论文标题
椭圆过程：肥胖的随机过程
The Elliptical Processes: a Family of Fat-tailed Stochastic Processes
论文作者
论文摘要
我们介绍椭圆过程 - 一个非参数概率模型的家族，该模型涵盖了高斯过程和学生-T过程。这种概括包括一系列新的脂肪尾行为，但保留了计算障碍。我们将椭圆过程基于椭圆形分布的表示，作为高斯分布的连续混合物，并为边缘和条件分布提供了封闭形式的表达式。我们使用由分段恒定混合分布定义的椭圆过程对鲁棒回归进行数值实验，并显示与高斯工艺相比的优势。椭圆过程可能会在多种设置中替代高斯过程，包括当可能性不是高斯或准确的尾巴建模至关重要时。
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.
