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.

我们提出了椭圆过程，这是一类非参数概率模型，它包含了高斯过程和学生 t 过程。通过连续高斯混合分布的表示，椭圆过程具有一系列新的重尾行为，同时保持计算可行性。使用样条标准化流的参数化混合分布来训练变分推断，并提出了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，我们强调了与高斯过程相比的优势。在非高斯似然函数或精确的尾部建模至关重要的情况下，椭圆过程可以取代高斯过程。