Gaussian meta-embeddings for efficient scoring of a heavy-tailed PLDA model

embeddings, machine learning, speaker recognition

Embeddings in machine learning are low-dimensional representations of complex input patterns, with the property that simple geometric operations like Euclidean distances and dot products can be used for classification and comparison tasks. We introduce meta-embeddings, which live in more general inner product spaces and which are designed to better propagate uncertainty through the embedding bottleneck. Traditional embeddings are trained to maximize between-class and minimize within-class distances. Meta-embeddings are trained to maximize relevant information throughput. As a proof of concept in speaker recognition, we derive an extractor from the familiar generative Gaussian PLDA model (GPLDA). We show that GPLDA likelihood ratio scores are given by Hilbert space inner products between Gaussian likelihood functions, which we term Gaussian meta-embeddings (GMEs). Meta-embedding extractors can be generatively or discriminatively trained. GMEs extracted by GPLDA have fixed precisions and do not propagate uncertainty. We show that a generalization to heavy-tailed PLDA gives GMEs with variable precisions, which do propagate uncertainty. Experiments on NIST SRE 2010 and 2016 show that the proposed method applied to i-vectors without length normalization is up to 20% more accurate than GPLDA applied to length-normalized i-vectors.