Gentle Introduction to Probabilistic Graphical Models Textbook ...

Seungjin Choi

Description

Gentle Introduction to Probabilistic Graphical Models Textbook ...

Sujets

• Arts

Informations

• Publié par: olonilux
• Nombre de lectures: 53
• Langue: English

Extrait

Gentle Introduction to Probabilistic Graphical Models

Seungjin Choi

Department of Computer Science Pohang University of Science and Technology, Korea [e-mail]

Probabilistic Graphical Models

￿ Learning with probabilistic models: Modeldistributions over observed data usingp(x 1 ,x 2 , . . . ,x N |θ). ￿ Probabilistic graphical models: ￿ A happy marriage between graph theory and probability theory. Consider a (directed or undirected)graphwherenodesare associated ￿ withrandom variablesandedgesrepresentstatistical dependencies between variables.

E

A

C

B

undirected graph

D

E

A

C

B

D

directed graph

E

A

C

B

D

factor graph

1 / 12

3 / 12

Textbook, References, and Web

￿ Primary textbook Draft chapters fromM. Jordan’sunpublished book,”An introduction to probabilistic graphical models”. References ￿ ￿ Z. Ghahramani’s lecture in ”Winter School:Mathematics for Data Modeling” ￿ K. Murphy’s note, ”An introduction to graphical models” ￿ C. Bishop’s book, ”Pattern Recognition and Machine Learning” ￿ Selected articles in reading list Web ￿ http://www.postech.ac.kr/∼seungjin/courses/pgm/pgm10.html

Why Graphical Models?

￿ Graphs are anintuitiveway of representing and visualizing the relationships between many variables. ￿ A graph allows us to abstract out theconditional independence relationships between the variables from the details of their parametric forms.Thus we can answer questions like:”IsA dependent onBgiven that we know the value ofC?” just by looking at the graph. ￿ Graphical models allow us to define generalmessage passing algorithmsThus wethat implement probabilistic inference directly. can answer queries like ”What isP(A|C=c) without enumerating all settings of all variables in the model.

”Taken from Z. Ghahramani’s talk.”

2 / 12

4 / 12