# A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes

arXiv: https://arxiv.org/abs/2012.06846 · HTML: https://mlsanity.com/paper/2012.06846/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2020.

## Built on by (most cited first, 6 of 6)

- [Towards Practical Preferential Bayesian Optimization with Skew Gaussian Processes](https://mlsanity.com/paper/2302.01513/) (2023)
- [Learning Choice Functions with Gaussian Processes](https://mlsanity.com/paper/2302.00406/) (2023)
- [Bayesian Optimisation for Sequential Experimental Design with Applications in Additive Manufacturing](https://mlsanity.com/paper/2107.12809/) (2021)
- [Choice functions based multi-objective Bayesian optimisation](https://mlsanity.com/paper/2110.08217/) (2021)
- [A Fast, Robust Elliptical Slice Sampling Implementation for Linearly Truncated Multivariate Normal Distributions](https://mlsanity.com/paper/2407.10449/) (2024)
- [The AI off-switch problem as a signalling game: bounded rationality and incomparability](https://mlsanity.com/paper/2502.06403/) (2025)

## Abstract (arXiv)

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. These two tasks are fundamental for design of experiments and in Data Science.