Slides Set 6: Building Bayesian Networks Rina Dechter Darwiche - PowerPoint PPT Presentation

Algorithms for Reasoning with graphical models Slides Set 6: Building Bayesian Networks Rina Dechter Darwiche chapters 5, slides6 828X 2019

Queries: Different queries may be relevant for different scenarios

http://reasoning.cs.ucla.edu/samiam For other tools see class page

Other type of evidence: We may want to know the probability that the patient has either a positive X-ray or dyspnoea, X =yes or D=yes.

C= lung cancer

Soft evidence of Positive x-ray or Dyspnoea (X=yes or D = yes) with odds of 2 to 1. Modelling: Add E variable and Add V to model soft evidence. P(V=yes|E=yes) =2 P(V=yes|E=no) Define a CPT for V that satisfies this constraint

MPE is also called MAP

MPE is also called MAP

MAP is also called Marginal Map (MMAP)

Is it correct?

What about the boundary strata?

Constructing a Bayesian Network for any Distribution P Intuition: The causes of X can serve as the parents

Variables? Arcs? Try it .

A naive Bayes structure What about? has the following edges C -> A1, . . . , C -> Am, where C is called the class variable and A1; : : : ;Am are called the attributes .

Learn the model from data

Learning the model

Try it: Variables and values? Structure? CPTs?

Read in the book. We will not cover this.

Try it: Variables? Values? Structure?

Variables? Values? Structure?

Try it: Variables, values, structure?

P(Y not equal U) = 0.01 What queries should we use here?

WER (word error rate), BER (bit error rate) MAP (MPE) minimizes WER, PM minimize BER… What do you think?

Notice: Odds: o(x) = P(x)\P(bar(x)) K =Bayes factor = o’(x) \ o(x) … the posterior odds after observing divided by prior odds For Gausian x: evidence on Y=y can be emulated with soft evidence on x with K =f(y|x) \f(y|bar(x)) = the expression above.

Two Loci Inheritance a a A A 1 2 b b B B A a a a 3 4 B b b b A a A a 5 6 b b B b Recombinant 152

Bayesian Network for Recombination L 11m L 11f L 12m L 12f Locus 1 S 13m X 11 X 12 S 13f y 2 y 1 L 13m L 13f Deterministic relationships X 13 y 3 Probabilistic relationships L 21m L 21f L 22m L 22f S 23m X 21 X 22 S 23f Locus 2 L 23m L 23f −     1 P(e| Θ ) ?  =  X 23 ( | , ) where P s s   t {m,f}  −  23 13 t t  1  153

Linkage analysis: 6 people, 3 markers L 12m L 12f L 11m L 11f X 12 X 11 S 15m S 13m L 13m L 13f L 14m L 14f X 14 X 13 S 15m S 15m L 15m L 15f L 16m L 16f S 15m S 16m X 15 X 16 L 22m L 22f L 21m L 21f X 21 X 22 S 25m S 23m L 23m L 23f L 24m L 24f X 23 X 24 S 25m S 25m L 25m L 25f L 26m L 26f S 25m S 26m X 25 X 26 L 32m L 32f L 31m L 31f X 32 X 31 S 35m S 33m L 33m L 33f L 34m L 34f X 33 X 34 S 35m S 35m L 35m L 35f L 36m L 36f 154 S 36m S 35m X 35 X 36

Outline • Bayesian networks and queries • Building Bayesian Networks • Special representations of CPTs • Causal Independence (e.g., Noisy OR) • Context Specific Independence • Determinism • Mixed Networks