Maximum a Posteriori Estimation for Multivariate Gaussian Mixture

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Maximum a Posteriori Estimation for Multivariate Gaussian Mixture Observations of Markov Chains Jean-Luc Gauvain

Maximum a Posteriori Estimation for Multivariate Gaussian Mixture Observations of Markov Chains Jean-Luc Gauvain and Chin-Hui Lee

• 最大後驗機率估計(maximum a posteriori estimation) • 最大似然線性迴歸(maximum likelihood linear regression) 2

• 最大後驗機率估計(maximum a posteriori estimation) • 最大似然線性迴歸(maximum likelihood linear regression) 2

Outline • Introduction • Choices of Prior Densities • MAP Estimates for Gaussian Mixture

Outline • Introduction • Choices of Prior Densities • MAP Estimates for Gaussian Mixture • MAP Estimates for HMM • Prior Density Estimation • Experimental Results • Conclusion 5

Introduction • The choice of the prior distribution family. • The specification of the

Introduction • The choice of the prior distribution family. • The specification of the parameters for the prior densities. • The evaluation of the MAP. •

Choices of Prior Densities •

Choices of Prior Densities •

Choices of Prior Densities •

Choices of Prior Densities •

Choices of Prior Densities •

Choices of Prior Densities •

Choices of Prior Densities •

Choices of Prior Densities •

MAP Estimates for Gaussian Mixture •

MAP Estimates for Gaussian Mixture •

MAP Estimates for Gaussian Mixture •

MAP Estimates for Gaussian Mixture •

MAP Estimates for Gaussian Mixture •

MAP Estimates for Gaussian Mixture •

Forward-Backward MAP Estimate

Forward-Backward MAP Estimate

Forward-Backward MAP Estimate

Forward-Backward MAP Estimate

MAP Estimates for HMM •

MAP Estimates for HMM •

Prior Density Estimation •

Prior Density Estimation •

Prior Density Estimation •

Prior Density Estimation •

Experimental Results

Experimental Results

Conclusion • The forward-backward MAP estimation and the segmental MAP estimation, were formulated(制定). •

Conclusion • The forward-backward MAP estimation and the segmental MAP estimation, were formulated(制定). • The proposed Bayesian estimation approach provides a framework to solve various HMM estimation problems posed by sparse training data. • The same framework can also be adopted for the smoothing and adaptation of discrete and tied-mixture hidden Markov models and N-gram stochastic language models.

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