Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 17
1
Outline
MAP estimation (13.1)
Exact methods (13.213.3)
Approx method based on clq graph (13.4)
Linear programming relaxation (13.5)
Graph cuts (13.6)
Search (13.7)
2
Querying a distribution (inference)
Suppose we have a joint p(X1
Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 11
1
Outline
Forward sampling (12.1)
Importance sampling (12.2)
MCMC (12.3)
Collapsed particles (12.4)
Deterministic search (12.5)
2
Monte Carlo integration
The goal is to approximate E[f(X)] for some function
f eg f(X) = I(Xi=k), so E[
Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 9
1
Outline
Exact inference in clique trees (10.2, 10.3)
Approximate inference overview
Loopy belief propagation (11.3)
Other entropy approximations (11.3.7)
2
Message passing on a clique tree
To compute p(Xi), find a clique that contai
Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 8
1
Outline
Forwards backwards on chains
FB on trees
FB on clique chains
FB on clique trees
Message passing on clique trees (10.210.3)
Creating clique trees (10.4)
2
Forwards algorithm
1. predi ct: compute the the onestepahead pr edic
Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 7
1
Outline
Variable elimination (9.29.3)
Complexity of VE (9.4)
Conditioning (9.5)
From VE to clique trees (10.1)
Message passing on clique trees (10.210.3)
Creating clique trees (10.4)
2
Inference
Consider the following distribution
Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 5
1
Outline
Template models (6.36.5)
Structural uncertainty (6.6)
Multivariate Gaussians (7.1)
Gaussian DAGs (7.2)
Gaussian MRFs (7.3)
2
Parameter tying
A DBN defines a distribution over an unboundedly
large number of variables by assu
Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 4
1
Admin
CS auditors: please turn in your form to Joyce
Poon, who will pass it to Laks for signing
2
Outline
Aside on canonical parameterization (ex 4.4.14)
Structured factors (4.4.1.2)
Structured CPDs (5.25.6)
Temporal models (6.2)
3
Topics in multivariate analysis: Probabilistic graphical models
STAT 521

Spring 2009
Stat 521A
Lecture 2
1
Outline
DAGs
global Markov (3.3)
deriving graphs from distributions (3.4)
UGs
Global Markov property (4.3.1)
Parameterization (4.2)
Gibbs distributions, energy based models (4.4.1)
Local and pairwise Markov properties (4.3.2)
Fro