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We propose an information theoretic framework for quantitative assessment of acoustic modeling for hidden Markov model (HMM) based automatic speech recognition (ASR). Acoustic modeling yields the probabilities of HMM sub-word states for a short temporal window of speech acoustic features. We cast ASR as a communication channel where the input sub-word probabilities convey the information about the output HMM state sequence. The quality of the acoustic model is thus quantified in terms of the information transmitted through this channel. The process of inferring the most likely HMM state sequence from the sub-word probabilities is known as decoding. HMM based decoding assumes that an acoustic model yields accurate state-level probabilities and the data distribution given the underlying hidden state is independent of any other state in the sequence. We quantify 1) the acoustic model accuracy and 2) its robustness to mismatch between data and the HMM conditional independence assumption in terms of some mutual information quantities. In this context, exploiting deep neural network (DNN) posterior probabilities leads to a simple and straightforward analysis framework to assess shortcomings of the acoustic model for HMM based decoding. This analysis enables us to evaluate the Gaussian mixture acoustic model (GMM) and the importance of many hidden layers in DNNs without any need of explicit speech recognition. In addition, it sheds light on the contribution of low-dimensional models to enhance acoustic modeling for better compliance with the HMM based decoding requirements., Comment: Theoretical flaw, needs major revision

Conventional deep neural networks (DNN) for speech acoustic modeling rely on Gaussian mixture models (GMM) and hidden Markov model (HMM) to obtain binary class labels as the targets for DNN training. Subword classes in speech recognition systems correspond to context-dependent tied states or senones. The present work addresses some limitations of GMM-HMM senone alignments for DNN training. We hypothesize that the senone probabilities obtained from a DNN trained with binary labels can provide more accurate targets to learn better acoustic models. However, DNN outputs bear inaccuracies which are exhibited as high dimensional unstructured noise, whereas the informative components are structured and low-dimensional. We exploit principle component analysis (PCA) and sparse coding to characterize the senone subspaces. Enhanced probabilities obtained from low-rank and sparse reconstructions are used as soft-targets for DNN acoustic modeling, that also enables training with untranscribed data. Experiments conducted on AMI corpus shows 4.6% relative reduction in word error rate.

Most current very low bit rate (VLBR) speech coding systems use hidden Markov model (HMM) based speech recognition/synthesis techniques. This allows transmission of information (such as phonemes) segment by segment that decreases the bit rate. However, the encoder based on a phoneme speech recognition may create bursts of segmental errors. Segmental errors are further propagated to optional suprasegmental (such as syllable) information coding. Together with the errors of voicing detection in pitch parametrization, HMM-based speech coding creates speech discontinuities and unnatural speech sound artefacts. In this paper, we propose a novel VLBR speech coding framework based on neural networks (NNs) for end-to-end speech analysis and synthesis without HMMs. The speech coding framework relies on phonological (sub-phonetic) representation of speech, and it is designed as a composition of deep and spiking NNs: a bank of phonological analysers at the transmitter, and a phonological synthesizer at the receiver, both realised as deep NNs, and a spiking NN as an incremental and robust encoder of syllable boundaries for coding of continuous fundamental frequency (F0). A combination of phonological features defines much more sound patterns than phonetic features defined by HMM-based speech coders, and the finer analysis/synthesis code contributes into smoother encoded speech. Listeners significantly prefer the NN-based approach due to fewer discontinuities and speech artefacts of the encoded speech. A single forward pass is required during the speech encoding and decoding. The proposed VLBR speech coding operates at a bit rate of approximately 360 bits/s.

We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables projection to the space of training data. Relying on the fact that the intrinsic dimensions of the posterior subspaces are indeed very small and the matrix of all posteriors belonging to a class has a very low rank, we demonstrate how low-dimensional structures enable further enhancement of the posteriors and rectify the spurious errors due to mismatch conditions. The enhanced acoustic modeling method leads to improvements in continuous speech recognition task using hybrid DNN-HMM (hidden Markov model) framework in both clean and noisy conditions, where upto 15.4% relative reduction in word error rate (WER) is achieved.

The speech signal conveys information on different time scales from short time scale or segmental, associated to phonological and phonetic information to long time scale or supra segmental, associated to syllabic and prosodic information. Linguistic and neurocognitive studies recognize the phonological classes at segmental level as the essential and invariant representations used in speech temporal organization. In the context of speech processing, a deep neural network (DNN) is an effective computational method to infer the probability of individual phonological classes from a short segment of speech signal. A vector of all phonological class probabilities is referred to as phonological posterior. There are only very few classes comprising a short term speech signal; hence, the phonological posterior is a sparse vector. Although the phonological posteriors are estimated at segmental level, we claim that they convey supra-segmental information. Specifically, we demonstrate that phonological posteriors are indicative of syllabic and prosodic events. Building on findings from converging linguistic evidence on the gestural model of Articulatory Phonology as well as the neural basis of speech perception, we hypothesize that phonological posteriors convey properties of linguistic classes at multiple time scales, and this information is embedded in their support (index) of active coefficients. To verify this hypothesis, we obtain a binary representation of phonological posteriors at the segmental level which is referred to as first-order sparsity structure; the high-order structures are obtained by the concatenation of first-order binary vectors. It is then confirmed that the classification of supra-segmental linguistic events, the problem known as linguistic parsing, can be achieved with high accuracy using asimple binary pattern matching of first-order or high-order structures.

Measuring the Time delay of Arrival (TDOA) between a set of sensors is the basic setup for many applications, such as localization or signal beamforming. This paper presents the set of TDOA matrices, which are built from noise-free TDOA measurements, not requiring knowledge of the sensor array geometry. We prove that TDOA matrices are rank-two and have a special SVD decomposition that leads to a compact linear parametric representation. Properties of TDOA matrices are applied in this paper to perform denoising, by finding the TDOA matrix closest to the matrix composed with noisy measurements. The paper shows that this problem admits a closed-form solution for TDOA measurements contaminated with Gaussian noise which extends to the case of having missing data. The paper also proposes a novel robust denoising method resistant to outliers, missing data and inspired in recent advances in robust low-rank estimation. Experiments in synthetic and real datasets show TDOA-based localization, both in terms of TDOA accuracy estimation and localization error.

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation $Ax=b$, where $A$ is an $m\times n$ full-rank matrix, $b$ is a column-vector of dimension $m$, and $m$ (the number of equations) is larger than or equal to $n$ (the dimension of the unknown vector $x$). Generally, the equations are inconsistent and there is no feasible solution for $x$ unless $b$ belongs to the column-span of $A$. In the least-square approach, a candidate solution is found as the unique $x$ that minimizes the error function $\|Ax-b\|_2$. We propose a more general approach that consist in considering all the consistent subset of the equations, finding their solutions, and taking a weighted average of them to build a candidate solution. In particular, we show that by weighting the solutions with the squared determinant of their coefficient matrix, the resulting candidate solution coincides with the least square solution.

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matrix completion algorithm by alternative low-rank matrix completion and projection onto the Euclidean distance space. This approach confines the recovered matrix to the EDM cone at each iteration of the matrix completion algorithm. The theoretical guarantees of the calibration performance are obtained considering the random and locally structured missing entries as well as the measurement noise on the known distances. This study elucidates the links between the calibration error and the number of microphones along with the noise level and the ratio of missing distances. Thorough experiments on real data recordings and simulated setups are conducted to demonstrate these theoretical insights. A significant improvement is achieved by the proposed Euclidean distance matrix completion algorithm over the state-of-the-art techniques for ad hoc microphone array calibration., Comment: In Press, available online, August 1, 2014. http://www.sciencedirect.com/science/article/pii/S0165168414003508, Signal Processing, 2014

Source separation or demixing is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these applications, advances in high-throughput sensor technology place demixing algorithms under pressure to accommodate extremely high-dimensional signals, separate an ever larger number of sources, and cope with more sophisticated signal and mixing models. These difficulties are exacerbated by the need for real-time action in automated decision-making systems. Recent advances in convex optimization provide a simple framework for efficiently solving numerous difficult demixing problems. This article provides an overview of the emerging field, explains the theory that governs the underlying procedures, and surveys algorithms that solve them efficiently. We aim to equip practitioners with a toolkit for constructing their own demixing algorithms that work, as well as concrete intuition for why they work.

We tackle the multi-party speech recovery problem through modeling the acoustic of the reverberant chambers. Our approach exploits structured sparsity models to perform room modeling and speech recovery. We propose a scheme for characterizing the room acoustic from the unknown competing speech sources relying on localization of the early images of the speakers by sparse approximation of the spatial spectra of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings demonstrate the effectiveness of the proposed approach for multi-party speech recovery and recognition., Comment: 31 pages