  Flexible regression methods where interest centres on the way that the whole
distribution of a response vector changes with covariates are very useful in
some applications. A recently developed technique in this regard uses the
matrix-variate Dirichlet process as a prior for a mixing distribution on a
coefficient in a multivariate linear regression model. The method is
attractive, particularly in the multivariate setting, for the convenient way
that it allows for borrowing strength across different component regressions
and for its computational simplicity and tractability. The purpose of the
present article is to develop fast online variational Bayes approaches to
fitting this model and to investigate how they perform compared to MCMC and
batch variational methods in a number of scenarios.
