In speaker recognition, where speech segments are mapped to embeddings on the unit hypersphere, two scoring back-ends are commonly used, namely cosine scoring and PLDA. We have recently proposed PSDA, an analog to PLDA that uses Von Mises-Fisher distributions instead of Gaussians. In this paper, we present toroidal PSDA (T-PSDA). It extends PSDA with the ability to model within and between-speaker variabilities in toroidal submanifolds of the hypersphere. Like PLDA and PSDA, the model allows closed-form scoring and closed-form EM updates for training. On VoxCeleb, we find T-PSDA accu-racy on par with cosine scoring, while PLDA accuracy is inferior. On NIST SRE’21 we find that T-PSDA gives large accuracy gains compared to both cosine scoring and PLDA. 1

In this paper, we address the problem of speaker verification in conditions unseen or unknown during development. A standard method for speaker verification consists of extracting speaker embeddings with a deep neural network and processing them through a backend composed of probabilistic linear discriminant analysis (PLDA) and global logistic regression score calibration. This method is known to result in systems that work poorly on conditions different from those used to train the calibration model. We propose to modify the standard backend, introducing an adaptive calibrator that uses duration and other automatically extracted side-information to adapt to the conditions of the inputs. The backend is trained discriminatively to optimize binary cross-entropy. When trained on a number of diverse datasets that are labeled only with respect to speaker, the proposed backend consistently and, in some cases, dramatically improves calibration, compared to the standard PLDA approach, on a number of held-out datasets, some of which are markedly different from the training data. Discrimination performance is also consistently improved. We show that joint training of the PLDA and the adaptive calibrator is essential -- the same benefits cannot be achieved when freezing PLDA and fine-tuning the calibrator. To our knowledge, the results in this paper are the first evidence in the literature that it is possible to develop a speaker verification system with robust out-of-the-box performance on a large variety of conditions.

In this paper, we analyze the behavior and performance of speaker embeddings and the back-end scoring model under domain and language mismatch. We present our findings regarding ResNet-based speaker embedding architectures and show that reduced temporal stride yields improved performance. We then consider a PLDA back-end and show how a combination of small speaker subspace, language-dependent PLDA mixture, and nuisance-attribute projection can have a drastic impact on the performance of the system. Besides, we present an efficient way of scoring and fusing class posterior logit vectors recently shown to perform well for speaker verification task. The experiments are performed using the NIST SRE 2021 setup.

In speaker recognition, where speech segments are mapped to embeddings on the unit hypersphere, two scoring backends are commonly used, namely cosine scoring or PLDA. Both have advantages and disadvantages, depending on the context. Cosine scoring follows naturally from the spherical geometry, but for PLDA the blessing is mixed -- length normalization Gaussianizes the between-speaker distribution, but violates the assumption of a speaker-independent within-speaker distribution. We propose PSDA, an analogue to PLDA that uses Von Mises-Fisher distributions on the hypersphere for both within and between-class distributions. We show how the self-conjugacy of this distribution gives closed-form likelihood-ratio scores, making it a drop-in replacement for PLDA at scoring time. All kinds of trials can be scored, including single-enroll and multi-enroll verification, as well as more complex likelihood-ratios that could be used in clustering and diarization. Learning is done via an EM-algorithm with closed-form updates. We explain the model and present some first experiments.

We describe the Phonexia submission for the VoxCeleb Speaker Recognition Challenge 2021 (VoxSRC-21) in the unsupervised speaker verification track. Our solution was very similar to IDLab's winning submission for VoxSRC-20. An embedding extractor was bootstrapped using momentum contrastive learning, with input augmentations as the only source of supervision. This was followed by several iterations of clustering to assign pseudo-speaker labels that were then used for supervised embedding extractor training. Finally, a score fusion was done, by averaging the zt-normalized cosine scores of five different embedding extractors. We briefly also describe unsuccessful solutions involving i-vectors instead of DNN embeddings and PLDA instead of cosine scoring.

The Wishart distribution is the standard conjugate prior for the precision of the multivariate Gaussian likelihood, when the mean is known -- while the normal-Wishart can be used when the mean is also unknown. It is however not so obvious how to assign values to the hyperparameters of these distributions. In particular, when forming non-informative limits of these distributions, the shape (or degrees of freedom) parameter of the Wishart must be handled with care. The intuitive solution of directly interpreting the shape as a pseudocount and letting it go to zero, as proposed by some authors, violates the restrictions on the shape parameter. We show how to use the scaled KL-divergence between multivariate Gaussians as an energy function to construct Wishart and normal-Wishart conjugate priors. When used as informative priors, the salient feature of these distributions is the mode, while the KL scaling factor serves as the pseudocount. The scale factor can be taken down to the limit at zero, to form non-informative priors that do not violate the restrictions on the Wishart shape parameter. This limit is non-informative in the sense that the posterior mode is identical to the maximum likelihood estimate of the parameters of the Gaussian.

Out of a hundred trials, how many errors does your speaker verifier make? For the user this is an important, practical question, but researchers and vendors typically sidestep it and supply instead the conditional error-rates that are given by the ROC/DET curve. We posit that the user's question is answered by the Bayes error-rate. We present a tutorial to show how to compute the error-rate that results when making Bayes decisions with calibrated likelihood ratios, supplied by the verifier, and an hypothesis prior, supplied by the user. For perfect calibration, the Bayes error-rate is upper bounded by min(EER,P,1-P), where EER is the equal-error-rate and P, 1-P are the prior probabilities of the competing hypotheses. The EER represents the accuracy of the verifier, while min(P,1-P) represents the hardness of the classification problem. We further show how the Bayes error-rate can be computed also for non-perfect calibration and how to generalize from error-rate to expected cost. We offer some criticism of decisions made by direct score thresholding. Finally, we demonstrate by analyzing error-rates of the recently published DCA-PLDA speaker verifier.

Speaker embeddings (x-vectors) extracted from very short segments of speech have recently been shown to give competitive performance in speaker diarization. We generalize this recipe by extracting from each speech segment, in parallel with the x-vector, also a diagonal precision matrix, thus providing a path for the propagation of information about the quality of the speech segment into a PLDA scoring backend. These precisions quantify the uncertainty about what the values of the embeddings might have been if they had been extracted from high quality speech segments. The proposed probabilistic embeddings (x-vectors with precisions) are interfaced with the PLDA model by treating the x-vectors as hidden variables and marginalizing them out. We apply the proposed probabilistic embeddings as input to an agglomerative hierarchical clustering (AHC) algorithm to do diarization in the DIHARD'19 evaluation set. We compute the full PLDA likelihood 'by the book' for each clustering hypothesis that is considered by AHC. We do joint discriminative training of the PLDA parameters and of the probabilistic x-vector extractor. We demonstrate accuracy gains relative to a baseline AHC algorithm, applied to traditional xvectors (without uncertainty), and which uses averaging of binary log-likelihood-ratios, rather than by-the-book scoring.

This paper describes our initial efforts to build a large-scale speaker diarization (SD) and identification system on a recently digitized radio broadcast archive from the Netherlands which has more than 6500 audio tapes with 3000 hours of Frisian-Dutch speech recorded between 1950-2016. The employed large-scale diarization scheme involves two stages: (1) tape-level speaker diarization providing pseudo-speaker identities and (2) speaker linking to relate pseudo-speakers appearing in multiple tapes. Having access to the speaker models of several frequently appearing speakers from the previously collected FAME! speech corpus, we further perform speaker identification by linking these known speakers to the pseudo-speakers identified at the first stage. In this work, we present a recently created longitudinal and multilingual SD corpus designed for large-scale SD research and evaluate the performance of a new speaker linking system using x-vectors with PLDA to quantify cross-tape speaker similarity on this corpus. The performance of this speaker linking system is evaluated on a small subset of the archive which is manually annotated with speaker information. The speaker linking performance reported on this subset (53 hours) and the whole archive (3000 hours) is compared to quantify the impact of scaling up in the amount of speech data.

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.

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.

Neural network architectures mapping variable-length speech utterances into fixed dimensional embeddings have started to outperform state-of-the-art i-vector systems in speaker and language recognition tasks. However, neural networks are prone to over-fit to the training domain and may be difficult to adapt to new domains with limited development data. A successful solu-tion, used in recent NIST 2017 language recognition evaluation, consists of training the embedding extractor on out-of-domain data and applying a back-end classifier adapted to the target domain. In this paper, we compare the embedding+back-end approach with the end-to-end evaluation of the neural network to obtain language log-likelihoods. Doing careful adaptation of the networks, we show that end-to-end improved detection cost by 6% relative w.r.t. the best embedding system. We compared two embedding architectures. First, we evaluated embeddings using a temporal mean+stddev pooling layer to capture the long-term sequence information (a.k.a. x-vectors). Second, we present a novel probabilistic embedding framework where the embedding is a hidden variable. The network predicts a Gaussian posterior distribution for the embedding given each feature frame. Finally, the frame level posteriors can be combined in a principled way to obtain sequence level posteriors. In this manner, we obtain an uncertainty measure about the embedding value. Language scores are obtained integrating over the embedding posterior distribution. In our experiments, x-vectors outperformed probabilistic embeddings for embedding+back-end systems but both attained comparable results for end-to-end systems.

We present a condensed description and analysis of the joint submission for NIST SRE 2016, by Agnitio, BUT and CRIM (ABC). We concentrate on challenges that arose during development and we analyze the results obtained on the evaluation data and on our development sets. We show that testing on mismatched, non-English and short duration data introduced in NIST SRE 2016 is a difficult problem for current state-of-theart systems. Testing on this data brought back the issue of score normalization and it also revealed that the bottleneck features (BN), which are superior when used for telephone English, are lacking in performance against the standard acoustic features like Mel Frequency Cepstral Coefficients (MFCCs). We offer ABC’s insights, findings and suggestions for building a robust system suitable for mismatched, non-English and relatively noisy data such as those in NIST SRE 2016.

Probabilistic linear discriminant analysis (PLDA) is the de facto standard for backends in i-vector speaker recognition. If we try to extend the PLDA paradigm using non-linear models, e.g., deep neural networks, the posterior distributions of the latent variables and the marginal likelihood become intractable. In this paper, we propose to approach this problem using stochastic gradient variational Bayes. We generalize the PLDA model to let i-vectors depend non-linearly on the latent factors. We approximate the evidence lower bound (ELBO) by Monte Carlo sampling using the reparametrization trick. This enables us to optimize of the ELBO using backpropagation to jointly estimate the parameters that define the model and the approximate posteriors of the latent factors. We also present a reformulation of the likelihood ratio, which we call Q-scoring. Q-scoring makes possible to efficiently score the speaker verification trials for this model. Experimental results on NIST SRE10 suggest that more data might be required to exploit the potential of this method.

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.

A standard recipe for spoken language recognition is to apply a Gaussian back-end to i-vectors. This ignores the uncertainty in the i-vector extraction, which could be important especially for short utterances. A recent paper by Cumani, Plchot and Fer proposes a solution to propagate that uncertainty into the backend. We propose an alternative method of propagating the uncertainty.