1. INC 551 Artificial Intelligence Lecture 8 Models of Uncertainty

2. Inference by Enumeration

3. Bayesian Belief Network Model Causes -> Effect Graph Structure shows dependency

4. Burglar Alarm Example My house has a burglar alarm but sometimes it rings because of an earthquake. My neighbors, John and Mary promise me to call if they hear the alarm. However, their ears are not perfect.

5. One Way to Create BBN

6. Computing Probability = 0.90x0.70x0.001x0.999x0.998 = 0.00062

7. BBN Construction There are many ways to construct BBN of a problem because the events depend on each other (related). Therefore, it depends on the order of events that you consider. The most simple is the most compact.

11. Not compact

12. Inference Problem Find For example, find

13. Inference by Enumeration Note: let α is called “Normalized Constant” y are other events

14. (summation of all events)

15. Calculation Tree Inefficient,Compute P(j|a)P(m|a) for every value of e

16. Next, we have to find P(~b|j,m) and find α = 1/P(j,m)

17. Approximate Inference Idea: Count from real examples We call this procedure “Sampling” Sampling = get real examples from the world model

18. Sampling Example Cloudy = มีเมฆ Sprinkler = ละอองน้ำ

24. 1 Sample

25. Rejection Sampling Idea: Count only the sample that agree with e To find

26. Rejection Sampling Drawback: There are not many samples that agree with e From the example above, from 100 samples, only 27 are Usable.

27. Likelihood Weighting Idea: Generate only samples that are relevant with e However, we must use “weighted sampling” e.g. Find

28. Fix sprinkler = TRUE Wet Grass = TRUE Weighted Sampling Sample from P(Cloudy)=0.5, suppose we get “true”

31. Sprinkler already has value = true, therefore we multiply with weight = 0.1

32. Sample from P(Rain)=0.8, suppose we get “true”

33. WetGrass already has value = true, therefore we multiply with weight = 0.99

34. Finally, we got a sample (t,t,t,t) With weight = 0.099

35. Temporal Model (Time) When the events are tagged with timestamp Each node is considered “state”

36. Markov Process Let Xt = state For Markov processes, Xt depends only on finite number of previous xt

37. Hidden Markov Model (HMM) Each state has observation, Et. We cannot see “state”, but we see “observation”.