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

Embeddings in machine learning are low-dimensional representationsof complex input patterns, with the property that simplegeometric operations like Euclidean distances and dot productscan be used for classification and comparison tasks. Weintroduce meta-embeddings, which live in more general innerproduct spaces and which are designed to better propagate uncertaintythrough the embedding bottleneck. Traditional embeddingsare trained to maximize between-class and minimizewithin-class distances. Meta-embeddings are trained to maximizerelevant information throughput. As a proof of conceptin speaker recognition, we derive an extractor from the familiargenerative Gaussian PLDA model (GPLDA). We show thatGPLDA likelihood ratio scores are given by Hilbert space innerproducts between Gaussian likelihood functions, which weterm Gaussian meta-embeddings (GMEs). Meta-embedding extractorscan be generatively or discriminatively trained. GMEsextracted by GPLDA have fixed precisions and do not propagateuncertainty. We show that a generalization to heavy-tailedPLDA gives GMEs with variable precisions, which do propagateuncertainty. Experiments on NIST SRE 2010 and 2016show that the proposed method applied to i-vectors withoutlength normalization is up to 20% more accurate than GPLDAapplied to length-normalized i-vectors.