Probabilistic Reasoning with Bayesian Networks and BayesiaLab

Transcription

1 The presentation will start at: 13:00:00 The current time is: 13:00:42 Central Standard Time, UTC-6 Probabilistic Reasoning with Bayesian Networks and BayesiaLab

2 Introduction Your Hosts Today Stefan Conrady Stacey Blodgett BayesiaLab.com 2

3 Today s Agenda Motivation & Background Logic vs. Probabilistic Reasoning 10 min. Examples of Probabilistic Reasoning Example 1: What color is the taxi? Bayesian Networks to the Rescue! Knowledge Encoding & Inference with Bayesian Networks & BayesiaLab 50 min. Example 2: Where is my bag? stefan.conrady@bayesia.us 3

4 Webinar Slides & Recording Available 4

5 BayesiaLab Trial Try BayesiaLab Today! Download Demo Version: Apply for Unrestricted Evaluation Version: BayesiaLab.com 5

6 Questions 6

7 User Forum: bayesia.com/community BayesiaLab.com 7

8 Motivation & Background: Reasoning

9 Deductive Logic Aristotle ( BC) BayesiaLab.com 9

10 Deductive Logic Limitations of Logic Classical logic has no explicit mechanism for representing the degree of certainty of premises in an argument, nor the degree of certainty in a conclusion, given those premises. Source: J. Williamson, Handbook of the Logic of Argument and Inference: The Turn Toward the Practical LOGIC IS NOT ENOUGH! BayesiaLab.com 10

11 Inductive vs. Deductive Logic Formal Deductive Logic Weak Strong Strength of Argument Inductive Logic = Probabilistic Reasoning BayesiaLab.com 11

12 2000 Years Later Bayes Theorem for Conditional Probabilities 1763 PHILOSOPHICAL TRANSACTIONS H: Hypothesis E: Evidence P(H E) = P(E H)P(H) P(E) Probability of H given E stefan.conrady@bayesia.us 12

13 Probabilistic Reasoning Mathematical Formulation of Inductive Reasoning Bayesian inference is important because it provides a normative and general-purpose procedure for reasoning under uncertainty. Source: Inductive Reasoning: Experimental, Developmental, and Computational Approaches, edited by Aidan Feeney and Evan Heit BayesiaLab.com 13

14 Probabilistic Reasoning Human reasoning is flawed! BayesiaLab.com 14

15 Why is this so important? Human Cognitive Limitations and Biases Under Uncertainty Human Reasoning Normative Reasoning Disease Symptom FALLACIES Human Reasoning Normative Reasoning BayesiaLab.com 15

16 250 Years Later despite the mathematization of probability in the Enlightenment, mathematical probability theory remains, to this very day, entirely unused in criminal courtrooms, when evaluating the probability of the guilt of a suspected criminal. James Franklin, The Science of Conjecture: Evidence and Probability before Pascal, 2001 The Johns Hopkins Press BayesiaLab.com 16

17 Example 1: What Color is the Taxi? Knowledge Modeling & Reasoning Under Uncertainty

18 What Color is the Taxi? *adapted from Kahneman & Tversky, 1980 Human Reasoning Experiment* A taxi was involved in a hit-and-run accident at night. Only two taxi companies operate in this city, the Yellow Cab Co. and the White Cab Co. 85% of taxis belong to the Yellow Cab Co. YELLOW CAB CO. 15% of taxis belong to the White Cab Co. WHITE CAB COMPANY BayesiaLab.com 18

19 What Color is the Taxi? A witness says that the taxi involved in the accident was white. 19

20 What Color is the Taxi? At the trial in Logiland, where formal deductive logic rules Premise 1 Taxi caused accident Premise 2 Two taxi companies in town, yellow and white Premise 3 Accident witness: Taxi was white Conclusion White Taxi Co. is responsible for accident 20

21 What Color is the Taxi? At the Trial in Likeliland An expert witness explains that human vision has an 80% accuracy in terms of distinguishing between white and yellow given light conditions at the time of the accident. P(Witness=white Color=white)=80% P(Witness=yellow Color=white)=20% P(Witness=yellow Color=yellow)=80% P(Witness=white Color=yellow)=20% 21

22 What Color is the Taxi? You are the jury in Likeliland! Given the three premises and the expert witness statement, what is the probability that the taxi was white? WHITE CAB COMPANY 22

23 What Color is the Taxi? Results from Webinar Poll Correct Answer: 41.38% Correct Answer WHITE CAB COMPANY 23

24 What Color is the Taxi? We need to perform probabilistic inference to answer this question. Bayes Rule allows us to compute the probability P(Taxi=white Witness=white): P(H E) = P(E H)P(H) P(E) Correct, but impractical 24

25 Bayesian Networks to the Rescue! Overcoming our Limitations Human Reasoning Normative Reasoning Encode Domain Knowledge as Bayesian Network Computer-aided inference Use the Bayesian Network for Inference BayesiaLab.com 25

26 The BayesiaLab Workflow BayesiaLab.com 26

27 A desktop software for: encoding learning editing performing inference analyzing simulating optimizing with Bayesian networks. BayesiaLab.com 27

28 BayesiaLab Graph Panel Monitor Panel BayesiaLab.com 28

29 What Color is the Taxi? We encode our domain knowledge regarding the taxi cab example: Node: Variable of Interest Taxi Yellow White 85% 15% 29

30 What Color is the Taxi? We encode our domain knowledge regarding the taxi cab example: Node: Variable of Interest Taxi Yellow White 85% 15% Node: Variable of Interest Witness Yellow White?? Arc 30

31 What Color is the Taxi? We encode our domain knowledge regarding the taxi cab example: Node: Variable of Interest Taxi Yellow White 85% 15% Arc: Discrete & Nonparametric Probabilistic Relationship Taxi Node: Variable of Interest Witness Yellow White Yellow 80% 20% White 20% 80% Witness Yellow White?? Arc 31

32 What Color is the Taxi? We encode our domain knowledge regarding the taxi cab example: Marginal Distribution Conditional Probability Table 32

33 What Color is the Taxi? Inference based on evidence: Simulation Taxi 0.00% Yellow % White Simulation Witness 20.00% Yellow 80.00% White 33

34 What Color is the Taxi? Performing inference based on observing evidence: Diagnosis? Diagnosis Witness 0.00% Yellow % White 34

35 What Color is the Taxi? Performing inference based on observing evidence: Diagnosis Taxi 58.62% Yellow 41.38% White Diagnosis Witness 0.00% Yellow % White 35

36 See Chapter 4 Example 2: Where is my bag? Knowledge Modeling & Reasoning Under Uncertainty

37 Example 2: Where is my bag? Travel Route: Singapore (SIN) Tokyo/Narita (NRT) Los Angeles (LAX) NRT LAX SIN BayesiaLab.com 37

38 Where is my bag? 50/50 Singapore SIN Tokyo Narita NRT Los Angeles LAX? BayesiaLab.com 38

39 Where is my bag? Scenario 1 Luggage delivery starts onto the carousel. After 5 minutes, I still do not see my bag. What is the probability that I will still get my bag? 39

40 But we only have observational data 40

41 Airport Is my bag in there? BayesiaLab.com 41

42 Where is my bag? Results from Webinar Poll Correct Answer: 33% Correct Answer 42

43 Where is my bag? Proposed Workflow Encode the available albeit very limited knowledge into a Bayesian network. Use BayesiaLab to perform probabilistic inference given our observations. 43

44 Where is my bag? Bayesian Network BayesiaLab.com 44

45 BayesiaLab.com 45

46 BayesiaLab.com 46

47 Where is my bag? Scenario 2 Luggage delivery starts onto the carousel. After 5 minutes, I still do not see my bag. However, now I see a colleague, who traveled on the same itinerary, pick up his bag. What is now the probability that I will still get my bag? 47

48 BayesiaLab.com 48

49 BayesiaLab.com 49

50 BayesiaLab.com 50

51 BayesiaLab.com 51

52 Where is my bag? Scenario 3 Luggage is delivered on the carousel, a total of 50 bags in the first 5 minutes, yet I still do not see my bag. What is the probability that I will still get my bag? 52

53 Where is my bag? Extended Model BayesiaLab.com 53

54 Where is my bag? More important questions: Will the patient ultimately respond to the current treatment? Should we continue a search and rescue effort? Should we still follow the original business strategy, i.e. hold the course? BayesiaLab.com 54

55 Where is my bag? Key Points Encoding of knowledge Reasoning under uncertainty Reasoning from cause to effect (simulation) from effect to cause (diagnosis) Inter-causal reasoning 55

56 VR In Conclusion 56

57 User Forum: bayesia.com/community BayesiaLab.com 57

58 bayesia.com/pricing-2018 BayesiaLab.com 58

59 store.bayesia.us BayesiaLab.com 59

60 Webinar Series: Friday at 1 p.m. (Central) Upcoming Webinars: March 9 March 16 March 23 Bayesian Networks for Risk Management without Data Optimizing Health Policies with Bayesian Networks t.b.d. Register here: bayesia.com/events stefan.conrady@bayesia.us 60

61 BayesiaLab Courses Around the World in 2018 March San Francisco, CA May Seattle, WA June Boston, MA September New Delhi, India October Chicago, IL December 4 6 New York, NY August London, UK Learn More & Register: bayesia.com/events stefan.conrady@bayesia.us 61

62 San Francisco Introductory BayesiaLab Course in San Francisco, California March 13 15, 2018 BayesiaLab.com 62

63 6th Annual BayesiaLab Conference in Chicago November 1 2, 2018 Chicago BayesiaLab.com 63

64 Thank You! BayesianNetwork linkedin.com/in/stefanconrady facebook.com/bayesia BayesiaLab.com 64