论文标题
闭合形式的非参数回归，分类，偏好和混合问题的统一框架
A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with Skew Gaussian Processes
论文作者
论文摘要
偏度高斯工艺（Skewgps）将多元统一偏度分布扩展到有限尺寸向量上，以在功能上分布。与高斯工艺相比，Skewgps更一般，更灵活，因为skewgps也可能代表不对称的分布。在最近的贡献中，我们表明偏斜和概率的可能性是共轭物，这使我们能够计算非参数二进制分类和偏好学习的确切后验。在本文中，我们概括了先前的结果，并证明了SkeWGP与正常和仿射概率的可能性以及更多的产品相结合。这使我们能够（i）处理统一框架中的分类，偏好，数字和序数回归以及混合问题； （ii）得出相应后验分布的闭合形式表达。我们从经验上表明，基于SkeWGP的拟议框架比主动学习和贝叶斯（受约束）优化的高斯过程提供了更好的性能。这两个任务是设计实验和数据科学的基础。
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.
