Non-stationary, online variational Bayesian learning, with circular variables

摘要

This paper introduces a method for achieving online Bayesian learning:•for time series data of indefinite (possibly infinite) length,•where the model is statistically non-stationary over time, and•the model includes a circular variable.The integrals required for full Bayesian inference are intractable, so we use a varational approximation method and place priors over precision hyperparameters to ensure that•the posterior probability distributions do not become overly tight, which would impede its ability to recognise and track changes, and•no values in the system are able to continuously increase and hence exceed the numerical representation of the programming language.With only a single round of updates in the variational Bayesian scheme per observation, a processing rate of at least 11 kHz is achieved.