@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://arxiv.org/abs/2012.06846},
year = {2021},
date = {2021-01-01},
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}
}

@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}
}

@article{corani2020automatic,
title = {Automatic Forecasting using Gaussian Processes},
author = {Giorgio Corani and Alessio Benavoli and Joao Augusto and Marco Zaffalon},
url = {https://arxiv.org/abs/2009.08102},
year = {2020},
date = {2020-01-01},
keywords = {bayesian nonparametric, Gaussian Process},
pubstate = {published},
tppubtype = {article}
}