We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational tractability. Elliptical processes are based on a representation of elliptical distributions as a continuous mixture of Gaussian distributions. We parameterize this mixture distribution as a spline normalizing flow, which we train using variational inference. The proposed form of the variational posterior enables a sparse variational elliptical process applicable to large-scale problems. We highlight advantages compared to Gaussian processes through regression and classification experiments. Elliptical processes can supersede Gaussian processes in several settings, including cases where the likelihood is non-Gaussian or when accurate tail modeling is essential.

翻译：我们提出了椭圆过程，这是一种非参数化概率模型家族，它涵盖了高斯过程和学生t过程。该泛化在保持计算可处理性的同时，引入了一系列新的重尾行为。椭圆过程基于椭圆分布表示为高斯分布连续混合的形式。我们将这种混合分布参数化为样条归一化流，并通过变分推断进行训练。所提出的变分后验形式支持适用于大规模问题的稀疏变分椭圆过程。通过回归和分类实验，我们突出了与高斯过程相比的优势。椭圆过程可在多种场景下替代高斯过程，包括似然函数非高斯或需要精确尾部分布建模的情况。