Abstract

For one-dimensional continuous time series, the stochastic volatility model and its inference methods have long been a subject of active research. Their extensions to multidimensional cases, however, have met a lot of challenges ranging from modeling to computation. We here introduce a generalized mixture model and variational Bayes inference procedures for handling multidimensional volatility processes. The introduced model is then used as a latent structure for constructing heteroscedastic Gaussian processes, which is an attempt to address a key drawback of the standard Gaussian process that its structure is completely by one kernel function. We further demonstrate how to use variational approximations to carry out an explicit marginalization of the hidden functions, resulting in efficient parameter estimation and process forecasting. We demonstrate its advantages by both simulations and applications to real-data examples of regression, classification and state-space models.