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Algorithms for Reasoning with graphical models
Slides Set 6:
Rina Dechter
slides6 828X 2019
Darwiche chapters 5,
Slides Set 6: Building Bayesian Networks Rina Dechter Darwiche - - PowerPoint PPT Presentation
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
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Queries: Different queries may be relevant for different scenarios
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For other tools see class page http://reasoning.cs.ucla.edu/samiam
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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
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P(V=yes|E=yes) P(V=yes|E=no) =2 Define a CPT for V that satisfies this constraint
Soft evidence of Positive x-ray or Dyspnoea (X=yes or D = yes) with odds
- f 2 to 1.
Modelling: Add E variable and Add V to model soft evidence.
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MPE is also called MAP
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MPE is also called MAP
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MAP is also called Marginal Map (MMAP)
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Is it correct?
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What about the boundary strata?
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Constructing a Bayesian Network for any Distribution P
Intuition: The causes of X can serve as the parents
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Variables? Arcs? Try it.
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What about?
A naive Bayes structure has the following edges C -> A1, . . . , C -> Am, where C is called the class variable and A1; : : : ;Am are called the attributes.
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Learn the model from data
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Learning the model
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Try it: Variables and values? Structure? CPTs?
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Read in the book. We will not cover this.
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Try it: Variables? Values? Structure?
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Variables? Values? Structure?
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Try it: Variables, values, structure?
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What queries should we use here? P(Y not equal U) = 0.01
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WER (word error rate), BER (bit error rate) MAP (MPE) minimizes WER, PM minimize BER… What do you think?
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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.
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152
Two Loci Inheritance
Recombinant 2 1 A A B B a a b b A a B b 3 4 a a b b A a b b 5 6 A a B b
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153
Bayesian Network for Recombination
S23m L21f L21m L23m X21 S23f L22f L22m L23f X22 X23 S13m L11f L11m L13m X11 S13f L12f L12m L13f X12 X13 y3 y2 y1
{m,f} t s s P
t t
− − = where 1 1 ) , | (
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Locus 1 Locus 2
P(e|Θ) ?
Deterministic relationships Probabilistic relationships
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154
L11m L11f X11 L12m L12f X12 L13m L13f X13 L14m L14f X14 L15m L15f X15 L16m L16f X16 S13m S15m S16m S15m S15m S15m L21m L21f X21 L22m L22f X22 L23m L23f X23 L24m L24f X24 L25m L25f X25 L26m L26f X26 S23m S25m S26m S25m S25m S25m L31m L31f X31 L32m L32f X32 L33m L33f X33 L34m L34f X34 L35m L35f X35 L36m L36f X36 S33m S35m S36m S35m S35m S35m
Linkage analysis: 6 people, 3 markers
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Outline
- Bayesian networks and queries
- Building Bayesian Networks
- Special representations of CPTs
- Causal Independence (e.g., Noisy OR)
- Context Specific Independence
- Determinism
- Mixed Networks