Tied Normal Variance-Mean Mixtures for Linear Score Calibration

A speaker verification system decides whether two voice segments belong to the same speaker based on a threshold. An optimal threshold can be set if the recognition scores are well calibrated, i.e., they represent Log–Likelihood Ratios. Logistic Regression (LogReg) is a standard approach for score calibration. While training this discriminative model requires labeled scores, Gaussian and non–Gaussian generative calibration models have been recently proposed. They not only have similar or better performance with respect to LogReg, but also allow for unsupervised or semi–supervised training of the models.The goal of this work is to extend these models. In particular, we show that normal variance–mean mixture distributions are able to model well–calibrated non–Gaussian distributed scores, provided that their parameters for the target and non–target score distributions are properly tied. As for the Gaussian case, a linear calibration model can then be estimated by computing Maximum Likelihood estimates of the distributions parameters and of the score transformation. The quality of all these approaches has been compared on a dataset of segments of variable duration obtained by cutting the NIST 2010 evaluation test data.