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.

中文翻译：

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用于分类的偏斜高斯过程

高斯过程 (GP) 是函数上的分布，它为回归和分类提供贝叶斯非参数方法。尽管它们取得了成功，但 GP 在某些应用中的用途有限，例如，在某些情况下，关于其均值的对称分布是一个不合理的模型。例如，这意味着平均值和中位数重合，而不对称（偏斜）分布中的平均值和中位数可能是不同的数字。在本文中，我们提出斜高斯过程（SkewGPs）作为函数的非参数先验。SkewGP 将有限维向量上的多元统一偏斜正态分布扩展为随机过程。SkewGP 分布类包括 GP，因此，SkewGPs 继承了 GPs 的所有优良特性，并通过允许概率模型中的不对称性来增加它们的灵活性。通过利用 SkewGP 和 probit 似然是共轭模型这一事实，我们推导出了这个新的非参数分类器的边际似然和预测分布的封闭形式表达式。我们凭经验验证所提出的 SkewGP 分类器比基于拉普拉斯方法或期望传播的 GP 分类器提供更好的性能。