossref = {ProbProg21},
abstract = {We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and the difference w.r.t. previous works, is the ability to learn the target distribution from scratch (while sampling), and so without the need of pre-training the GP. This is fundamental for automatic and inference in Probabilistic Programming Languages In particular, we present an alternative first stage acceptance scheme by marginalising out the GP distributed function, which makes the acceptance ratio explicitly dependent on the variance of the GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and the difference w.r.t. previous works, is the ability to learn the target distribution from scratch (while sampling), and so without the need of pre-training the GP. This is fundamental for automatic and inference in Probabilistic Programming Languages In particular, we present an alternative first stage acceptance scheme by marginalising out the GP distributed function, which makes the acceptance ratio explicitly dependent on the variance of the GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).
Benavoli, Alessio; Azzimonti, Dario; Piga, Dario
Choice functions based multi-objective Bayesian optimisation Technical Report
2021.
Abstract | Links | BibTeX | Tags: bayesian nonparametric, bayesian optimisation, Gaussian Process
@techreport{Benavoli2021bb,
title = {Choice functions based multi-objective Bayesian optimisation},
author = {Benavoli , Alessio and Azzimonti, Dario and Piga, Dario },
url = {https://arxiv.org/pdf/2110.08217.pdf},
year = {2021},
date = {2021-10-18},
abstract = {In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as “I pick options x1, x2, x3 among this set of five options x1, x2, . . . , x5”. The fact that the option x4 is rejected means that there is at least one option
among the selected ones x1, x2, x3 that I strictly prefer over x4 (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension ne which embeds the options into the real vector space of dimension ne, so that the choice set can be represented through a Pareto set of non-dominated
options. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning. We then apply this surrogate model to solve a novel multi-objective Bayesian optimisation from choice data problem.},
keywords = {bayesian nonparametric, bayesian optimisation, Gaussian Process},
pubstate = {published},
tppubtype = {techreport}
}
In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as “I pick options x1, x2, x3 among this set of five options x1, x2, . . . , x5”. The fact that the option x4 is rejected means that there is at least one option
among the selected ones x1, x2, x3 that I strictly prefer over x4 (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension ne which embeds the options into the real vector space of dimension ne, so that the choice set can be represented through a Pareto set of non-dominated
options. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning. We then apply this surrogate model to solve a novel multi-objective Bayesian optimisation from choice data problem.
among the selected ones x1, x2, x3 that I strictly prefer over x4 (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension ne which embeds the options into the real vector space of dimension ne, so that the choice set can be represented through a Pareto set of non-dominated
options. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning. We then apply this surrogate model to solve a novel multi-objective Bayesian optimisation from choice data problem.
Benavoli, Alessio; de Campos, Cassio
Bayesian Kernelised Test of (In)dependence with Mixed-type Variables Conference
The 8th IEEE International Conference on Data Science and Advanced Analytics (DSAA). Porto, Portugal, 2021.
Abstract | Links | BibTeX | Tags: bayesian nonparametric
@conference{benavoli2021bayesian,
title = {Bayesian Kernelised Test of (In)dependence with Mixed-type Variables},
author = {Benavoli, Alessio and de Campos, Cassio },
url = {https://arxiv.org/abs/2105.04001},
year = {2021},
date = {2021-10-04},
booktitle = {The 8th IEEE International Conference on Data Science and Advanced Analytics (DSAA). Porto, Portugal},
abstract = {A fundamental task in AI is to assess (in)dependence between mixed-type variables (text, image, sound). We propose a Bayesian kernelised correlation test of (in)dependence using a Dirichlet process model. The new measure of (in)dependence allows us to answer some fundamental questions: Based on data, are (mixed-type) variables independent? How likely is dependence/independence to hold? How high is the probability that two mixed-type variables are more than just weakly dependent? We theoretically show the properties of the approach, as well as algorithms for fast computation with it. We empirically demonstrate the effectiveness of the proposed method by analysing its performance and by comparing it with other frequentist and Bayesian approaches on a range of datasets and tasks with mixed-type variables. },
keywords = {bayesian nonparametric},
pubstate = {published},
tppubtype = {conference}
}
A fundamental task in AI is to assess (in)dependence between mixed-type variables (text, image, sound). We propose a Bayesian kernelised correlation test of (in)dependence using a Dirichlet process model. The new measure of (in)dependence allows us to answer some fundamental questions: Based on data, are (mixed-type) variables independent? How likely is dependence/independence to hold? How high is the probability that two mixed-type variables are more than just weakly dependent? We theoretically show the properties of the approach, as well as algorithms for fast computation with it. We empirically demonstrate the effectiveness of the proposed method by analysing its performance and by comparing it with other frequentist and Bayesian approaches on a range of datasets and tasks with mixed-type variables.
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
The Weirdness Theorem and the Origin of Quantum Paradoxes Journal Article
In: Foundations of Physics, vol. 51, no. 95, 2021.
Abstract | Links | BibTeX | Tags: Quantum mechanics
@article{Benavoli2021f,
title = {The Weirdness Theorem and the Origin of Quantum Paradoxes},
author = {Benavoli , Alessio and Facchini, Alessandro and Zaffalon, Marco},
url = {https://link.springer.com/article/10.1007/s10701-021-00499-w},
doi = {10.1007/s10701-021-00499-w},
year = {2021},
date = {2021-09-28},
journal = {Foundations of Physics},
volume = {51},
number = {95},
abstract = {We argue that there is a simple, unique, reason for all quantum paradoxes, and that such a reason is not uniquely related to quantum theory. It is rather a mathematical question that arises at the intersection of logic, probability, and computation. We give our ‘weirdness theorem’ that characterises the conditions under which the weirdness will show up. It shows that whenever logic has bounds due to the algorithmic nature of its tasks, then weirdness arises in the special form of negative probabilities or non-classical evaluation functionals. Weirdness is not logical inconsistency, however. It is only the expression of the clash between an unbounded and a bounded view of computation in logic. We discuss the implication of these results for quantum mechanics, arguing in particular that its interpretation should ultimately be computational rather than exclusively physical. We develop in addition a probabilistic theory in the real numbers that exhibits the phenomenon of entanglement, thus concretely showing that the latter is not specific to quantum mechanics.},
keywords = {Quantum mechanics},
pubstate = {published},
tppubtype = {article}
}
We argue that there is a simple, unique, reason for all quantum paradoxes, and that such a reason is not uniquely related to quantum theory. It is rather a mathematical question that arises at the intersection of logic, probability, and computation. We give our ‘weirdness theorem’ that characterises the conditions under which the weirdness will show up. It shows that whenever logic has bounds due to the algorithmic nature of its tasks, then weirdness arises in the special form of negative probabilities or non-classical evaluation functionals. Weirdness is not logical inconsistency, however. It is only the expression of the clash between an unbounded and a bounded view of computation in logic. We discuss the implication of these results for quantum mechanics, arguing in particular that its interpretation should ultimately be computational rather than exclusively physical. We develop in addition a probabilistic theory in the real numbers that exhibits the phenomenon of entanglement, thus concretely showing that the latter is not specific to quantum mechanics.
Benavoli, Alessio; Azzimonti, Dario; Piga, Dario
A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes Journal Article
In: Machine Learning, pp. 1-39, 2021.
Abstract | Links | BibTeX | Tags: bayesian nonparametric, Gaussian Process
@article{benavoli2021,
title = {A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes},
author = {Alessio Benavoli and Dario Azzimonti and Dario Piga},
url = {https://link.springer.com/article/10.1007/s10994-021-06039-x},
doi = {10.1007/s10994-021-06039-x},
year = {2021},
date = {2021-09-13},
journal = {Machine Learning},
pages = {1-39},
abstract = {Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also represent asymmetric distributions. In a recent contribution we showed that SkewGP and probit likelihood are conjugate, which allows us to compute the exact posterior for non-parametric binary classification and preference learning. In this paper, we generalize previous results and we prove that SkewGP is conjugate with both the normal and affine probit likelihood, and more in general, with their product. This allows us to (i) handle classification, preference, numeric and ordinal regression, and mixed problems in a unified framework; (ii) derive closed-form expression for the corresponding posterior distributions. We show empirically that the proposed framework based on SkewGP provides better performance than Gaussian processes in active learning and Bayesian (constrained) optimization},
keywords = {bayesian nonparametric, Gaussian Process},
pubstate = {published},
tppubtype = {article}
}
Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also represent asymmetric distributions. In a recent contribution we showed that SkewGP and probit likelihood are conjugate, which allows us to compute the exact posterior for non-parametric binary classification and preference learning. In this paper, we generalize previous results and we prove that SkewGP is conjugate with both the normal and affine probit likelihood, and more in general, with their product. This allows us to (i) handle classification, preference, numeric and ordinal regression, and mixed problems in a unified framework; (ii) derive closed-form expression for the corresponding posterior distributions. We show empirically that the proposed framework based on SkewGP provides better performance than Gaussian processes in active learning and Bayesian (constrained) optimization
Kania, Lucas; Schürch, Manuel; Azzimonti, Dario; Benavoli, Alessio
Sparse Information Filter for Fast Gaussian Process Regression Conference
European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases ECML PKDD, 2021.
Abstract | Links | BibTeX | Tags: bayesian nonparametric, Gaussian Process
@conference{Kania2021,
title = { Sparse Information Filter for Fast Gaussian Process Regression},
author = {Kania, Lucas and Schürch, Manuel and Azzimonti, Dario and Benavoli, Alessio},
url = {https://2021.ecmlpkdd.org/wp-content/uploads/2021/07/sub_854.pdf
http://alessiobenavoli.com/wp-content/uploads/2021/07/sub_854.pdf
},
year = {2021},
date = {2021-09-01},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases ECML PKDD},
abstract = {Gaussian processes (GPs) are an important tool in machine
learning and applied mathematics with applications ranging from Bayesian
optimization to calibration of computer experiments. They constitute
a powerful kernelized non-parametric method with well-calibrated un-
certainty estimates, however, off-the-shelf GP inference procedures are
limited to datasets with a few thousand data points because of their cubic
computational complexity. For this reason, many sparse GPs techniques
were developed over the past years. In this paper, we focus on GP regression tasks and propose a new algorithm to train variational sparse GP
models. An analytical posterior update expression based on the Information Filter is derived for the variational sparse GP model. We benchmark
our method on several real datasets with millions of data points against
the state-of-the-art Stochastic Variational GP (SVGP) and sparse orthogonal variational inference for Gaussian Processes (SOLVEGP). Our
method achieves comparable performances to SVGP and SOLVEGP while
providing considerable speed-ups. Specifically, it is consistently four times
faster than SVGP and on average 2.5 times faster than SOLVEGP.},
keywords = {bayesian nonparametric, Gaussian Process},
pubstate = {published},
tppubtype = {conference}
}
Gaussian processes (GPs) are an important tool in machine
learning and applied mathematics with applications ranging from Bayesian
optimization to calibration of computer experiments. They constitute
a powerful kernelized non-parametric method with well-calibrated un-
certainty estimates, however, off-the-shelf GP inference procedures are
limited to datasets with a few thousand data points because of their cubic
computational complexity. For this reason, many sparse GPs techniques
were developed over the past years. In this paper, we focus on GP regression tasks and propose a new algorithm to train variational sparse GP
models. An analytical posterior update expression based on the Information Filter is derived for the variational sparse GP model. We benchmark
our method on several real datasets with millions of data points against
the state-of-the-art Stochastic Variational GP (SVGP) and sparse orthogonal variational inference for Gaussian Processes (SOLVEGP). Our
method achieves comparable performances to SVGP and SOLVEGP while
providing considerable speed-ups. Specifically, it is consistently four times
faster than SVGP and on average 2.5 times faster than SOLVEGP.
learning and applied mathematics with applications ranging from Bayesian
optimization to calibration of computer experiments. They constitute
a powerful kernelized non-parametric method with well-calibrated un-
certainty estimates, however, off-the-shelf GP inference procedures are
limited to datasets with a few thousand data points because of their cubic
computational complexity. For this reason, many sparse GPs techniques
were developed over the past years. In this paper, we focus on GP regression tasks and propose a new algorithm to train variational sparse GP
models. An analytical posterior update expression based on the Information Filter is derived for the variational sparse GP model. We benchmark
our method on several real datasets with millions of data points against
the state-of-the-art Stochastic Variational GP (SVGP) and sparse orthogonal variational inference for Gaussian Processes (SOLVEGP). Our
method achieves comparable performances to SVGP and SOLVEGP while
providing considerable speed-ups. Specifically, it is consistently four times
faster than SVGP and on average 2.5 times faster than SOLVEGP.
Casanova, Arianna; Benavoli, Alessio; Zaffalon, Marco
Nonlinear Desirability as a Linear Classification Problem Proceedings Article
In: ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR, 2021.
Abstract | Links | BibTeX | Tags: desirability, imprecise probability
@inproceedings{Casanova2021,
title = {Nonlinear Desirability as a Linear Classification Problem},
author = {Casanova, Arianna and Benavoli, Alessio and Zaffalon, Marco},
url = {http://alessiobenavoli.com/wp-content/uploads/2021/07/casanova21-1.pdf},
year = {2021},
date = {2021-07-07},
booktitle = {ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR},
abstract = {The present paper proposes a generalization of linearity axioms of coherence through a geometrical approach, which leads to an alternative interpretation of desirability as a classification problem. In particular,we analyze different sets of rationality axioms and,for each one of them, we show that proving that a subject, who provides finite accept and reject statements, respects these axioms, corresponds to solving a binary classification task using, each time, a different (usually nonlinear) family of classifiers. Moreover,by borrowing ideas from machine learning, we show the possibility to define a feature mapping allowing us to reformulate the above nonlinear classification problems as linear ones in a higher-dimensional space.This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to reduce the task of proving the rationality of a subject to a linear classification task},
keywords = {desirability, imprecise probability},
pubstate = {published},
tppubtype = {inproceedings}
}
The present paper proposes a generalization of linearity axioms of coherence through a geometrical approach, which leads to an alternative interpretation of desirability as a classification problem. In particular,we analyze different sets of rationality axioms and,for each one of them, we show that proving that a subject, who provides finite accept and reject statements, respects these axioms, corresponds to solving a binary classification task using, each time, a different (usually nonlinear) family of classifiers. Moreover,by borrowing ideas from machine learning, we show the possibility to define a feature mapping allowing us to reformulate the above nonlinear classification problems as linear ones in a higher-dimensional space.This allows us to interpret gambles directly as payoffs vectors of monetary lotteries, as well as to reduce the task of proving the rationality of a subject to a linear classification task
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Quantum indistinguishability through exchangeable desirable gambles Proceedings Article
In: ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR, 2021.
Abstract | Links | BibTeX | Tags: desirability, Quantum mechanics
@inproceedings{benavoli2021quantum,
title = {Quantum indistinguishability through exchangeable desirable gambles},
author = {Alessio Benavoli and Alessandro Facchini and Marco Zaffalon},
url = {https://arxiv.org/abs/2105.04336},
year = {2021},
date = {2021-06-01},
booktitle = {ISIPTA'21 Int. Symposium on Imprecise Probability: Theories and Applications, PJMLR},
abstract = {Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems. },
keywords = {desirability, Quantum mechanics},
pubstate = {published},
tppubtype = {inproceedings}
}
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
Corani, Giorgio; Benavoli, Alessio; Augusto, Joao; Zaffalon, Marco
Time series forecasting with Gaussian Processes needs priors Proceedings Article
In: European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases ECML PKDD , 2021.
Links | BibTeX | Tags: bayesian nonparametric, Gaussian Process, Gaussian processes
@inproceedings{corani2020automatic,
title = {Time series forecasting with Gaussian Processes needs priors},
author = {Giorgio Corani and Alessio Benavoli and Joao Augusto and Marco Zaffalon},
url = {https://arxiv.org/abs/2009.08102},
year = {2021},
date = {2021-06-01},
booktitle = { European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases ECML PKDD },
keywords = {bayesian nonparametric, Gaussian Process, Gaussian processes},
pubstate = {published},
tppubtype = {inproceedings}
}
Benavoli, Alessio; Balleri, Alessio; Farina, Alfonso
Joint Waveform and Guidance Control Optimization by Statistical Linearisation for Target Rendezvous Conference
IEEE Radar Conference 2021, May 8-14, Atlanta (USA), 2021.
Abstract | Links | BibTeX | Tags: Cognitive radar, radar tracking
@conference{Benavoli2021d,
title = {Joint Waveform and Guidance Control Optimization by Statistical Linearisation for Target Rendezvous},
author = {Alessio Benavoli and Alessio Balleri and Alfonso Farina},
url = {http://alessiobenavoli.com/wp-content/uploads/2021/05/ieee_radarconf_21.pdf},
year = {2021},
date = {2021-05-18},
booktitle = { IEEE Radar Conference 2021, May 8-14, Atlanta (USA)},
abstract = {The algorithm proposed in this paper jointly selects the transmitted waveform and the control input
so that a radar sensor on a moving platform can prosecute a target by minimising a predefined cost
that accounts for the energy of the transmitted radar signal, the energy of the platform control input
and the relative position error between the platform and the target. The cost is a function of the
waveform design and control input. The algorithm extends the existing Joint Waveform Guidance
and Control Optimisation (JWGCO) solution to non-linear equations to account for the dependency
of the radar measurement accuracies on Signal to Noise Ratio (SNR) ratio and, as a consequence,
the target position. The performance of the proposed solution based on statistical linearisation
is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency
modulated chirps.},
keywords = {Cognitive radar, radar tracking},
pubstate = {published},
tppubtype = {conference}
}
The algorithm proposed in this paper jointly selects the transmitted waveform and the control input
so that a radar sensor on a moving platform can prosecute a target by minimising a predefined cost
that accounts for the energy of the transmitted radar signal, the energy of the platform control input
and the relative position error between the platform and the target. The cost is a function of the
waveform design and control input. The algorithm extends the existing Joint Waveform Guidance
and Control Optimisation (JWGCO) solution to non-linear equations to account for the dependency
of the radar measurement accuracies on Signal to Noise Ratio (SNR) ratio and, as a consequence,
the target position. The performance of the proposed solution based on statistical linearisation
is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency
modulated chirps.
so that a radar sensor on a moving platform can prosecute a target by minimising a predefined cost
that accounts for the energy of the transmitted radar signal, the energy of the platform control input
and the relative position error between the platform and the target. The cost is a function of the
waveform design and control input. The algorithm extends the existing Joint Waveform Guidance
and Control Optimisation (JWGCO) solution to non-linear equations to account for the dependency
of the radar measurement accuracies on Signal to Noise Ratio (SNR) ratio and, as a consequence,
the target position. The performance of the proposed solution based on statistical linearisation
is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency
modulated chirps.
Benavoli, Alessio; Azzimonti, Dario; Piga, Dario
Preferential Bayesian optimisation with Skew Gaussian Processes Proceedings Article
In: 2021 Genetic and Evolutionary Computation Conference Companion (GECCO '21 Companion), July 10--14, 2021, Lille, France , ACM, New York, NY, USA, 2021, ISBN: 978-1-4503-8351-6/21/07.
Abstract | Links | BibTeX | Tags: Skew Gaussian Process; Bayesian Optimisation
@inproceedings{benavoli2020preferential,
title = {Preferential Bayesian optimisation with Skew Gaussian Processes},
author = {Alessio Benavoli and Dario Azzimonti and Dario Piga},
url = {https://arxiv.org/abs/2008.06677},
doi = {10.1145/3449726.3463128},
isbn = {978-1-4503-8351-6/21/07},
year = {2021},
date = {2021-05-01},
booktitle = {2021 Genetic and Evolutionary Computation Conference Companion (GECCO '21 Companion), July 10--14, 2021, Lille, France
},
journal = {arXiv preprint arXiv:2008.06677},
publisher = {ACM},
address = {New York, NY, USA},
abstract = {Bayesian optimisation (BO) is a very effective approach for sequential black-box optimization where direct queries of the objective function are expensive. However, there are cases where the objective function can only be accessed via preference judgments, such as "this is better than that" between two candidate solutions (like in A/B tests or recommender systems). The state-of-the-art approach to Preferential Bayesian Optimization (PBO) uses a Gaussian process to model the preference function and a Bernoulli likelihood to model the observed pairwise comparisons. Laplace's method is then employed to compute posterior inferences and, in particular, to build an appropriate acquisition function. In this paper, we prove that the true posterior distribution of the preference function is a Skew Gaussian Process (SkewGP), with highly skewed pairwise marginals and, thus, show that Laplace's method usually provides a very poor approximation. We then derive an efficient method to compute the exact SkewGP posterior and use it as surrogate model for PBO employing standard acquisition functions (Upper Credible Bound, etc.). We illustrate the benefits of our exact PBO-SkewGP in a variety of experiments, by showing that it consistently outperforms PBO based on Laplace's approximation both in terms of convergence speed and computational time. We also show that our framework can be extended to deal with mixed preferential-categorical BO, typical for instance in smart manufacturing, where binary judgments (valid or non-valid) together with preference judgments are available. },
keywords = {Skew Gaussian Process; Bayesian Optimisation},
pubstate = {published},
tppubtype = {inproceedings}
}
Bayesian optimisation (BO) is a very effective approach for sequential black-box optimization where direct queries of the objective function are expensive. However, there are cases where the objective function can only be accessed via preference judgments, such as "this is better than that" between two candidate solutions (like in A/B tests or recommender systems). The state-of-the-art approach to Preferential Bayesian Optimization (PBO) uses a Gaussian process to model the preference function and a Bernoulli likelihood to model the observed pairwise comparisons. Laplace's method is then employed to compute posterior inferences and, in particular, to build an appropriate acquisition function. In this paper, we prove that the true posterior distribution of the preference function is a Skew Gaussian Process (SkewGP), with highly skewed pairwise marginals and, thus, show that Laplace's method usually provides a very poor approximation. We then derive an efficient method to compute the exact SkewGP posterior and use it as surrogate model for PBO employing standard acquisition functions (Upper Credible Bound, etc.). We illustrate the benefits of our exact PBO-SkewGP in a variety of experiments, by showing that it consistently outperforms PBO based on Laplace's approximation both in terms of convergence speed and computational time. We also show that our framework can be extended to deal with mixed preferential-categorical BO, typical for instance in smart manufacturing, where binary judgments (valid or non-valid) together with preference judgments are available.
Benavoli, Alessio; Corani, Giorgio
State Space Approximation of Gaussian Processes for Time Series Forecasting Proceedings Article
In: Lemaire, Vincent; Malinowski, Simon; Bagnall, Anthony; Guyet, Thomas; Tavenard, Romain; Ifrim, Georgiana (Ed.): pp. 21–35, Springer International Publishing, Cham, 2021, ISBN: 978-3-030-91445-5.
Abstract | Links | BibTeX | Tags:
@inproceedings{Benavoli2021eb,
title = {State Space Approximation of Gaussian Processes for Time Series Forecasting},
author = {Alessio Benavoli and Giorgio Corani},
editor = {Vincent Lemaire and Simon Malinowski and Anthony Bagnall and Thomas Guyet and Romain Tavenard and Georgiana Ifrim},
url = {http://alessiobenavoli.com/wp-content/uploads/2021/07/TS_final.pdf
https://project.inria.fr/aaltd21/},
isbn = {978-3-030-91445-5},
year = {2021},
date = {2021-01-01},
pages = {21--35},
publisher = {Springer International Publishing},
address = {Cham},
abstract = {Gaussian Processes (GPs), with a complex enough additive kernel, provide competitive results in time series forecasting compared to state-of-the-art approaches (arima, ETS) provided that: (i) during training the unnecessary components of the kernel are made irrelevant by automatic relevance determination; (ii) priors are assigned to each hyperparameter. However, GPs computational complexity grows cubically in time and quadratically in memory with the number of observations. The state space (SS) approximation of GPs allows to compute GPs based inferences with linear complexity. In this paper, we apply the SS representation to time series forecasting showing that SS models provide a performance comparable with that of full GP and better than state-of-the-art models (arima, ETS). Moreover, the SS representation allows us to derive new models by, for instance, combining ETS with kernels.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Gaussian Processes (GPs), with a complex enough additive kernel, provide competitive results in time series forecasting compared to state-of-the-art approaches (arima, ETS) provided that: (i) during training the unnecessary components of the kernel are made irrelevant by automatic relevance determination; (ii) priors are assigned to each hyperparameter. However, GPs computational complexity grows cubically in time and quadratically in memory with the number of observations. The state space (SS) approximation of GPs allows to compute GPs based inferences with linear complexity. In this paper, we apply the SS representation to time series forecasting showing that SS models provide a performance comparable with that of full GP and better than state-of-the-art models (arima, ETS). Moreover, the SS representation allows us to derive new models by, for instance, combining ETS with kernels.
2020
Benavoli, Alessio; Azzimonti, Dario; Piga, Dario
Skew Gaussian Processes for Classification Journal Article
In: Machine Learning, vol. 109, pp. 1877–1902, 2020.
Abstract | Links | BibTeX | Tags: bayesian nonparametric, Gaussian Process
@article{benavoli2020skew,
title = {Skew Gaussian Processes for Classification},
author = {Alessio Benavoli and Dario Azzimonti and Dario Piga},
url = {https://arxiv.org/abs/2005.12987},
doi = {10.1007/s10994-020-05906-3},
year = {2020},
date = {2020-09-04},
journal = {Machine Learning},
volume = {109},
pages = {1877–1902},
abstract = {Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a symmetric distribution with respect to its mean is an unreasonable model. This implies, for instance, that the mean and the median coincide, while the mean and median in an asymmetric (skewed) distribution can be different numbers. In this paper, we propose Skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions. A SkewGP extends the multivariate Unified Skew-Normal distribution over finite dimensional vectors to a stochastic processes. The SkewGP class of distributions includes GPs and, therefore, SkewGPs inherit all good properties of GPs and increase their flexibility by allowing asymmetry in the probabilistic model. By exploiting the fact that SkewGP and probit likelihood are conjugate model, we derive closed form expressions for the marginal likelihood and predictive distribution of this new nonparametric classifier. We verify empirically that the proposed SkewGP classifier provides a better performance than a GP classifier based on either Laplace's method or Expectation Propagation. },
keywords = {bayesian nonparametric, Gaussian Process},
pubstate = {published},
tppubtype = {article}
}
Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a symmetric distribution with respect to its mean is an unreasonable model. This implies, for instance, that the mean and the median coincide, while the mean and median in an asymmetric (skewed) distribution can be different numbers. In this paper, we propose Skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions. A SkewGP extends the multivariate Unified Skew-Normal distribution over finite dimensional vectors to a stochastic processes. The SkewGP class of distributions includes GPs and, therefore, SkewGPs inherit all good properties of GPs and increase their flexibility by allowing asymmetry in the probabilistic model. By exploiting the fact that SkewGP and probit likelihood are conjugate model, we derive closed form expressions for the marginal likelihood and predictive distribution of this new nonparametric classifier. We verify empirically that the proposed SkewGP classifier provides a better performance than a GP classifier based on either Laplace's method or Expectation Propagation.
Ristic, Branko; Gilliam, Christopher; Byrne, Marion; Benavoli, Alessio
A tutorial on uncertainty modeling for machine reasoning Journal Article
In: Information Fusion, vol. 55, pp. 30 - 44, 2020, ISSN: 1566-2535.
Abstract | Links | BibTeX | Tags: imprecise probability
@article{RISTIC2019,
title = {A tutorial on uncertainty modeling for machine reasoning},
author = {Branko Ristic and Christopher Gilliam and Marion Byrne and Alessio Benavoli},
url = {http://alessiobenavoli.com/wp-content/uploads/2019/08/Uncertainty_tutorial.pdf},
doi = {https://doi.org/10.1016/j.inffus.2019.08.001},
issn = {1566-2535},
year = {2020},
date = {2020-01-01},
journal = {Information Fusion},
volume = {55},
pages = {30 - 44},
abstract = {Increasingly we rely on machine intelligence for reasoning and decision making under uncertainty. This tutorial reviews the prevalent methods for model-based autonomous decision making based on observations and prior knowledge, primarily in the context of classification. Both observations and the knowledge-base available for reasoning are treated as being uncertain. Accordingly, the central themes of this tutorial are quantitative modeling of uncertainty, the rules required to combine such uncertain information, and the task of decision making under uncertainty. The paper covers the main approaches to uncertain knowledge representation and reasoning, in particular, Bayesian probability theory, possibility theory, reasoning based on belief functions and finally imprecise probability theory. The main feature of the tutorial is that it illustrates various approaches with several testing scenarios, and provides MATLAB solutions for them as a supplementary material for an interested reader.},
keywords = {imprecise probability},
pubstate = {published},
tppubtype = {article}
}
Increasingly we rely on machine intelligence for reasoning and decision making under uncertainty. This tutorial reviews the prevalent methods for model-based autonomous decision making based on observations and prior knowledge, primarily in the context of classification. Both observations and the knowledge-base available for reasoning are treated as being uncertain. Accordingly, the central themes of this tutorial are quantitative modeling of uncertainty, the rules required to combine such uncertain information, and the task of decision making under uncertainty. The paper covers the main approaches to uncertain knowledge representation and reasoning, in particular, Bayesian probability theory, possibility theory, reasoning based on belief functions and finally imprecise probability theory. The main feature of the tutorial is that it illustrates various approaches with several testing scenarios, and provides MATLAB solutions for them as a supplementary material for an interested reader.
Piga, Dario; Bemporad, Alberto; Benavoli, Alessio
Rao-Blackwellized sampling for batch and recursive Bayesian inference of Piecewise Affine models Journal Article
In: Automatica, vol. 117, 2020, ISSN: 0005-1098.
Abstract | Links | BibTeX | Tags: Bayesian inference, Markov Chain Monte Carlo, Particle filters, Piecewise-affine regression, Recursive identification
@article{PIGA2020109002,
title = {Rao-Blackwellized sampling for batch and recursive Bayesian inference of Piecewise Affine models},
author = {Dario Piga and Alberto Bemporad and Alessio Benavoli},
url = {http://alessiobenavoli.com/wp-content/uploads/2020/05/piga2020a-2.pdf},
doi = {https://doi.org/10.1016/j.automatica.2020.109002},
issn = {0005-1098},
year = {2020},
date = {2020-01-01},
journal = {Automatica},
volume = {117},
abstract = {This paper addresses batch (offline) and recursive (online) Bayesian inference of Piecewise Affine (PWA) regression models. By exploiting the particular structure of PWA models, efficient Rao-Blackwellized Monte Carlo sampling algorithms are developed to approximate the joint posterior distribution of the model parameters. Only the marginal posterior of the parameters used to describe the regressor-space partition is approximated, either in a batch mode using a Metropolis–Hastings Markov-Chain Monte Carlo (MCMC) sampler, or sequentially using particle filters, while the conditional distribution of the other model parameters is computed analytically. Probability distributions for the predicted outputs given new test inputs are derived and modifications of the proposed approaches to address maximum-a-posteriori estimate are discussed. The performance of the proposed algorithms is shown via a numerical example and through a benchmark case study on data-driven modelling of the electronic component placement process in a pick-and-place machine.},
keywords = {Bayesian inference, Markov Chain Monte Carlo, Particle filters, Piecewise-affine regression, Recursive identification},
pubstate = {published},
tppubtype = {article}
}
This paper addresses batch (offline) and recursive (online) Bayesian inference of Piecewise Affine (PWA) regression models. By exploiting the particular structure of PWA models, efficient Rao-Blackwellized Monte Carlo sampling algorithms are developed to approximate the joint posterior distribution of the model parameters. Only the marginal posterior of the parameters used to describe the regressor-space partition is approximated, either in a batch mode using a Metropolis–Hastings Markov-Chain Monte Carlo (MCMC) sampler, or sequentially using particle filters, while the conditional distribution of the other model parameters is computed analytically. Probability distributions for the predicted outputs given new test inputs are derived and modifications of the proposed approaches to address maximum-a-posteriori estimate are discussed. The performance of the proposed algorithms is shown via a numerical example and through a benchmark case study on data-driven modelling of the electronic component placement process in a pick-and-place machine.
Azzimonti, Dario; Schürch, Manuel; Benavoli, Alessio; Zaffalon, Marco
Orthogonally Decoupled Variational Fourier Features Journal Article
In: arXiv preprint arXiv:2007.06363, 2020.
@article{azzimonti2020orthogonally,
title = {Orthogonally Decoupled Variational Fourier Features},
author = {Dario Azzimonti and Manuel Schürch and Alessio Benavoli and Marco Zaffalon},
url = {https://arxiv.org/pdf/2007.06363.pdf},
year = {2020},
date = {2020-01-01},
journal = {arXiv preprint arXiv:2007.06363},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Schürch, Manuel; Azzimonti, Dario; Benavoli, Alessio; Zaffalon, Marco
Recursive estimation for sparse Gaussian process regression Journal Article
In: Automatica, vol. 120, pp. 109-127, 2020, ISSN: 0005-1098.
Abstract | Links | BibTeX | Tags: Gaussian processes, Kalman filter, Non-parametric regression, Parameter estimation, Recursive estimation
@article{SCHURCH2020109127,
title = {Recursive estimation for sparse Gaussian process regression},
author = {Manuel Schürch and Dario Azzimonti and Alessio Benavoli and Marco Zaffalon},
url = {http://alessiobenavoli.com/wp-content/uploads/2020/07/2020automatica-gps-2.pdf},
doi = {https://doi.org/10.1016/j.automatica.2020.109127},
issn = {0005-1098},
year = {2020},
date = {2020-01-01},
journal = {Automatica},
volume = {120},
pages = {109-127},
abstract = {Gaussian Processes (GPs) are powerful kernelized methods for non-parametric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs to larger datasets, several sparse approximations based on so-called inducing points have been proposed in the literature. In this work we investigate the connection between a general class of sparse inducing point GP regression methods and Bayesian recursive estimation which enables Kalman Filter like updating for online learning. The majority of previous work has focused on the batch setting, in particular for learning the model parameters and the position of the inducing points, here instead we focus on training with mini-batches. By exploiting the Kalman filter formulation, we propose a novel approach that estimates such parameters by recursively propagating the analytical gradients of the posterior over mini-batches of the data. Compared to state of the art methods, our method keeps analytic updates for the mean and covariance of the posterior, thus reducing drastically the size of the optimization problem. We show that our method achieves faster convergence and superior performance compared to state of the art sequential Gaussian Process regression on synthetic GP as well as real-world data with up to a million of data samples.},
keywords = {Gaussian processes, Kalman filter, Non-parametric regression, Parameter estimation, Recursive estimation},
pubstate = {published},
tppubtype = {article}
}
Gaussian Processes (GPs) are powerful kernelized methods for non-parametric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs to larger datasets, several sparse approximations based on so-called inducing points have been proposed in the literature. In this work we investigate the connection between a general class of sparse inducing point GP regression methods and Bayesian recursive estimation which enables Kalman Filter like updating for online learning. The majority of previous work has focused on the batch setting, in particular for learning the model parameters and the position of the inducing points, here instead we focus on training with mini-batches. By exploiting the Kalman filter formulation, we propose a novel approach that estimates such parameters by recursively propagating the analytical gradients of the posterior over mini-batches of the data. Compared to state of the art methods, our method keeps analytic updates for the mean and covariance of the posterior, thus reducing drastically the size of the optimization problem. We show that our method achieves faster convergence and superior performance compared to state of the art sequential Gaussian Process regression on synthetic GP as well as real-world data with up to a million of data samples.
2019
Benavoli, A; Balleri, A; Farina, A
Joint Waveform and Guidance Control Optimization for Target Rendezvous Journal Article
In: IEEE Transactions on Signal Processing, vol. 67, no. 16, pp. 4357-4369, 2019, ISSN: 1053-587X.
Abstract | Links | BibTeX | Tags: Cognitive radar, Kalman filter, linear quadratic Gaussian control
@article{Benavoli2019d,
title = {Joint Waveform and Guidance Control Optimization for Target Rendezvous},
author = {A Benavoli and A Balleri and A Farina},
url = {http://alessiobenavoli.com/wp-content/uploads/2019/08/Joint_waveform_and_guidance_control.pdf},
doi = {10.1109/TSP.2019.2929951},
issn = {1053-587X},
year = {2019},
date = {2019-08-01},
journal = {IEEE Transactions on Signal Processing},
volume = {67},
number = {16},
pages = {4357-4369},
abstract = {The algorithm developed in this paper jointly selects the optimal transmitted waveform and the control input so that a radar sensor on a moving platform with linear dynamics can reach a target by minimizing a predefined cost. The cost proposed in this paper accounts for the energy of the transmitted radar signal, the energy of the platform control input, and the relative position error between the platform and the target, which is a function of the waveform design and control input. Similarly to the linear quadratic Gaussian control problem, we demonstrate that the optimal solution satisfies the separation principle between filtering and optimization and, therefore, the optimum can be found analytically. The performance of the proposed solution is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency modulated chirps. Results show the effectiveness of the proposed approach for optimal waveform design and optimal guidance control.},
keywords = {Cognitive radar, Kalman filter, linear quadratic Gaussian control},
pubstate = {published},
tppubtype = {article}
}
The algorithm developed in this paper jointly selects the optimal transmitted waveform and the control input so that a radar sensor on a moving platform with linear dynamics can reach a target by minimizing a predefined cost. The cost proposed in this paper accounts for the energy of the transmitted radar signal, the energy of the platform control input, and the relative position error between the platform and the target, which is a function of the waveform design and control input. Similarly to the linear quadratic Gaussian control problem, we demonstrate that the optimal solution satisfies the separation principle between filtering and optimization and, therefore, the optimum can be found analytically. The performance of the proposed solution is assessed with a set of simulations for a pulsed Doppler radar transmitting linearly frequency modulated chirps. Results show the effectiveness of the proposed approach for optimal waveform design and optimal guidance control.
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Bernstein's socks, polynomial-time provable coherence and entanglement Proceedings Article
In: Bock, J De; de Campos, C; de Cooman, G; Quaeghebeur, E; Wheeler, G (Ed.): ISIPTA ;'19: Proceedings of the Eleventh International Symposium on Imprecise Probability: Theories and Applications, JMLR, 2019.
Abstract | Links | BibTeX | Tags: bounded rationality, Sum-of-squares polynomials
@inproceedings{zaffalon2019b,
title = {Bernstein's socks, polynomial-time provable coherence and entanglement},
author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco},
editor = {J De Bock and C de Campos and G de Cooman and E Quaeghebeur and G Wheeler},
url = {http://alessiobenavoli.com/wp-content/uploads/2019/05/benavoli19-1.pdf},
year = {2019},
date = {2019-07-07},
booktitle = {ISIPTA ;'19: Proceedings of the Eleventh International Symposium on Imprecise Probability: Theories and Applications},
publisher = {JMLR},
series = {PJMLR},
abstract = {We recently introduced a bounded rationality ap-
proach for the theory of desirable gambles. It is
based on the unique requirement that being non-
negative for a gamble has to be defined so that
it can be provable in polynomial time. In this
paper we continue to investigate properties of
this class of models. In particular we verify that
the space of Bernstein polynomials in which non-
negativity is specified by the Krivine-Vasilescu
certificate is yet another instance of this theory.
As a consequence, we show how it is possible to
construct in it a thought experiment uncovering
entanglement with classical (hence non quantum)
coins.},
keywords = {bounded rationality, Sum-of-squares polynomials},
pubstate = {published},
tppubtype = {inproceedings}
}
We recently introduced a bounded rationality ap-
proach for the theory of desirable gambles. It is
based on the unique requirement that being non-
negative for a gamble has to be defined so that
it can be provable in polynomial time. In this
paper we continue to investigate properties of
this class of models. In particular we verify that
the space of Bernstein polynomials in which non-
negativity is specified by the Krivine-Vasilescu
certificate is yet another instance of this theory.
As a consequence, we show how it is possible to
construct in it a thought experiment uncovering
entanglement with classical (hence non quantum)
coins.
proach for the theory of desirable gambles. It is
based on the unique requirement that being non-
negative for a gamble has to be defined so that
it can be provable in polynomial time. In this
paper we continue to investigate properties of
this class of models. In particular we verify that
the space of Bernstein polynomials in which non-
negativity is specified by the Krivine-Vasilescu
certificate is yet another instance of this theory.
As a consequence, we show how it is possible to
construct in it a thought experiment uncovering
entanglement with classical (hence non quantum)
coins.
Piga, Dario; Benavoli, Alessio
Semialgebraic Outer Approximations for Set-Valued Nonlinear Filtering Proceedings Article
In: Proc. on European Control Conference (ECC), 2019.
Links | BibTeX | Tags: filtering, set of probabilities, SOS
@inproceedings{Piga2019,
title = {Semialgebraic Outer Approximations for Set-Valued Nonlinear Filtering},
author = {Piga, Dario and Benavoli, Alessio},
url = {http://alessiobenavoli.com/wp-content/uploads/2019/03/main_v5.pdf},
year = {2019},
date = {2019-03-24},
booktitle = {Proc. on European Control Conference (ECC)},
keywords = {filtering, set of probabilities, SOS},
pubstate = {published},
tppubtype = {inproceedings}
}
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Computational Complexity and the Nature of Quantum Mechanics Technical Report
2019.
Abstract | Links | BibTeX | Tags: Quantum mechanics
@techreport{Benavoli2019bb,
title = {Computational Complexity and the Nature of Quantum Mechanics},
author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco },
url = {https://arxiv.org/abs/1902.04569},
year = {2019},
date = {2019-02-14},
abstract = {Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from two main postulates (i) the theory should be logically consistent; (ii) inferences in the theory should be computable in polynomial time. The first postulate is what we require to each well-founded mathematical theory. The computation postulate defines the physical component of the theory. We show that the computation postulate is the only true divide between QT, seen as a generalised theory of probability, and classical probability. All quantum paradoxes, and entanglement in particular, arise from the clash of trying to reconcile a computationally intractable, somewhat idealised, theory (classical physics) with a computationally tractable theory (QT) or, in other words, from regarding physics as fundamental rather than computation. },
keywords = {Quantum mechanics},
pubstate = {published},
tppubtype = {techreport}
}
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from two main postulates (i) the theory should be logically consistent; (ii) inferences in the theory should be computable in polynomial time. The first postulate is what we require to each well-founded mathematical theory. The computation postulate defines the physical component of the theory. We show that the computation postulate is the only true divide between QT, seen as a generalised theory of probability, and classical probability. All quantum paradoxes, and entanglement in particular, arise from the clash of trying to reconcile a computationally intractable, somewhat idealised, theory (classical physics) with a computationally tractable theory (QT) or, in other words, from regarding physics as fundamental rather than computation.
Benavoli, Alessio; Facchini, Alessandro; Piga, Dario; Zaffalon, Marco
Sum-of-squares for bounded rationality Journal Article
In: International Journal of Approximate Reasoning, vol. 105, pp. 130 - 152, 2019, ISSN: 0888-613X.
Abstract | Links | BibTeX | Tags: Sum-of-squares polynomials
@article{Benavoli2019b,
title = {Sum-of-squares for bounded rationality},
author = {Alessio Benavoli and Alessandro Facchini and Dario Piga and Marco Zaffalon},
url = {https://arxiv.org/abs/1705.02663},
doi = {10.1016/j.ijar.2018.11.012},
issn = {0888-613X},
year = {2019},
date = {2019-01-01},
journal = {International Journal of Approximate Reasoning},
volume = {105},
pages = {130 - 152},
abstract = {In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in Rn, the problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable theory of desirable gambles. Instead of requiring the subject to desire all nonnegative gambles, we only require her to desire gambles for which she can efficiently determine the nonnegativity (in particular sum-of-squares polynomials). We refer to this new criterion as bounded rationality.},
keywords = {Sum-of-squares polynomials},
pubstate = {published},
tppubtype = {article}
}
In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in Rn, the problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable theory of desirable gambles. Instead of requiring the subject to desire all nonnegative gambles, we only require her to desire gambles for which she can efficiently determine the nonnegativity (in particular sum-of-squares polynomials). We refer to this new criterion as bounded rationality.
2018
Benavoli, Alessio
Dual Probabilistic Programming Proceedings
PROBPROG 2018 The International Conference on Probabilistic Programming, Wiesner Building E15 MIT, Cambridge, MA, USA 2018.
Links | BibTeX | Tags: dual probabilistic programming, rationality
@proceedings{Benavoli2018,
title = {Dual Probabilistic Programming},
author = {Benavoli, Alessio },
url = {http://alessiobenavoli.com/wp-content/uploads/2018/09/dual_PP.pdf},
year = {2018},
date = {2018-10-04},
organization = {PROBPROG 2018 The International Conference on Probabilistic Programming, Wiesner Building E15 MIT, Cambridge, MA, USA},
keywords = {dual probabilistic programming, rationality},
pubstate = {published},
tppubtype = {proceedings}
}
2017
Benavoli, Alessio; Corani, Giorgio; Demsar, Janez; Zaffalon, Marco
Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis Journal Article
In: Journal of Machine Learning Research, vol. 18, no. 77, pp. 1-36, 2017.
Abstract | Links | BibTeX | Tags: bayesian statistics, machine learning
@article{benavoli2016e,
title = {Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis},
author = {Benavoli, Alessio and Corani, Giorgio and Demsar, Janez and Zaffalon, Marco},
url = {http://jmlr.org/papers/v18/16-305.html},
year = {2017},
date = {2017-10-02},
journal = {Journal of Machine Learning Research},
volume = {18},
number = {77},
pages = {1-36},
abstract = {The machine learning community adopted the use of null hypothesis significance testing (NHST) in order to ensure the statistical validity of results. Many scientific fields however realized the shortcomings of frequentist reasoning and in the most radical cases even banned its use in publications. We should do the same: just as we have embraced the Bayesian paradigm in the development of new machine learning methods, so we should also use it in the analysis of our own results. We argue for abandonment of NHST by exposing its fallacies and, more importantly, offer better - more sound and useful - alternatives for it. },
keywords = {bayesian statistics, machine learning},
pubstate = {published},
tppubtype = {article}
}
The machine learning community adopted the use of null hypothesis significance testing (NHST) in order to ensure the statistical validity of results. Many scientific fields however realized the shortcomings of frequentist reasoning and in the most radical cases even banned its use in publications. We should do the same: just as we have embraced the Bayesian paradigm in the development of new machine learning methods, so we should also use it in the analysis of our own results. We argue for abandonment of NHST by exposing its fallacies and, more importantly, offer better - more sound and useful - alternatives for it.
Piga, Dario; Benavoli, Alessio
A unified framework for deterministic and probabilistic D-stability analysis of uncertain polynomial matrices Journal Article
In: Automatic Control, IEEE Transactions on, vol. 62, no. 10, pp. 5437-5444, 2017.
Abstract | Links | BibTeX | Tags: Control
@article{benavoli2016c,
title = {A unified framework for deterministic and probabilistic D-stability analysis of uncertain polynomial matrices},
author = {Piga, Dario and Benavoli, Alessio},
url = {http://arxiv.org/abs/1604.02031},
doi = {10.1109/TAC.2017.2699281},
year = {2017},
date = {2017-10-01},
journal = {Automatic Control, IEEE Transactions on},
volume = {62},
number = {10},
pages = {5437-5444},
abstract = { Many problems in systems and control theory can be formulated in terms of robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D of the complex plane. Robust D-stability analysis is an NP-hard problem and many polynomial-time algorithms providing either sufficient or necessary conditions for an uncertain matrix to be robustly D-stable have been developed in the past decades. Despite the vast literature on the subject, most of the contributions consider specific families of uncertain matrices, mainly with interval or polytopic uncertainty. In this work, we present a novel approach providing sufficient conditions to verify if a family of matrices, whose entries depend polynomially on some uncertain parameters, is robustly D-stable. The only assumption on the stability region D is that its complement is a semialgebraic set described by polynomial constraints, which comprises the main important cases in stability analysis. Furthermore, the D-stability analysis problem is formulated in a probabilistic framework. In this context, the uncertain parameters characterizing the considered family of matrices are described by a set of non a priori specified probability measures. Only the support and some of the moments (e.g., expected values) are assumed to be known and, among all possible probability measures, we seek the one which provides the minimum probability of D-stability. The robust and the probabilistic D-stability analysis problems are formulated in a unified framework, and relaxations based on the theory of moments are used to solve the D-stability analysis problem through convex optimization. Application to robustness and probabilistic analysis of dynamical systems is discussed. },
keywords = {Control},
pubstate = {published},
tppubtype = {article}
}
Many problems in systems and control theory can be formulated in terms of robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D of the complex plane. Robust D-stability analysis is an NP-hard problem and many polynomial-time algorithms providing either sufficient or necessary conditions for an uncertain matrix to be robustly D-stable have been developed in the past decades. Despite the vast literature on the subject, most of the contributions consider specific families of uncertain matrices, mainly with interval or polytopic uncertainty. In this work, we present a novel approach providing sufficient conditions to verify if a family of matrices, whose entries depend polynomially on some uncertain parameters, is robustly D-stable. The only assumption on the stability region D is that its complement is a semialgebraic set described by polynomial constraints, which comprises the main important cases in stability analysis. Furthermore, the D-stability analysis problem is formulated in a probabilistic framework. In this context, the uncertain parameters characterizing the considered family of matrices are described by a set of non a priori specified probability measures. Only the support and some of the moments (e.g., expected values) are assumed to be known and, among all possible probability measures, we seek the one which provides the minimum probability of D-stability. The robust and the probabilistic D-stability analysis problems are formulated in a unified framework, and relaxations based on the theory of moments are used to solve the D-stability analysis problem through convex optimization. Application to robustness and probabilistic analysis of dynamical systems is discussed.
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
Bayes + Hilbert = Quantum Mechanics Conference
Proceedings of the 14th International Conference on Quantum Physics and Logic (QPL 2017), Nijmegen, The Netherlands, 3-7 July, 2017.
Links | BibTeX | Tags: Quantum mechanics
@conference{Benavoli2017m,
title = {Bayes + Hilbert = Quantum Mechanics},
author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco },
url = {http://qpl.science.ru.nl/papers/QPL_2017_paper_4.pdf},
year = {2017},
date = {2017-07-05},
booktitle = {Proceedings of the 14th International Conference on Quantum Physics and Logic (QPL 2017), Nijmegen, The Netherlands, 3-7 July},
keywords = {Quantum mechanics},
pubstate = {published},
tppubtype = {conference}
}
Balleri, Alessio; Farina, Alfonso; Benavoli, Alessio
Coordination of optimal guidance law and adaptive radiated waveform for interception and rendezvous problems Journal Article
In: IET Radar, Sonar & Navigation, vol. 11, no. 7, pp. 1132 - 1139, 2017, ISSN: 1751-8784.
Abstract | Links | BibTeX | Tags: Control
@article{benavoli2017a,
title = {Coordination of optimal guidance law and adaptive radiated waveform for interception and rendezvous problems},
author = { Balleri, Alessio and Farina, Alfonso and Benavoli, Alessio},
url = {http://digital-library.theiet.org/content/journals/10.1049/iet-rsn.2016.0547},
doi = {10.1049/iet-rsn.2016.0547},
issn = {1751-8784},
year = {2017},
date = {2017-07-01},
journal = {IET Radar, Sonar & Navigation},
volume = {11},
number = {7},
pages = {1132 - 1139},
publisher = {Institution of Engineering and Technology},
abstract = {We present an algorithm that allows an interceptor aircraft equipped with an airborne radar to meet another air target (the intercepted) by developing a guidance law and automatically adapting and optimising the transmitted waveform on a pulse to pulse basis. The algorithm uses a Kalman filter to predict the relative position and speed of the interceptor with respect to the target. The transmitted waveform is automatically selected based on its ambiguity function and accuracy properties along the approaching path. For each pulse, the interceptor predicts its position and velocity with respect to the target, takes a measurement of range and radial velocity and, with the Kalman filter, refines the relative range and range rate estimates. These are fed into a Linear Quadratic Gaussian (LQG) controller that ensures the interceptor reaches the target automatically and successfully with minimum error and with the minimum guidance energy consumption. },
keywords = {Control},
pubstate = {published},
tppubtype = {article}
}
We present an algorithm that allows an interceptor aircraft equipped with an airborne radar to meet another air target (the intercepted) by developing a guidance law and automatically adapting and optimising the transmitted waveform on a pulse to pulse basis. The algorithm uses a Kalman filter to predict the relative position and speed of the interceptor with respect to the target. The transmitted waveform is automatically selected based on its ambiguity function and accuracy properties along the approaching path. For each pulse, the interceptor predicts its position and velocity with respect to the target, takes a measurement of range and radial velocity and, with the Kalman filter, refines the relative range and range rate estimates. These are fed into a Linear Quadratic Gaussian (LQG) controller that ensures the interceptor reaches the target automatically and successfully with minimum error and with the minimum guidance energy consumption.