Online Student-$t$ Processes with an Overall-local Scale Structure for Modelling Non-stationary Data
This work addresses the problem of flexible time-series modeling for practitioners dealing with non-stationary and heavy-tailed data, though it appears incremental as it builds on existing mixture and student-t process frameworks.
The authors tackled modeling non-stationary and heavy-tailed time-dependent data by proposing a Bayesian mixture of student-t processes with an overall-local scale structure, using sequential Monte Carlo for online inference, and demonstrated superiority over Gaussian process-based models on real-world datasets.
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.