Variational Elliptical Processes
Maria Bånkestad Jens Sjölund Jalil Taghia Thomas B. Schöon
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.