Causal and Bayesian Network (Chapter 2)
description
Transcript of Causal and Bayesian Network (Chapter 2)
![Page 1: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/1.jpg)
Causal and Bayesian Network(Chapter 2)
Book: Bayesian Networks and Decision GraphsAuthor: Finn V. Jensen, Thomas D. Nielsen
CSE 655 Probabilistic ReasoningFaculty of Computer Science,
Institute of Business Administration
Presented byQuratulain
![Page 2: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/2.jpg)
Quratulain 2
OutlineReasoning under uncertainty
Causal network and d-separation
Bayesian networkGraphical model
9/16/2009
![Page 3: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/3.jpg)
Quratulain 3
Reasoning Under UncertaintyWhy Reason Probabilistically?In many problem domains it isn't possible to
create complete, consistent models of the world.
If information is given with certainty then Propositional logic (Truth table) can be used.
Want to make rational decisions even when there is not enough information to prove that an action will work.
To deal with uncertain events, we extend truth value of propositional logic to certainties which are number between 0 and 1.
9/16/2009
![Page 4: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/4.jpg)
4
Example (Type of reasoning that human do daily)
“In the morning, my car will not start.”Reasons:
◦I can here starter tune, so must be power in battery
◦May be fuel has been stolen overnight◦The spark plug are dirty◦May be due to the dirt in carburetor◦A loose connection in ignition system or
any thing serious
9/16/2009 Quratulain
![Page 5: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/5.jpg)
Quratulain 5
A Causal Perspective – Car Example Construct a graph to represent
causal relationship between events which gives structure to the situation for reasoning.
9/16/2009
Variable (node)
States
Fuel {yes, no}
CleanSparkPlugs
{yes, no}
Fuel Meter {full, half , empty}
Start {yes, no}
![Page 6: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/6.jpg)
Quratulain 6
OutlineReasoning under uncertaintyCausal network and d-separation
Bayesian networkGraphical model
9/16/2009
![Page 7: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/7.jpg)
Quratulain 7
Causal network and d-separationA causal network consists of a
set of variables and a set of directed links between variables.
Mathematically, the structure is called a directed graph.
Causal networks can be used to follow how a change of certainty in one variable may change the certainty for other variables.
9/16/2009
![Page 8: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/8.jpg)
Quratulain 8
3-Cases of evidence transmitionSerial Connections
Diverging Connections (common cause)
Converging Connection (common effect)
9/16/2009
P(C|A^B)=P(C|B)
P(C|A^B)=P(C|B)
![Page 9: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/9.jpg)
Quratulain 9
Serial ConnectionsEvidence about A will influence the
certainty of B, which then influences the certainty of C.
Similarly, evidence about C will influence the certainty of A through B.
If the state of B is known, then the channel is blocked, A and C become independent.
we say that A and C are d-separated given B.
9/16/2009
![Page 10: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/10.jpg)
Quratulain 10
Diverging Connections Influence can pass between all
the children of A if A is not known. That is, B,C, . . . , E are d-separated given A.
9/16/2009
Sex (male, female),length of hair (long, short), and stature (<168 cm, ≥168 cm)
![Page 11: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/11.jpg)
Quratulain 11
Converging ConnectionIf nothing is known about A then
the parents are independent evidence about one of them cannot influence the certainties of the others through A.
9/16/2009
![Page 12: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/12.jpg)
Quratulain 12
D-separationTwo distinct variables A and B in a
causal network are d-separated such that either:◦The connection is serial or diverging
and V is instantiated.◦The connection is converging, and
neither V nor any of V ’s descendants have received evidence.
9/16/2009
![Page 13: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/13.jpg)
Quratulain 13
ExampleAre B and C independent given
A?
Are B and C independent given F
9/16/2009
![Page 14: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/14.jpg)
Quratulain 14
Markov Blanket
The Markov blanket of a variable A is the set consisting of:◦the parents of A, ◦the children of A, and ◦the variables sharing a child with A.
The Markov blanket has the property that when instantiated, A is d-separated from the rest of the network.
9/16/2009
![Page 15: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/15.jpg)
Quratulain 15
OutlineReasoning under uncertaintyCausal network and d-separation
Bayesian networkGraphical model
9/16/2009
![Page 16: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/16.jpg)
16
Bayesian NetworkA Bayesian network consists of the
following◦A set of variables and a set of directed
edges between variables.◦Each variable has a finite set of mutually
exclusive states.◦The variables together with the directed
edges form an acyclic directed graph.◦To each variable A with parents B1, . . . ,
Bn, a conditional probability table P(A|B1, . . . , Bn) is attached.
9/16/2009 Quratulain
![Page 17: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/17.jpg)
Quratulain 17
Bayesian Network The probabilities to specify are: P(A), P(B), P(C | A,B), P(E |C), P(D|C), P(F |E), and P(G| D,E,F)
It has been claimed that prior probabilities are bias to the model
Prior probabilities are necessary because prior certainty assessments are an integral part of human reasoning about certainty
The model should not include conditional independences that do not hold in the real world.
The d-separation properties check’s Conditional independences in model.
9/16/2009
![Page 18: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/18.jpg)
Quratulain 18
Chain Rule for Bayesian NetworkLet BN be a Bayesian network
over U = {A1, . ..,An}. Then BN specifies a unique joint probability distribution P(U) given by the product of all conditional probability tables specified in BN:
9/16/2009
![Page 19: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/19.jpg)
Quratulain 19
OutlineReasoning under uncertainty
Causal network and d-separation
Bayesian networkGraphical model
9/16/2009
![Page 20: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/20.jpg)
Quratulain 20
Graphical ModelGraphical specification is easy for
humans to read, and helps focus attention.
The basic property of the Bayesian networks is the chain rule for compact representation of joint probability distribution.
Graphical model represents a causal relation in a knowledge domain.
9/16/2009
![Page 21: Causal and Bayesian Network (Chapter 2)](https://reader035.fdocuments.us/reader035/viewer/2022081502/56815ee8550346895dcd96b7/html5/thumbnails/21.jpg)
Quratulain 21
Questions
9/16/2009