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Structure Learning in Undirected Graphical Models

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171 pages
Structure Learning in Undirected Graphical Models Mark Schmidt INRIA - SIERRA team Laboratoire d'Informatique de l'Ecole Normale Suprieure January 20, 2011

  • laboratoire d'informatique de l'ecole normale

  • regularization high-order

  • ising graphical

  • classical methods

  • regularization


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Structure Learning in Undirected Graphical Models
Mark Schmidt
INRIA - SIERRA team
Laboratoire d’Informatique de l’Ecole Normale Suprieure
January 20, 2011Motivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization1
General pairwise models: Group ‘1
High-order models: Structured Sparsity
Further Extensions
Outline
1 Motivation, Classical Methods
2 Gausian and Ising graphical models: ‘ -Regularization1
3 General pairwise models: Group ‘ -Regularization1
4 High-order models: Structured Sparsity
5 Further Extensions
Mark Schmidt Structure Learning in Undirected Graphical ModelsMotivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization Motivation1
General pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
Further Extensions
Motivation for Graphical Model Structure Learning
car drive les hockey mac league pc win
0 0 1 0 1 0 1 0
0 0 0 1 0 1 0 1
1 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 0 1 0 0 0 1 1
What words are related?
Is a post with (car,drive,hockey,pc,win) spam?
What is p(carjdrive)? What about p(carjdrive; les)?
Can we ‘ ll in’ some variables given the others?
Can we generate more items that look like this?
Mark Schmidt Structure Learning in Undirected Graphical ModelsMotivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization Motivation1
General pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
Further Extensions
Motivation for Graphical Model Structure Learning
car drive les hockey mac league pc win
0 0 1 0 1 0 1 0
0 0 0 1 0 1 0 1
1 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 0 1 0 0 0 1 1
What words are related?
Is a post with (car,drive,hockey,pc,win) spam?
What is p(carjdrive)? What about p(carjdrive; les)?
Can we ‘ ll in’ some variables given the others?
Can we generate more items that look like this?
Mark Schmidt Structure Learning in Undirected Graphical ModelsMotivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization Motivation1
General pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
Further Extensions
Motivation for Graphical Model Structure Learning
car drive les hockey mac league pc win
0 0 1 0 1 0 1 0
0 0 0 1 0 1 0 1
1 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 0 1 0 0 0 1 1
What words are related?
Is a post with (car,drive,hockey,pc,win) spam?
What is p(carjdrive)? What about p(carjdrive; les)?
Can we ‘ ll in’ some variables given the others?
Can we generate more items that look like this?
Mark Schmidt Structure Learning in Undirected Graphical ModelsMotivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization Motivation1
General pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
Further Extensions
Motivation for Graphical Model Structure Learning
car drive les hockey mac league pc win
0 0 1 0 1 0 1 0
0 0 0 1 0 1 0 1
1 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 0 1 0 0 0 1 1
What words are related?
Is a post with (car,drive,hockey,pc,win) spam?
What is p(carjdrive)? What about p(carjdrive; les)?
Can we ‘ ll in’ some variables given the others?
Can we generate more items that look like this?
Mark Schmidt Structure Learning in Undirected Graphical ModelsMotivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization Motivation1
General pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
Further Extensions
Motivation for Graphical Model Structure Learning
car drive les hockey mac league pc win
0 0 1 0 1 0 1 0
0 0 0 1 0 1 0 1
1 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 0 1 0 0 0 1 1
What words are related?
Is a post with (car,drive,hockey,pc,win) spam?
What is p(carjdrive)? What about p(carjdrive; les)?
Can we ‘ ll in’ some variables given the others?
Can we generate more items that look like this?
Mark Schmidt Structure Learning in Undirected Graphical ModelsMotivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization Motivation1
General pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
Further Extensions
Motivation for Graphical Model Structure Learning
car drive les hockey mac league pc win
0 0 1 0 1 0 1 0
0 0 0 1 0 1 0 1
1 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 0 1 0 0 0 1 1
What words are related?
Is a post with (car,drive,hockey,pc,win) spam?
What is p(carjdrive)? What about p(carjdrive; les)?
Can we ‘ ll in’ some variables given the others?
Can we generate more items that look like this?
Mark Schmidt Structure Learning in Undirected Graphical ModelsMotivation, Classical Methods
Gausian and Ising graphical models: ‘ -Regularization Motivation1
General pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
Further Extensions
Example of Learned Graph Structure
case children bible health
course christian insurance
computer evidence
disk email display card fact earth
files graphics government god
dos format help data image video gun human car president israel jesus
drive memory number power law engine dealer jews baseball
ftp mac scsi problem rights war religion games fans
pc program phone nasa state question hockey
software research shuttle league nhl
launch moon science orbit players
space university world season
system driver team
version technology win
windows won
Mark Schmidt Structure Learning in Undirected Graphical Modelscase children bible health
course christian insurance
computer evidence
Motivation, Classical Methods
disk email display card fact earth
Gausian and Ising graphical models: ‘ -Regularization Motivation1
case children bible healthGeneral pairwise models: Group ‘ Classical Methods1
High-order models: Structured Sparsity Regularization Methods
files graphics government god Further Extensions
course christian insuranceExample of Learned Graph Structuredos format help data image video gun human car president israel jesus
drive memory number power law engine dealer jews baseball computer evidence
ftp mac scsi problem rights war religion games fans
disk email display card fact earth
pc program phone nasa state question hockey
files graphics government god
software research shuttle league nhl
dos format help data image video gun human car president israel jesuslaunch moon science orbit players
space university world season
drive memory number power law engine dealer jews baseball
system driver team
ftp mac scsi problem rights war religion games fans
version technology win
pc program phone nasa state question hockey
windows won
Mark Schmidt Structure Learning in Undirected Graphical Models
software research shuttle league nhl
launch moon science orbit players
space university world season
system driver team
version technology win
windows won