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Variational Bayes Model Selection for Mixture Distribution. Authors: Adrian Corduneanu & Christopher M. Bishop. Presented by Shihao Ji Duke University Machine Learning Group Jan. 20, 2006 . Outline. Introduction – model selection Automatic Relevance Determination (ARD) Experimental Results

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Variational Bayes Model Selection for Mixture Distribution

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Variational Bayes Model Selectionfor Mixture Distribution

Authors: Adrian Corduneanu & Christopher M. Bishop

Presented by Shihao Ji

Duke University Machine Learning Group

Jan. 20, 2006


Outline

  • Introduction – model selection

  • Automatic Relevance Determination (ARD)

  • Experimental Results

  • Application to HMMs


Introduction

  • Cross validation

  • Bayesian approaches

    • MCMC and Laplace approximation

    • (Traditional) variational method

    • (Type II) variational method


Automatic Relevance Determination (ARD)

  • relevance vector regression

  • Given a dataset , we assume is Gaussian

Likelihood:

Prior:

Posterior:

Determination of hyperparameters:

Type II ML


Automatic Relevance Determination (ARD)

  • mixture of Gaussian

  • Given an observed dataset , we assume each data point is drawn

  • independently from a mixture of Gaussian density

Likelihood:

Prior:

Posterior:

VB

Determination of mixing coefficients:

Type II ML


Automatic Relevance Determination (ARD)

  • model selection

Bayesian method: ,

Component elimination: if ,

i.e.,


Experimental Results

  • Bayesian method vs. cross-validation

600 points drawn from a mixture of 5 Gaussians.


Experimental Results

  • Component elimination

Initially the model had 15 mixtures, finally was pruned down to 3 mixtures


Experimental Results


Automatic Relevance Determination (ARD)

  • hidden Markov model

  • Given an observed dataset , we assume each data sequence is

  • generated independently from an HMM

Likelihood:

Prior:

Posterior:

VB

Determination of p and A:

Type II ML


Automatic Relevance Determination (ARD)

  • model selection

Bayesian method: ,

State elimination: if ,

Define -- visiting frequency

where


Experimental Results (1)


Experimental Results (2)


Experimental Results (3)


Questions?


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