An MAP Estimation for Between-Class Variance

TL;DR

This paper introduces a Maximum A Posteriori (MAP) estimation method for the between-class variance in probabilistic linear discriminant analysis (PLDA), improving generalization in open-set verification tasks by addressing limited class data issues.

Contribution

It proposes a novel MAP estimation approach using an Inverse-Wishart prior for the between-class variance in hierarchical models like PLDA, with a tractable inference method.

Findings

MAP estimation improves verification performance

Method enhances generalization in limited class scenarios

Effective in PLDA scoring and length normalization

Abstract

Probabilistic linear discriminant analysis (PLDA) has been widely used in open-set verification tasks, such as speaker verification. A potential issue of this model is that the training set often contains limited number of classes, which makes the estimation for the between-class variance unreliable. This unreliable estimation often leads to degraded generalization. In this paper, we present an MAP estimation for the between-class variance, by employing an Inverse-Wishart prior. A key problem is that with hierarchical models such as PLDA, the prior is placed on the variance of class means while the likelihood is based on class members, which makes the posterior inference intractable. We derive a simple MAP estimation for such a model, and test it in both PLDA scoring and length normalization. In both cases, the MAP-based estimation delivers interesting performance improvement.