Reasoning with Graphical Models Slides Set 3: Building Bayesian Networks Rina Dechter Darwiche chapters 5 slides3 COMPSCI 2020
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Queries: Different queries may be relevant for different scenarios
http://reasoning.cs.ucla.edu/samiam For other tools (e.g., GeNie/Smile) 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.
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C= lung cancer slides3 COMPSCI 2020
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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 slides3 COMPSCI 2020
MPE is also called MAP
MPE is also called MAP
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MAP is also called Marginal Map (MMAP)
Is it correct? slides3 COMPSCI 2020
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Probabilistic Reasoning Problems Tasks: Max-Inference (most likely config, MPE.) Harder Sum-Inference (data likelihood, P(evidence) Mixed-Inference (optimal prediction, MAP, Marginal Map) Combinatorial search / counting queries Exact reasoning NP-complete (or worse)
What about the boundary strata? slides3 COMPSCI 2020
Constructing a Bayesian Network for any Distribution P Intuition: The causes of X can serve as the parents slides3 COMPSCI 2020
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Variables? Arcs? Try it . slides3 COMPSCI 2020
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 . slides3 COMPSCI 2020
I(ST, Cond=cold,Fever)? slides3 COMPSCI 2020
Learn the model from data slides3 COMPSCI 2020
Learning the model slides3 COMPSCI 2020
Try it: Variables and values? Structure? CPTs?
Try with GeNie slides3 COMPSCI 2020
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Read in the book. We will not cover this. Also about level of granularity
Try it: Variables? Values? Structure? slides3 COMPSCI 2020
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slides3 COMPSCI 2020 Variables? Values? Structure?
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slides3 COMPSCI 2020 Try it: Variables, values, structure?
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P(Y not equal U) = 0.01 What queries should we use here?
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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 slides3 COMPSCI 2020 K =f(y|x) \f(y|bar(x)) = the expression above. Read chapter 5
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The excitement about probabilistic decoding in the 90’s And the rise of belief propagation Task (PM for each bit) slides3 COMPSCI 2020
Read on your own Commonsense reasoning When SamBot goes home at night, he wants to know if his family is home before he tries the doors. Often when SamBot's wife leaves the house she turns on an outdoor light. However, she sometimes turns on this light if she is expecting a guest. Also, SamBot's family has a dog. When nobody is home, the dog is in the back yard. The same is true if the dog has bowel trouble. If the dog is in the back yard, SamBot will probablyhear her barking, but sometimes he can be confused by other dogs barking. SamBot is equipped with two sensors: a light-sensor for detecting outdoor lights and a sound-sensor for detecting the barking of dogs. Both of these sensors are not completely reliable and can break. Moreover, they both require SamBot's battery to be in good condition. slides3 COMPSCI 2020
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If G1 and G2 are close then they are likely to pass down from the same haplotype (grandmother or grandfather)
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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 slides3 COMPSCI 2020
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 slides3 COMPSCI 2020 1 151
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 22 X 21 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 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 slides3 COMPSCI 2020
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Think about headache and 10 different conditions that may cause it. A noisy-or circuit slides3 COMPSCI 2020 We wish to specify cpt with less parameters
Binary OR A B X A B P(X=0|A,B) P(X=1|A,B) 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 slides3 COMPSCI 2020
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