%%%%%  LaTeX template for submission of abstracts to  MaxEnt 2009
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%%%%% Use this template to generate a pdf version of your abstract for submission. This is
%%%%% most easily accomplished using a LaTeX compiler that outputs directly to pdf.
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%%%%% Your abstract may be no more that one page in length and that all text and figures must
%%%%% fit in a 16.0 cm x 23.0 cm frame.
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%%%%% When you submit the pdf version of your abstract on the conference web site
%%%%% you will be ask if your are requesting an Oral presentation or a Poster.  You will
%%%%% also be ask it this is a student presentation.
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\documentclass[letterpaper,12pt]{article}

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\usepackage{amsmath}


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\begin{document}


%%%%%  The title of your contribution in all capital letters.
\title{NONLINEAR STATISTICAL MODELING OF SPEECH}

%%%%%  Author's name (underline presenter's author)
\author{\underline{S. Srinivasan}$^{1}$, T. Ma$^{1}$, D. May$^{1}$, G. Lazarou$^{2}$, J. Picone$^{1}$ \\
        (1) Department of Electrical and Computer Eng.,\\ Mississippi State University, MS, USA\\
        (2) New York City Transit Authority, New York, New York, USA\\
        \{ss754, tm334, dom5\}@ece.msstate.edu,\\ \{georgios.lazarou, joseph.picone\}@gmail.com
       }

\date{}
\maketitle

%%%%%               Abstract begins here
\begin{abstract}
\noindent
Contemporary approaches to speech and speaker recognition decompose the problem into
four components: feature extraction, acoustic modeling, language modeling and search.
Statistical signal processing is an integral part of each of these components, and Bayes Rule is
used to merge these components into a single optimal choice. Acoustic models typically use
hidden Markov models based on Gaussian mixture models for state output probabilities. This
popular approach suffers from an inherent assumption of linearity in speech signal dynamics.
Language models often employ a variety of maximum entropy techniques, but can employ
many of the same statistical techniques used for acoustic models.

In this paper, we focus on introducing nonlinear statistical models to the feature extraction
and acoustic modeling problems as a first step towards speech and speaker recognition
systems based on notions of chaos and strange attractors. Our goal in this work is to improve
the generalization and robustness properties of a speech recognition system. Three nonlinear
invariants are proposed for feature extraction: Lyapunov exponents, correlation fractal
dimension, and correlation entropy. We demonstrate an 11\% relative improvement on speech
recorded under noise-free conditions, but show a comparable degradation occurs for
mismatched training conditions on noisy speech. We conjecture that the degradation is due to
difficulties in estimating invariants reliably from noisy data.

To circumvent these problems, we introduce two dynamic models to the acoustic modeling
problem: (1) a linear dynamic model (LDM) that uses a state space-like formulation to
explicitly model the evolution of hidden states using an autoregressive process, and (2) a data-dependent
mixture of autoregressive (MixAR) models. Results show that LDM and
MixAR models can achieve comparable performance with HMM systems while using
significantly fewer parameters. Currently we are developing Bayesian parameter estimation and
discriminative training algorithms for these new models to improve noise robustness.

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%%%%%       OPTIONAL: Key Words (delete if not used)
\medskip\noindent{Key Words: }
{nonlinear statistical models, chaos, machine learning, speech recognition}
%%%%%        END of Key Words

\end{abstract}
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\end{document}
