Online Student-$t$ Processes with an Overall-local Scale Structure for Modelling Non-stationary Data

Published: 23 Oct 2023, Last Modified: 13 Nov 2023HeavyTails 2023EveryoneRevisionsBibTeX
Keywords: Student-$t$ Processes, Online model, Non-stationary data
TL;DR: We introduce in this paper a mixture of TPs with an SMC sampler, so that we may take advantage of the additional flexibility of a mixture-of-experts model with a convenient online inference algorithm.
Abstract: Time-dependent data often exhibit characteristics, such as non-stationarity and heavy-tailed errors, that would be inappropriate to model with the typical assumptions used in popular models. Thus, more flexible approaches are required to be able to accommodate such issues. To this end, we propose a Bayesian mixture of student-$t$ processes with an overall-local scale structure for the covariance. Moreover, we use a sequential Monte Carlo (SMC) sampler in order to perform online inference as data arrive in real-time. We demonstrate the superiority of our proposed approach compared to typical Gaussian process-based models on real-world data sets in order to prove the necessity of using mixtures of student-$t$ processes.
Submission Number: 5