On the Distribution of Speaker Verification Scores: Generative Models for Unsupervised Calibration

Speaker verification systems whose outputs can be interpreted as log-likelihood ratios (LLR) allow for cost-effective decisions by comparing the system outputs to application-defined thresholds depending only on prior information. Classifiers often produce uncalibrated scores, and require additional processing to produce well-calibrated LLRs. Recently, generative score calibration models have been proposed, which achieve calibration performance close to that of state-of-the-art discriminative techniques for supervised scenarios, while also allowing for unsupervised training. The effectiveness of these methods, however, strongly depends on their capabilities to correctly model the target and non-target score distributions. In this work we propose theoretically grounded and accurate models for characterizing the distribution of scores of speaker verification systems. Our approach is based on tied Generalized Hyperbolic distributions and overcomes many limitations of Gaussian models. Experimental results on different NIST benchmarks, using different utterance representation front-ends and different back-end classifiers, show that our method is effective not only in supervised scenarios, but also in unsupervised tasks characterized by very low proportion of target trials.