1. 1 Building Bayesian Networks COMPSCI 276, Fall 2009 Set 3: Rina Dechter (Reading: Darwiche chapter 5)

3. Queries: Different queries may be relevant for different scenarios

4. For other tools see class page

5. 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.

8. C= lung cancer

10. P(V=yes|E=yes) P(V=yes|E=no) =2 Define a cpt for V that satisfies this constraint

16. Is it correct?

20. Building email management network Step 1: define the variables: email characteristics Title, (values: any sequence of words.) sender-id, (values: # of id names) Recipients, #-of-recipients (Values, a sequence of id-names) topic, (values: a distribution over bag of words, or a set of key words) length, (values: natural numbers) time-sent : (time-of-week, time-of-day), (values: days of the week, time (discredized) time-read, (values: as above) current-time, (value: as above) max-reponse-time (value: as above) Evidence variables query

23. Variables? Arcs? Try it.

24. 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.

28. Learn the model from data

29. Learning the model

30. Try it: Variables and values? Structure? CPTs?

37. Skip if no time, this and the next 4 slides

42. Try it: Variables? Values? Structure?

62. Variables? Values? Structure?

68. Try it: Variables, values, structure?

79. What queries should we use here?

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

100. Building email management network Step 1: define the variables: email characteristics Title, (values: any sequence of words.) sender-id, (values: # of id names) Recipients, #-of-recipients (Values, a sequence of id-names) topic, (values: a distribution over bag of words, or a set of key words) length, (values: natural numbers) time-sent : (time-of-week, time-of-day), (values: days of the week, time (discredized) time-read, (values: as above) current-time, (value: as above) max-reponse-time (value: as above) Evidence variables query

101. Email network for a message Title Topic Sender-id recipients MaxWait Day-of-Week Time-of-Day Real-max-wait Time-now time-left #-of

102. Topic and title-subnetwork Topic Title w1w3w2w1 w100 tw2tw1 tw3tw4 Topics and titles will have a small number of categories Words are either present or not

103. Email network for a message Title Topic Sender-id recipients MaxWait Day-of-Week Time-of-Day Real-max-wait Time-now time-left #-of Topic

104. Slides 130-155 explain the domain. Read. Variables, values, structure?

152. Applications 152 Linkage Analysis LOD Scores Computing Haplotypes

153. 153 Two Loci Inheritance Recombinant 2 1 A B a b A a B b 34 a b A a b 56 A a B b

154. 154 Bayesian Network for Recombination S 23m L 21f L 21m L 23m X 21 S 23f L 22f L 22m L 23f X 22 X 23 S 13m L 11f L 11m L 13m X 11 S 13f L 12f L 12m L 13f X 12 X 13 y3y3 y2y2 y1y1 Locus 1 Locus 2 P(e|Θ) ? Deterministic relationships Probabilistic relationships

155. 155 L 11m L 11f X 11 L 12m L 12f X 12 L 13m L 13f X 13 L 14m L 14f X 14 L 15m L 15f X 15 L 16m L 16f X 16 S 13m S 15m S 16m S 15m L 21m L 21f X 21 L 22m L 22f X 22 L 23m L 23f X 23 L 24m L 24f X 24 L 25m L 25f X 25 L 26m L 26f X 26 S 23m S 25m S 26m S 25m L 31m L 31f X 31 L 32m L 32f X 32 L 33m L 33f X 33 L 34m L 34f X 34 L 35m L 35f X 35 L 36m L 36f X 36 S 33m S 35m S 36m S 35m Linkage analysis: 6 people, 3 markers