importance sampling & markov chain monte carlo (mcmc)nando/540-2013/lectures/l14.pdf ·...
TRANSCRIPT
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CPSC540
Nando de FreitasMarch, 2013University of British Columbia
Importance sampling &
Markov chain Monte Carlo (MCMC)
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Outline of the lecture
This is about Monte Carlo methods.
� We will revise importance sampling.� Revise how Google works (Markov chains).� Introduce Markov chain Monte Carlo (MCMC)
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Bayesian logistic regressionThe logistic regression model specifies the probability of a binary outputyi ∈ {0, 1} given the input xi as follows:
p(y|X, θ) =
n∏
i=1
Ber(yi|sigm(xiθ))
=n∏
i=1
[1
1 + e−xiθ
]yi [1−
1
1 + e−xiθ
]1−yi∏
i=1
[
−
] [
−
]
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Importance sampling
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Importance sampling
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Importance sampling
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Example: Logistic Regression
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Un-normalized importance sampling
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Markov Chain Monte Carlo
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Markov Chain Monte Carlo
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Markov Chain Monte Carlo
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Markov Chain Monte Carlo
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Markov Chain Monte Carlo
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Markov Chain Monte Carlo
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Markov Chain Monte Carlo
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Markov Chain Monte Carlo
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Metropolis-Hastings for logistic regression
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MCMC: Metropolis-Hastings
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MCMC: Metropolis-Hastings
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MCMC: Choosing the Right Proposal
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MCMC: Theory
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MCMC: Theory
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Variations of Metropolis-Hastings
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Extending MH to directed probabilistic graphical models
MINVOLSET
PCWP CO
HRBP
HREKG HRSAT
ERRCAUTERHRHISTORY
CATECHOL
SAO2 EXPCO2
ARTCO2
VENTALV
VENTLUNG VENITUBE
DISCONNECTVENTMACHKINKEDTUBEINTUBATIONPULMEMBOLUS
PAP SHUNT
ANAPHYLAXIS
MINOVL
PVSAT
FIO2PRESS
INSUFFANESTHTPR
LVFAILURE
ERRBLOWOUTPUTSTROEVOLUMELVEDVOLUME
HYPOVOLEMIA
CVP
BP
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Bayesian graphical models and Gibbs
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Gibbs Sampling
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Gibbs Sampling
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Gibbs Sampling For Graphical models
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Auxiliary Variable Samplers
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Hybrid (Hamiltonian) Monte Carlo
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Hybrid Monte Carlo
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Next lecture
In the next lecture, we look at constrained optimization and sparse methods in learning.