CSIT 5220 Lecture 04: Building Models l Objective n Discuss practical considerations in model building l Reading n Jensen and Nielsen, Chapter 3 l Outline n Catching the structure n Determining probabilities n Reducing the number of parameters n Other Issues Page 1

CSIT 5220 Catching the Structure l Identify the variables n Hypothesis variables  Those whose values are not directly observed, and we wish to estimate n Information variables  Those whose values are observed directly observed and contain information about the hypothesis variables n Mediating variables  Those that provide information channels between the information variables and the hypothesis variables l Build the structure n Begin with causality n Consider conditional independence Page 2

CSIT 5220 Example: Sore Throat Page 3 l Angina is chest pain or discomfort that occurs when an area of your heart muscle doesn't get enough oxygen-rich blood.

CSIT 5220 Example: Sore Throat l Check conditional independence n Fever independent of Spots given Angina? Page 4

CSIT 5220 Example: Infected Milk Page 5

CSIT 5220 Example: Infected Milk Page 6

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CSIT 5220 Example: Insemination of a cow Page 8 l Insemination is the process of impregnating the femalemale

CSIT 5220 Example: Insemination of a cow Page 9

CSIT 5220 Why Mediating Variables Page 10

CSIT 5220 Example: Simplified Poker Game Page 11

CSIT 5220 Example: Simplified Poker Game Page 12

CSIT 5220 Page 13 l P(OH0), P(FC|OH0), P(OH1|OH0, FC), P(SC|OH1), P(OH|OH1, SC) are easier to obtain than P(OH|FC, SC) l Will see later

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CSIT 5220 Outline l Outline n Catching the structure n Determining probabilities n Reducing the number of parameters l Other Issues Page 15

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CSIT 5220 P(Test|Inf) from Sensitivity & Specificity of Test l P( Test=y | Inf=y ) = sensitivity l P( Test=y| inf=n) = 1-specificity

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CSIT 5220 Stud Farm Inference Results

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CSIT 5220 Outline l Outline n Catching the structure n Determining probabilities n Reducing the number of parameters l Other Issues Page 31

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CSIT 5220 Outline l Outline n Catching the structure n Determining probabilities n Reducing the number of parameters n Other issues Page 39

CSIT 5220 Logical Constraints l Sometimes relationships among variables are undirected Page 40

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CSIT 5220 Probabilities need not be exact to be useful l Some people have shied away from using Bayes nets because they imagine they will only work well, if the probabilities upon which they are based are exact. l This is not true. It turns out very often that approximate probabilities, even subjective ones that are guessed at, give very good results. Bayes nets are generally quite robust to imperfect knowledge. l Often the combination of several strands of imperfect knowledge can allow us to make surprisingly strong conclusions. l In some cases, we have no choice but trust judgments by experts n If we can trust decisions by experts, then we can trust the probability assessments by experts n Bayes nets can help experts make better decisions, albeit subjective. Page 44

CSIT 5220 Causal Conditional Probabilities are easier to estimate than the reverse l Studies have shown people are better at estimating probabilities "in the forward direction". l For example, doctors are quite good at giving the probability estimates for "if the patient has lung cancer, what are the chances their X-ray will be abnormal?", l rather than the reverse, "if the X-ray is abnormal, what are the chances of lung cancer being the cause?" (Jensen96)Jensen96 Page 45