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Bayesian Networks Yeni Herdiyeni Departemen Ilmu Komputer 1.

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Presentasi berjudul: "Bayesian Networks Yeni Herdiyeni Departemen Ilmu Komputer 1."— Transcript presentasi:

1

2 Bayesian Networks Yeni Herdiyeni Departemen Ilmu Komputer 1

3 Overview Decision-theoretic techniques – Explicit management of uncertainty and tradeoffs – Probability theory – Maximization of expected utility Applications to AI problems – Diagnosis – Expert systems – Planning – Learning 2

4 Course Contents »Concepts in Probability – Probability – Random variables – Basic properties (Bayes rule) Bayesian Networks Inference Applications 3

5 Probabilities Probability distribution P(X|  – X is a random variable Discrete Continuous –  is background state of information 4

6 Discrete Random Variables Finite set of possible outcomes 5 X binary:

7 Continuous Random Variable Probability distribution (density function) over continuous values 6 5 7

8 More Probabilities Joint – Probability that both X=x and Y=y Conditional – Probability that X=x given we know that Y=y 7

9 Rules of Probability Product Rule Marginalization 8 X binary:

10 Bayes Rule 9

11 Course Contents Concepts in Probability »Bayesian Networks – Basics – Additional structure – Knowledge acquisition Inference Decision making Learning networks from data Reasoning over time Applications 10

12 Bayesian networks Basics – Structured representation – Conditional independence – Naïve Bayes model – Independence facts 11

13 Naïve Bayes vs Bayesian Network Pada Naïve Bayes, mengabaikan korelasi antar variabel. Sedangkan pada Bayesian Network, variabel input bisa saling dependent.

14 Bayesian Networks 13 Cancer Smoking P(S=no)0.80 P(S=light)0.15 P(S=heavy)0.05 Smoking=nolightheavy P(C=none) P(C=benign) P(C=malig)

15 Product Rule P(C,S) = P(C|S) P(S) 14

16 Marginalization 15 P(Cancer) P(Smoke)

17 Bayes Rule Revisited 16 Cancer=nonebenignmalignant P(S=no) P(S=light) P(S=heavy)

18 A Bayesian Network 17 Smoking GenderAge Cancer Lung Tumor Serum Calcium Exposure to Toxics

19 Independence 18 Age and Gender are independent. P(A|G) = P(A) A  G P(G|A) = P(G) G  A GenderAge P(A,G) = P(G|A) P(A) = P(G)P(A) P(A,G) = P(A|G) P(G) = P(A)P(G) P(A,G) = P(G)P(A)

20 Conditional Independence 19 Smoking GenderAge Cancer Cancer is independent of Age and Gender given Smoking. P(C|A,G,S) = P(C|S) C  A,G | S

21 More Conditional Independence: Naïve Bayes 20 Cancer Lung Tumor Serum Calcium Serum Calcium is independent of Lung Tumor, given Cancer P(L|SC,C) = P(L|C) Serum Calcium and Lung Tumor are dependent

22 More Conditional Independence: Explaining Away 21 Exposure to Toxics is dependent on Smoking, given Cancer Exposure to Toxics and Smoking are independent Smoking Cancer Exposure to Toxics E  S P(E = heavy | C = malignant) > P(E = heavy | C = malignant, S=heavy)

23 Put it all together 22 Smoking GenderAge Cancer Lung Tumor Serum Calcium Exposure to Toxics

24 General Product (Chain) Rule for Bayesian Networks 23 Pa i =parents(X i )

25 Conditional Independence 24 Smoking GenderAge Cancer Lung Tumor Serum Calcium Exposure to Toxics Cancer is independent of Age and Gender given Exposure to Toxics and Smoking. Descendants Parents Non-Descendants A variable (node) is conditionally independent of its non-descendants given its parents.

26 Another non-descendant 25 Diet Cancer is independent of Diet given Exposure to Toxics and Smoking. Smoking GenderAge Cancer Lung Tumor Serum Calcium Exposure to Toxics

27 Bayesian Network Bayesian Network atau Belief Network atau Probabilistik Network adalah model grafik untuk merepresentasikan interaksi antar variabel. Bayesian Network digambarkan seperti graf yang terdiri dari simpul (node) dan busur (arc). Simpul menunjukkan variabel misal X beserta nilai probabilitasnya P(X) dan busur menunjukkan hubungan antar simpul. Jika ada hubungan dari simpul X ke simpul Y, ini mengindikasikan bahwa variabel X ada pengaruh terhadap variabel Y. Pengaruh ini dinyatakan dengan peluang bersyarat P(Y|X).

28 Bayesian Network - Latihan Yeni Herdiyeni

29 Bayesian Network Dari gambar tersebut dapat diketahui peluang gabungan dari P(R,W). Jika P(R) = 0.4, maka P(~R) = 0.6 dan jika P(~W|~R) = 0.8. Kaidah Bayes dapat digunakan untuk membuat diagnosa.

30 Bayesian Network Sebagai contoh jika diketahui bahwa rumput basah, maka peluang hujan dapat dihitung sebagai berikut :

31 Bayesian Network Berapa peluang rumput basah jika Springkler menyala (tidak diketahui hujan atau tidak)

32 Bayesian Network Berapa peluang Springkler menyala setelah diketahui rumput basah P(S|W)?

33 Bayesian Network Jika diketahui hujan, berapa peluang Springkler menyala?

34 Bayesian Network Bagaimana jika ada asumsi : Jika cuacanya mendung (cloudy), maka Springkler kemungkinan besar tidak menyala.

35 Bayesian Network Berapa peluang rumput basah jika diketahui cloudy?

36 Bayesian Network Berapa peluang rumput basah jika diketahui cloudy?

37 Latihan Jika ada seekor kucing yang suka berjalan di atap dan membuat keributan. Jika hujan, kucing tidak keluar. Berapa peluang kita akan mendengar kucing diatap jika cuaca Cloudy? P(F|C)

38 Course Contents Concepts in Probability Bayesian Networks »Inference Decision making Learning networks from data Reasoning over time Applications 37

39 Inference Patterns of reasoning Basic inference Exact inference Exploiting structure Approximate inference 38

40

41 Predictive Inference 40 How likely are elderly males to get malignant cancer? P(C=malignant | Age>60, Gender= male) Smoking GenderAge Cancer Lung Tumor Serum Calcium Exposure to Toxics

42 Combined 41 How likely is an elderly male patient with high Serum Calcium to have malignant cancer? P(C=malignant | Age>60, Gender= male, Serum Calcium = high) Smoking GenderAge Cancer Lung Tumor Serum Calcium Exposure to Toxics

43 Explaining away If we see a lung tumor, the probability of heavy smoking and of exposure to toxics both go up. 42 Smoking GenderAge Cancer Lung Tumor Serum Calcium Exposure to Toxics n If we then observe heavy smoking, the probability of exposure to toxics goes back down. Smoking

44 Inference in Belief Networks Find P(Q=q|E= e) – Q the query variable – E set of evidence variables 43 P(q | e) = P(q, e) P(e) X 1,…, X n are network variables except Q, E P(q, e) =  P(q, e, x 1,…, x n ) x 1,…, x n

45 Basic Inference 44 AB P(b) = 

46 Product Rule P(C,S) = P(C|S) P(S) 45 SC

47 Marginalization 46 P(Cancer) P(Smoke)

48 Basic Inference 47 AB =  P(c | b)  P(b | a) P(a) ba P(b) P(c) =  P(a, b, c) b,a P(b) =  P(a, b) =  P(b | a) P(a) aa C b P(c) =  P(c | b) P(b) b,a =  P(c | b) P(b | a) P(a)

49 Inference in trees 48 X Y1Y1 Y2Y2 P(x) =  P(x | y 1, y 2 ) P(y 1, y 2 ) y 1, y 2 because of independence of Y 1, Y 2 : y 1, y 2 =  P(x | y 1, y 2 ) P(y 1 ) P(y 2 ) X

50 Course Contents Concepts in Probability Bayesian Networks Inference Learning networks from data Reasoning over time Applications 49

51 Course Contents Concepts in Probability Bayesian Networks Inference Applications 50

52 Applications Medical expert systems – Pathfinder – Parenting MSN Fault diagnosis – Ricoh FIXIT – Decision-theoretic troubleshooting Vista Collaborative filtering 51

53 Why use Bayesian Networks? Explicit management of uncertainty/tradeoffs Modularity implies maintainability Better, flexible, and robust recommendation strategies 52

54 Pathfinder Pathfinder is one of the first BN systems. It performs diagnosis of lymph-node diseases. It deals with over 60 diseases and 100 findings. Commercialized by Intellipath and Chapman Hall publishing and applied to about 20 tissue types. 53

55 Commercial system: Integration Expert System with advanced diagnostic capabilities – uses key features to form the differential diagnosis – recommends additional features to narrow the differential diagnosis – recommends features needed to confirm the diagnosis – explains correct and incorrect decisions Video atlases and text organized by organ system “Carousel Mode” to build customized lectures Anatomic Pathology Information System 54

56 55 On Parenting: Selecting problem n Diagnostic indexing for Home Health site on Microsoft Network n Enter symptoms for pediatric complaints n Recommends multimedia content

57 On Parenting : MSN 56 Original Multiple Fault Model

58 Single Fault approximation 57

59 58 On Parenting: Selecting problem

60 59 Performing diagnosis/indexing

61 RICOH Fixit Diagnostics and information retrieval 60

62 FIXIT: Ricoh copy machine 61

63 Online Troubleshooters 62

64 Define Problem 63

65 Gather Information 64

66 Get Recommendations 65

67 Vista Project: NASA Mission Control 66 Decision-theoretic methods for display for high-stakes aerospace decisions

68 What is Collaborative Filtering? A way to find cool websites, news stories, music artists etc Uses data on the preferences of many users, not descriptions of the content. Firefly, Net Perceptions (GroupLens), and others offer this technology. 67

69 Bayesian Clustering for Collaborative Filtering 68 P(Like title i | Like title j, Like title k) n Probabilistic summary of the data n Reduces the number of parameters to represent a set of preferences n Provides insight into usage patterns. n Inference:

70 Applying Bayesian clustering 69 class1 class2... title1p(like)=0.2p(like)=0.8 title2p(like)=0.7p(like)=0.1 title3p(like)=0.99p(like)= user classes title 1title 2title n...

71 Richer model 70 AgeGender Likes soaps User class Watches Seinfeld Watches NYPD Blue Watches Power Rangers

72 What’s old? principled models of belief and preference; techniques for: – integrating evidence (conditioning); – optimal decision making (max. expected utility); – targeted information gathering (value of info.); – parameter estimation from data. 71 Decision theory & probability theory provide:

73 What’s new? 72 Knowledge Acquisition Inference Learning Bayesian networks exploit domain structure to allow compact representations of complex models. Structured Representation

74 Some Important AI Contributions Key technology for diagnosis. Better more coherent expert systems. New approach to planning & action modeling: – planning using Markov decision problems; – new framework for reinforcement learning; – probabilistic solution to frame & qualification problems. New techniques for learning models from data. 73

75 What’s in our future? Better models for: – preferences & utilities; – not-so-precise numerical probabilities. Inferring causality from data. More expressive representation languages: – structured domains with multiple objects; – levels of abstraction; – reasoning about time; – hybrid (continuous/discrete) models. 74 Structured Representation


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