Particle Filtered MCMC-MLEwith Connections to

Contrastive DivergenceArthur Asuncion (UC Irvine); Qiang Liu (UC Irvine); Alex Ihler (UC Irvine); Padhraic Smyth (UC Irvine)

ICML2010読む会 2010/8/18

東京大学中川研究室D3日本学術振興会特別研究員(DC1)

読む人：佐藤一誠1

紹介する論文

Problem definition

Model:

Goal:

Data:

intractable2

Table of Contents

• Problem definition

• Particle filter

• MCMC-MLE

• Particle filtered MCMC-MLE

• Connections to Contrastive Divergence

• Experiments

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Particle Filter[Kitagawa,1996][Doucet+, 2001]

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Particle Filter

Resampling

Rejuvenateby MCMC

[Kitagawa,1996][Doucet+, 2001]

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Table of Contents

• Problem definition

• Particle filter

• MCMC-MLE

• Particle filtered MCMC-MLE

• Connections to Contrastive Divergence

• Experiments

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MCMC-MLE[Geyer&Thompson,1992]

MCMC approximation)|( 0xp

Alternate distribution

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MCMC-MLE

MCMC approximation

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[Geyer&Thompson,1992]

Gradient of likelihood

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Importance weight

Monte Carlo Importance Weights

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MCMC-MLE algorithm

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Particle Filtered MCMC-MLE algorithm

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Particle Filtered MCMC-MLE :

MCMC-MLE :

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Importance weight of PF-MCMC-MLE

Effective sample size(ESS)

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Persistent Contrastive Divergence (PCD-n)[Tieleman,2008]

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Particle Filtered MCMC-MLE :

MCMC-MLE :

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Drown from via MCMCwhere CD-n initializes the chains from dataand n is often 1.

Contrastive Divergence (CD)[Hinton,2002]

)|( ixp

PCD does not reset the Markov Chain between parameter updates. 17

Table of Contents

• Problem definition

• Particle filter

• MCMC-MLE

• Particle filtered MCMC-MLE

• Connections to Contrastive Divergence

• Experiments

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Thank you for listening

Contrastive Divergence [Neural Computation2002]

Persistent Contrastive Divergence [ICML2008,2009]

MCMC-MLE[1992]

Particle filtered MCMC-MLE[ICML2010]

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