INC 551 Artificial Intelligence Lecture 8 Models of Uncertainty
Bayesian Belief Network Model Causes -> Effect Graph Structure shows dependency
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.
Computing Probability = 0.90x0.70x0.001x0.999x0.998 = 0.00062
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.
Inference Problem Find For example, find
Inference by Enumeration Note: let α is called “Normalized Constant” y are other events
Calculation Tree Inefficient, Compute P(j|a)P(m|a) for every value of e
Approximate Inference Idea: Count from real examples We call this procedure “Sampling” Sampling = get real examples from the world model
Sampling Example Cloudy = มีเมฆ Sprinkler = ละอองน้ำ
Rejection Sampling To find Idea: Count only the sample that agree with e
Rejection Sampling Drawback: There are not many samples that agree with e From the example above, from 100 samples, only 27 are Usable.
Likelihood Weighting Idea: Generate only samples that are relevant with e However, we must use “weighted sampling” e.g. Find
Weighted Sampling Fix sprinkler = TRUE Wet Grass = TRUE Sample from P(Cloudy)=0.5 , suppose we get “true”
Sprinkler already has value = true, therefore we multiply with weight = 0.1
WetGrass already has value = true, therefore we multiply with weight = 0.99
Finally, we got a sample (t,t,t,t) With weight = 0.099
Temporal Model (Time) When the events are tagged with timestamp Each node is considered “state”
Markov Process Let Xt = state For Markov processes, Xt depends only on finite number of previous xt
Hidden Markov Model (HMM) Each state has observation, Et. We cannot see “state”, but we see “observation”.