Solving large margin estimation of HMMS via semidefinite programming

In this paper, we propose to use a new optimization method, i.e., semidefinite programming (SDP), to solve the large-margin estimation (LME) problem of continuous-density hidden Markov model (CDHMM) in speech recognition. First, we introduce a new constraint for LME to guarantee the boundedness of the margin of CDHMM. Second, we show that the LME problem subject to this new constraint can be formulated as an SDP problem under some relaxation conditions. Therefore, it can be solved using many efficient optimization algorithms specially designed for SDP. The new LME/SDP method has been evaluated on a speaker independent E-set speech recognition task using the ISOLET database and a connected digit string recognition task using the TIDIGITS database. Experimental results clearly demonstrate that large-margin estimation via semidefinite programing (LME/SDP) can significantly reduce word error rate (WER) over other existing CDHMM training methods, such as MLE and MCE. It has also been shown that the new SDP-based method largely outperforms the previously proposed LME optimization methods using gradient descent search.

This paper describes the combination of two recent machine learning techniques for acoustic modeling in speech recognition: deep neural networks (DNNs) and graph-based semi-supervised learning (SSL). While DNNs have been shown to be powerful supervised classifiers and have achieved considerable success in speech recognition, graph-based SSL can exploit valuable complementary information derived from the manifold structure of the unlabeled test data. Previous work on graph-based SSL in acoustic modeling has been limited to frame-level classification tasks and has not been compared to, or integrated with, state-of-the-art DNN/HMM recognizers. This paper represents the first integration of graph-based SSL with DNN based speech recognition and analyzes its effect on word recognition performance. The approach is evaluated on two small vocabulary speech recognition tasks and shows a significant improvement in HMM state classification accuracy as well as a consistent reduction in word error rate over a state-of-the-art DNN/HMM baseline.

An investigation into the use of Bayesian learning of the parameters of a multivariate Gaussian mixture density has been carried out. In a continuous density hidden Markov model (CDHMM) framework, Bayesian learning serves as a unified approach for parameter smoothing, speaker adaptation, speaker clustering, and corrective training. The goal of this study is to enhance model robustness in a CDHMM-based speech recognition system so as to improve performance. Our approach is to use Bayesian learning to incorporate prior knowledge into the CDHMM training process in the form of prior densities of the HMM parameters. The theoretical basis for this procedure is presented and preliminary results applying to HMM parameter smoothing, speaker adaptation, and speaker clustering are given.Performance improvements were observed on tests using the DARPA RM task. For speaker adaptation, under a supervised learning mode with 2 minutes of speaker-specific training data, a 31% reduction in word error rate was obtained compared to speaker-independent results. Using Baysesian learning for HMM parameter smoothing and sex-dependent modeling, a 21% error reduction was observed on the FEB91 test.

Discriminative training has been a leading factor for improving automatic speech recognition (ASR) performance over the last decade. The traditional discriminative training, however, has been aimed to minimize empirical error rates on training sets, which may not be well generalized to test sets. Many attempts have been made recently to incorporate the principle of large margin (PLM) into the training of hidden Markov models (HMMs) in ASR to improve the generalization abilities. Significant error rate reduction on the test sets has been observed on both small vocabulary and large vocabulary continuous ASR tasks using large-margin discriminative training (LMDT) techniques. In this paper, we introduce the PLM, define the concept of margin in the HMMs, and survey a number of popular LMDT algorithms proposed and developed recently. Specifically, we review and compare the large-margin minimum classification error (LM-MCE) estimation, soft-margin estimation (SME), large margin estimation (LME), large relative margin estimation (LRME), and large margin training (LMT) with a focus on the insights, the training criteria, the optimization techniques used, and the strengths and weaknesses of these different approaches. We suggest future research directions in our conclusion of this paper.

We report on some recent improvements to an HMM-based, continuous speech recognition system which is being developed at AT&T Bell Laboratories. These advances, which include the incorporation of inter-word, context-dependent units and an improved feature analysis, lead to a recognition system which achieve better than 95% word accuracy for speaker independent recognition of the 1000-word, DARPA resource management task using the standard word-pair grammar (with a perplexity of about 60). It will be shown that the incorporation of inter-word units into training results in better acoustic models of word juncture coarticulation and gives a 20% reduction in error rate. The effect of an improved set of spectral and log energy features is to further reduce word error rate by about 30%. We also found that the spectral vectors, corresponding to the same speech unit, behave differently statistically, depending on whether they are at word boundaries or within a word. The results suggest that intra-word and inter-word units should be modeled independently, even when they appear in the same context. Using a set of sub-word units which included variants for intra-word and inter-word, context-dependent phones, an additional decrease of about 10% in word error rate resulted.

In this paper, we introduce a document-specific context probabilistic latent semantic analysis (DCPLSA) model for speech recognition. This is an extension of a CPLSA model [1] where the probability of word is conditioned only on topics. The CPLSA model uses the bigram counts that are the number of appearances of the bigrams in the corpus. These counts are the sum of the bigram counts in different documents where they could appear to describe different topics. We encounter this problem in the CPLSA model and introduce the document-specific CPLSA model (DCPLSA) where the probability of a word is conditioned on both topic and document. We carried out experiments on a continuous speech recognition (CSR) task using the Wall Street Journal (WSJ) corpus and have seen that the proposed DCPLSA approach yields significant reduction in both perplexity and word error rate (WER) measurements over the other approaches used in the literature.

In this paper, we consider a least square semidefinite programming problem under ellipsoidal data uncertainty. We show that the robustification of this uncertain problem can be reformulated as a semidefinite linear programming problem with an additional second-order cone constraint. We then provide an explicit quantitative sensitivity analysis on how the solution under the robustification depends on the size/shape of the ellipsoidal data uncertainty set. Next, we prove that, under suitable constraint qualifications, the reformulation has zero duality gap with its dual problem, even when the primal problem itself is infeasible. The dual problem is equivalent to minimizing a smooth objective function over the Cartesian product of second-order cones and the Euclidean space, which is easy to project onto. Thus, we propose a simple variant of the spectral projected gradient method (Birgin et al. in SIAM J. Optim. 10:1196---1211, 2000) to solve the dual problem. While it is well-known that any accumulation point of the sequence generated from the algorithm is a dual optimal solution, we show in addition that the dual objective value along the sequence generated converges to a finite value if and only if the primal problem is feasible, again under suitable constraint qualifications. This latter fact leads to a simple certificate for primal infeasibility in situations when the primal feasible set lies in a known compact set. As an application, we consider robust correlation stress testing where data uncertainty arises due to untimely recording of portfolio holdings. In our computational experiments on this particular application, our algorithm performs reasonably well on medium-sized problems for real data when finding the optimal solution (if exists) or identifying primal infeasibility, and usually outperforms the standard interior-point solver SDPT3 in terms of CPU time.

End-to-end (E2E) models fold the acoustic, pronunciation and language models of a conventional speech recognition model into one neural network with a much smaller number of parameters than a conventional ASR system, thus making it suitable for on-device applications. For example, recurrent neural network transducer (RNN-T) as a streaming E2E model has shown promising potential for on-device ASR [1]. For such applications, quality and latency are two critical factors. We propose to reduce E2E model's latency by extending the RNN-T endpointer (RNN-T EP) model [2] with additional early and late penalties. By further applying the minimum word error rate (MWER) training technique [3], we achieved 8.0% relative word error rate (WER) reduction and 130ms 90-percentile latency reduction over [2] on a Voice Search test set. We also experimented with a second-pass Listen, Attend and Spell (LAS) rescorer [4]. Although it did not directly improve the first pass latency, the large WER reduction provides extra room to trade WER for latency. RNN-T EP+LAS, together with MWER training brings in 18.7% relative WER reduction and 160ms 90-percentile latency reductions compared to the original proposed RNN-T EP [2] model.

Semidefinite programming (SDP) covers a wide range of applications such as robust optimization, polynomial optimization, combinatorial optimization, system and control theory, financial engineering, machine learning, quantum information and quantum chemistry. In those applications, SDP problems can be large scale easily. Such large scale SDP problems often satisfy a certain sparsity characterized by a chordal graph structure. This sparsity is classified in two types. The one is the domain space sparsity (d-space sparsity) for positive semidefinite symmetric matrix variables involved in SDP problems, and the other the range space sparsity (r-space sparsity) for matrix-inequality constraints in SDP problems. In this short note, we survey how we exploit these two types of sparsities to solve large scale linear and nonlinear SDP problems. We refer to the paper [7] for more details.

Automatic speech recognition (ASR) systems rely almost exclusively on short-term segment-level features (MFCCs), while ignoring higher level suprasegmental cues that are characteristic of human speech. However, recent experiments have shown that categorical representations of prosody, such as those based on the Tones and Break Indices (ToBI) annotation standard, can be used to enhance speech recognizers. However, categorical prosody models are severely limited in scope and coverage due to the lack of large corpora annotated with the relevant prosodic symbols (such as pitch accent, word prominence, and boundary tone labels). In this paper, we first present an architecture for augmenting a standard ASR with symbolic prosody. We then discuss two novel, un-supervised adaptation techniques for improving, respectively, the quality of the linguistic and acoustic components of our categorical prosody models. Finally, we implement the augmented ASR by enriching ASR lattices with the adapted categorical prosody models. Our experiments show that the proposed unsupervised adaptation techniques significantly improve the quality of the prosody models; the adapted prosodic language and acoustic models reduce binary pitch accent (presence versus absence) classification error rate by 13.8% and 4.3%, respectively (relative to the seed models) on the Boston University Radio News Corpus, while the prosody-enriched ASR exhibits a 3.1% relative reduction in word error rate (WER) over the baseline system.

Continuous density hidden Markov models (CD-HMMs) are an essential component of modern systems for automatic speech recognition (ASR). These models assign probabilities to the sequences of acoustic feature vectors extracted by signal processing of speech waveforms. In this chapter, we investigate a new framework for parameter estimation in CD-HMMs. Our framework is inspired by recent parallel trends in the fields of ASR and machine learning. In ASR, significant improvements in performance have been obtained by discriminative training of acoustic models. In machine learning, significant improvements in performance have been obtained by discriminative training of large margin classifiers. Building on both these lines of work, we show how to train CD-HMMs by maximizing an appropriately defined margin between correct and incorrect decodings of speech waveforms. We start by defining an objective function over a transformed parameter space for CD-HMMs, then describe how it can be optimized efficiently by simple gradient-based methods. Within this framework, we obtain highly competitive results for phonetic recognition on the TIMIT speech corpus. We also compare our framework for large margin training to other popular frameworks for discriminative training of CD-HMMs.

Incorporating biasing words obtained through contextual knowledge is paramount in automatic speech recognition (ASR) applications. This paper proposes an innovative method for achieving end-to-end contextual ASR using graph neural network (GNN) encodings based on the tree-constrained pointer generator method. GNN node encodings facilitate lookahead for future word pieces in the process of ASR decoding at each tree node by incorporating information about all word pieces on the tree branches rooted from it. This results in a more precise prediction of the generation probability of the biasing words. The study explores three GNN encoding techniques: namely the tree recursive neural network (Tree-RNN), the graph convolutional network (GCN), and GraphSAGE, along with different combinations of the complementary GCN and GraphSAGE structures. The performance of the systems was evaluated using both Librispeech and the AMI corpus with a visual-grounded contextual ASR pipeline. The findings indicate that using GNN encodings achieved consistent and significant reductions in word error rate (WER), particularly for words that are rare or have not been seen during the training process. Notably, on LibriSpeech test sets, the combined GNN proposed in this paper achieved a 20% relative rare word error rate reduction compared to Tree-RNN, 30%-40% compared to standard TCPGen and 60% compared to standard ASR systems without TCPGen.

Since the introduction of hidden Markov modelling there has been an increasing emphasis on data-driven approaches to automatic speech recognition. This derives from the fact that systems trained on substantial corpora readily outperform those that rely on more phonetic or linguistic priors. Similarly, extra training data almost always results in a reduction in word error rate - “there's no data like more data”. However, despite this progress, contemporary systems are not able to fulfill the requirements demanded by many potential applications, and performance is still significantly short of the capabilities exhibited by human listeners. For these reasons, the R&D community continues to call for even greater quantities of data in order to train their systems. This paper addresses the issue of just how much data might be required in order to bring the performance of an automatic speech recognition system up to that of a human listener.

Although the application of deep learning to automatic speech recognition (ASR) has resulted in dramatic reductions in word error rate for languages with abundant training data, ASR for languages with few resources has yet to benefit from deep learning to the same extent. In this paper, we investigate various methods of acoustic modeling and data augmentation with the goal of improving the accuracy of a deep learning ASR framework for a low-resource language with a high baseline word error rate. We compare several methods of generating synthetic acoustic training data via voice transformation and signal distortion, and we explore several strategies for integrating this data into the acoustic training pipeline. We evaluate our methods on an indigenous language of North America with minimal training resources. We show that training initially via transfer learning from an existing high-resource language acoustic model, refining weights using a heavily concentrated synthetic dataset, and finally fine-tuning to the target language using limited synthetic data reduces WER by 15% over just transfer learning using deep recurrent methods. Further, we show improvements over traditional frameworks by 19% using a similar multistage training with deep convolutional approaches.

Speech dynamic features are routinely used in current speech recognition systems in combination with short-term (static) spectral features. Although many existing speech recognition systems do not weight both kinds of features, it seems convenient to use some weighting in order to increase the recognition accuracy of the system. In the cases that this weighting is performed, it is manually tuned or it consists simply in compensating the variances. The aim of this paper is to propose a method to automatically estimate an optimum state-dependent stream weighting in a continuous density hidden Markov model (CDHMM) recognition system by means of a maximum-likelihood based training algorithm. Unlike other works, it is shown that simple constraints on the new weighting parameters permit to apply the maximum-likelihood criterion to this problem. Experimental results in speaker independent digit recognition show an important increase of recognition accuracy.