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Unformatted text preview: Speech Recognition Training Continuous Density HMMs Lecture Based on: Dr. Rita Singh’s Notes School of Computer Science Carnegie Mellon University February 13, 2012 Veton Këpuska 2 Table of Content Review of continuous density HMMs Training context independent subword units Outline Viterbi training BaumWelch training Training context dependent subword units State tying BaumWelch for shared parameters February 13, 2012 Veton Këpuska 3 Discrete HMM Data can take only a finite set of values Balls from an urn The faces of a dice Values from a codebook The state output distribution of any state is a normalized histogram Every state has its own distribution HMM outputs one of four colors at each instant. Each of the three states has a different probability distribution for the colors. Since the number of colors is discrete, the state output distributions are multinomial. February 13, 2012 Veton Këpuska 4 Continuous Density HMM There data can take a continuum of values: e.g., cepstral vectors Each state has a state output density. When the process visits a state, it draws from the state output density for that state. HMM outputs a continuous valued random variable at each state. State output densities are mixtures of Gaussians. The output at each state is drawn from this mixture. February 13, 2012 Veton Këpuska 5 Modeling Output State Densities The state output distributions might be anything in reality We model these state output distributions using various simple densities The models are chosen such that their parameters can be easily estimated Gaussian Mixture Gaussian Other exponential densities If the density model is inappropriate for the data, the HMM will be a poor statistical model Gaussians are poor models for the distribution of power spectra February 13, 2012 Veton Këpuska 6 Parameter Sharing Insufficient data to estimate all parameters of all Gaussians Assume states from different HMMs have the same state output distribution Tiedstate HMMs Assume all states have different mixtures of the same Gaussians Semicontinuous HMMs Assume all states have different mixtures of the same Gaussians and some states have the same mixtures Semicontinuous HMMs with tied states Other combinations are possible February 13, 2012 Veton Këpuska 7 Training Models for a Sound Unit Training involves grouping data from subword units followed by parameter estimation....
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 Summer '09
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 Computer Science, Variance, Probability theory, probability density function, Veton Këpuska

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