On the determination of epsilon during discriminative GMM training

Discriminative training of Gaussian Mixture Models (GMMs) for speech or speaker recognition purposes is usually based on the gradient descent method, in which the iteration step-size, ε, uses to be defined experimentally. In this letter, we derive an equation to adaptively determine ε, by showing that the second-order Newton-Raphson iterative method to find roots of equations is equivalent to the gradient descent algorithm. © 2010 IEEE.

Discriminative training of the hidden vector state model for semantic parsing

In this paper, we discuss how discriminative training can be applied to the hidden vector state (HVS) model in different task domains. The HVS model is a discrete hidden Markov model (HMM) in which each HMM state represents the state of a push-down automaton with a finite stack size. In previous applications, maximum-likelihood estimation (MLE) is used to derive the parameters of the HVS model. However, MLE makes a number of assumptions and unfortunately some of these assumptions do not hold. Discriminative training, without making such assumptions, can improve the performance of the HVS model by discriminating the correct hypothesis from the competing hypotheses. Experiments have been conducted in two domains: the travel domain for the semantic parsing task using the DARPA Communicator data and the Air Travel Information Services (ATIS) data and the bioinformatics domain for the information extraction task using the GENIA corpus. The results demonstrate modest improvements of the performance of the HVS model using discriminative training. In the travel domain, discriminative training of the HVS model gives a relative error reduction rate of 31 percent in F-measure when compared with MLE on the DARPA Communicator data and 9 percent on the ATIS data. In the bioinformatics domain, a relative error reduction rate of 4 percent in F-measure is achieved on the GENIA corpus.

Analyzing training dependencies and posterior fusion in discriminant classification of apnoea patients based on sustained and connected speech

We present a novel approach using both sustained vowels and connected speech, to detect obstructive sleep apnea (OSA) cases within a homogeneous group of speakers. The proposed scheme is based on state-of-the-art GMM-based classifiers, and acknowledges specifically the way in which acoustic models are trained on standard databases, as well as the complexity of the resulting models and their adaptation to specific data. Our experimental database contains a suitable number of utterances and sustained speech from healthy (i.e control) and OSA Spanish speakers. Finally, a 25.1% relative reduction in classification error is achieved when fusing continuous and sustained speech classifiers. Index Terms: obstructive sleep apnea (OSA), gaussian mixture models (GMMs), background model (BM), classifier fusion.

On Convergence Properties of the EM Algorithm for Gaussian Mixtures

"Expectation-Maximization'' (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix $P$, and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of $P$ and provide new results analyzing the effect that $P$ has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models.

Improving automatic detection of obstructive sleep apnea through nonlinear analysis of sustained speech

We present a novel approach for the detection of severe obstructive sleep apnea (OSA) based on patients' voices introducing nonlinear measures to describe sustained speech dynamics. Nonlinear features were combined with state-of-the-art speech recognition systems using statistical modeling techniques (Gaussian mixture models, GMMs) over cepstral parameterization (MFCC) for both continuous and sustained speech. Tests were performed on a database including speech records from both severe OSA and control speakers. A 10 % relative reduction in classification error was obtained for sustained speech when combining MFCC-GMM and nonlinear features, and 33 % when fusing nonlinear features with both sustained and continuous MFCC-GMM. Accuracy reached 88.5 % allowing the system to be used in OSA early detection. Tests showed that nonlinear features and MFCCs are lightly correlated on sustained speech, but uncorrelated on continuous speech. Results also suggest the existence of nonlinear effects in OSA patients' voices, which should be found in continuous speech.

Helicopter vibration sensor selection using data visualisation

The main objective of the project is to enhance the already effective health-monitoring system (HUMS) for helicopters by analysing structural vibrations to recognise different flight conditions directly from sensor information. The goal of this paper is to develop a new method to select those sensors and frequency bands that are best for detecting changes in flight conditions. We projected frequency information to a 2-dimensional space in order to visualise flight-condition transitions using the Generative Topographic Mapping (GTM) and a variant which supports simultaneous feature selection. We created an objective measure of the separation between different flight conditions in the visualisation space by calculating the Kullback-Leibler (KL) divergence between Gaussian mixture models (GMMs) fitted to each class: the higher the KL-divergence, the better the interclass separation. To find the optimal combination of sensors, they were considered in pairs, triples and groups of four sensors. The sensor triples provided the best result in terms of KL-divergence. We also found that the use of a variational training algorithm for the GMMs gave more reliable results.

Multivariate Density Estimation: An SVM Approach

We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solving inverse operator problems. The algorithm is implemented and tested on simulated data from different distributions and different dimensionalities, gaussians and laplacians in $R^2$ and $R^{12}$. A comparison in performance is made with Gaussian Mixture Models (GMMs). Our algorithm does as well or better than the GMMs for the simulations tested and has the added advantage of being automated with respect to parameters.

Phylogenetic mixture models can reduce node-density artifacts

We investigate the performance of phylogenetic mixture models in reducing a well-known and pervasive artifact of phylogenetic inference known as the node-density effect, comparing them to partitioned analyses of the same data. The node-density effect refers to the tendency for the amount of evolutionary change in longer branches of phylogenies to be underestimated compared to that in regions of the tree where there are more nodes and thus branches are typically shorter. Mixture models allow more than one model of sequence evolution to describe the sites in an alignment without prior knowledge of the evolutionary processes that characterize the data or how they correspond to different sites. If multiple evolutionary patterns are common in sequence evolution, mixture models may be capable of reducing node-density effects by characterizing the evolutionary processes more accurately. In gene-sequence alignments simulated to have heterogeneous patterns of evolution, we find that mixture models can reduce node-density effects to negligible levels or remove them altogether, performing as well as partitioned analyses based on the known simulated patterns. The mixture models achieve this without knowledge of the patterns that generated the data and even in some cases without specifying the full or true model of sequence evolution known to underlie the data. The latter result is especially important in real applications, as the true model of evolution is seldom known. We find the same patterns of results for two real data sets with evidence of complex patterns of sequence evolution: mixture models substantially reduced node-density effects and returned better likelihoods compared to partitioning models specifically fitted to these data. We suggest that the presence of more than one pattern of evolution in the data is a common source of error in phylogenetic inference and that mixture models can often detect these patterns even without prior knowledge of their presence in the data. Routine use of mixture models alongside other approaches to phylogenetic inference may often reveal hidden or unexpected patterns of sequence evolution and can improve phylogenetic inference.