  State-of-the-art speaker recognition relays on models that need a large
amount of training data. This models are successful in tasks like NIST SRE
because there is sufficient data available. However, in real applications, we
usually do not have so much data and, in many cases, the speaker labels are
unknown. We present a method to adapt a PLDA model from a domain with a large
amount of labeled data to another with unlabeled data. We describe a generative
model that produces both sets of data where the unknown labels are modeled like
latent variables. We used variational Bayes to estimate the hidden variables.
Here, we derive the equations for this model. This model has been used in the
papers: "UNSUPERVISED ADAPTATION OF PLDA BY USING VARIATIONAL BAYES METHODS"
publised at ICASSP 2014, "Unsupervised Training of PLDA with Variational Bayes"
published at Iberspeech 2014, and "VARIATIONAL BAYESIAN PLDA FOR SPEAKER
DIARIZATION IN THE MGB CHALLENGE" published at ASRU 2015.
