By: A. Nickabadi

PROBABILISTIC GRAPHICAL MODELS

1: INTRODUCTION

1

Motivation

2

Reasoning

(Inference)

Available

Information(Prior knowledge

+ Observations)

Conclusions

(New facts)

Motivation

Two approaches:

• Special-purpose programs

• Significant changes may be required

• Hard to extract lessons

• General Frameworks

• Declarative representation

• The separation of knowledge and reasoning

• Based on models

• Example: propositional logic

3

Motivation

4

Model

Data

Expert

Inference

algorithms

Motivation

Uncertainty:

• Partial and noisy observations

• Incomprehensive models

• Innate nondeterminism of the world

5

Probability theory

Probability theory:

• Considering probable not just possible facts

• Declarative representation with clear

semantics

• Powerful reasoning patterns

• Established learning methods

6

Probability theory

Probabilistic models:

• Random variables ��, ��, … , ��

• Joint distribution � ��, … , ��

• Example:

• Hayfever: � ∈ {ℎ�, ℎ�}

• Flu: � ∈ ��, ��

• Muscle-Pain: � ∈ {��, ��}

• Congestion: � ∈ {��, ��}

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� � � � �

ℎ� �� �� �� 0.870

ℎ� �� �� �� 0.005

…

ℎ� �� �� �� 0.008

…

ℎ� �� �� �� 0.010

…

Probability theory

Answering queries:

• � � = ℎ�, � = ��, � = ��, � = �� =?

• � � = ℎ�, � = ��, � = �� =?

• � � = �� =?

• � � = �� � = ��, � = ��) =?

• � � = �� � = ��) =?

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� � � � �

ℎ� �� �� �� 0.870

ℎ� �� �� �� 0.005

…

ℎ� �� �� �� 0.008

…

ℎ� �� �� �� 0.010

…

Probability theory

Problems of the joint distributions:

• Complexity

• Space complexity

• Computational complexity

• Hardness of the learning

9

Probabilistic Graphical Models (PGMs)

Structure probabilistic models

10

� �

�� 0.98

�� 0.02

� � �

�� �� 0.90

�� �� 0.10

�� �� 0.05

�� �� 0.95

PGMs

Applications:• Medical diagnosis

• Fault diagnosis

• Natural language processing

• Traffic analysis

• Social network models

• Message decoding

• Computer vision• Image segmentation

• 3D reconstruction

• Holistic scene analysis

• Speech recognition

• Robot localization & mapping

11

Applications

Medical diagnosis

12

Applications

Fault diagnosis

13

Applications

Natural language processing

14

Applications

Speech recognition

15

Applications

Image segmentation

16

Applications

Robot localization:

17

Applications

Biological network reconstruction

18

PGMs

Representation

• Directed

• Undirected

Inference

• Exact

• Approximate

Learning

• Parameters

• Structure

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� �

�� 0.98

�� 0.02

� � �

�� �� 0.90

�� �� 0.10

�� �� 0.05

�� �� 0.95

The End

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