We present the elliptical processes -- a family of non-parametric probabilistic models that subsumes the Gaussian process and the Student-t process. This generalization includes a range of new fat-tailed behaviors yet retains computational tractability. We base the elliptical processes on a representation of elliptical distributions as a continuous mixture of Gaussian distributions and derive closed-form expressions for the marginal and conditional distributions. We perform numerical experiments on robust regression using an elliptical process defined by a piecewise constant mixing distribution, and show advantages compared with a Gaussian process. The elliptical processes may become a replacement for Gaussian processes in several settings, including when the likelihood is not Gaussian or when accurate tail modeling is critical.
翻译:我们展示了椭圆过程 -- -- 一组非参数概率模型,它包含高斯进程和学生-t进程。这种概括化包括一系列新的脂肪尾细行为,但保留了可计算性。我们把椭圆过程建立在作为高斯分布的连续混合物的椭圆分布的表示之上,并为边际和有条件分布得出封闭式表达式。我们使用一个精细的常态混合分布定义的椭圆回归过程进行数字实验,并展示了与高斯进程相比的优势。椭圆过程可能在若干环境中取代高斯进程,包括在可能性不是高斯或准确尾部模型的关键情况下。