  The EM training algorithm of the classical i-vector extractor is often
incorrectly described as a maximum-likelihood method. The i-vector model is
however intractable: the likelihood itself and the hidden-variable posteriors
needed for the EM algorithm cannot be computed in closed form. We show here
that the classical i-vector extractor recipe is actually a mean-field
variational Bayes (VB) recipe.
  This theoretical VB interpretation turns out to be of further use, because it
also offers an interpretation of the newer phonetic i-vector extractor recipe,
thereby unifying the two flavours of extractor.
  More importantly, the VB interpretation is also practically useful: it
suggests ways of modifying existing i-vector extractors to make them more
accurate. In particular, in existing methods, the approximate VB posterior for
the GMM states is fixed, while only the parameters of the generative model are
adapted. Here we explore the possibility of also mildly adjusting (calibrating)
those posteriors, so that they better fit the generative model.
