The standard state-of-the-art backend for text-independent speaker recognizers that use i-vectors or x-vectors, is Gaussian PLDA (G-PLDA), assisted by a Gaussianization step involving length normalization. G-PLDA can be trained with both generative or discriminative methods. It has long been known that heavy-tailed PLDA (HT-PLDA), applied without length normalization, gives similar accuracy, but at considerable extra computational cost. We have recently introduced a fast scoring algorithm for a discriminatively trained HT-PLDA backend. This paper extends that work by introducing a fast, variational Bayes, generative training algorithm. We compare old and new backends, with and without length-normalization, with i-vectors and x-vectors, on SRE'10, SRE'16 and SITW.

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. The proposed meta-embeddings are special embeddings that live in more general inner product spaces. They are designed to propagate uncertainty to the final output in speaker recognition and similar applications. The familiar Gaussian PLDA model (GPLDA) can be re-formulated as an extractor for Gaussian meta-embeddings (GMEs), such that likelihood ratio scores are given by Hilbert space inner products between Gaussian likelihood functions. GMEs extracted by the GPLDA model 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 ivectors.

We propose a theoretical framework for thinking about score normalization, which confirms that normalization is not needed under (admittedly fragile) ideal conditions. If, however, these conditions are not met, e.g. under data-set shift between training and runtime, our theory reveals dependencies between scores that could be exploited by strategies such as score normalization. Indeed, it has been demonstrated over and over experimentally, that various ad-hoc score normalization recipes do work. We present a first attempt at using probability theory to design a generative score-space normalization model which gives similar improvements to ZT-norm on the text-dependent RSR 2015 database.

We trained on each acoustic feature a full covariance, genderindependent UBM model with 2048 Gaussians followed by a 600-dimensional i-vector extractor to establish our MFCCand PLP-based i-vector systems. The unlabeled set of development data was used in the training of both the UBM and the i-vector extractor. The open-source Kaldi software has been used for all these processing steps [20]. It has been shown that successive acoustic observation vectors tend to be highly correlated. This may be problematic for maximum a posteriori (MAP) estimation of i-vectors. To investigating this issue, scaling the zero and first order Baum-Welch statistics before presenting them to the i-vector extractor has been proposed. It turns out that a scale factor of 0.33 gives a slight edge, resulting in a better decision cost function [10]. This scaling factor has been performed in training the i-vector extractor as well as in the testing.