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CSIT 5220
Lecture 04: Building Models
Objective Discuss practical considerations in model building
Reading Jensen and Nielsen, Chapter 3
Outline Catching the structure Determining probabilities Reducing the number of parameters Other Issues
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CSIT 5220
Catching the Structure
Identify the variables
Hypothesis variables Those whose values are not directly observed, and we wish to estimate
Information variables Those whose values are observed directly observed and contain information
about the hypothesis variables
Mediating variables Those that provide information channels between the information variables and
the hypothesis variables
Build the structure
Begin with causality
Consider conditional independence
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Example: Sore ThroatPage 3
Angina is chest pain or discomfort that occurs when an area of your heart muscle doesn't get enough oxygen-rich blood.
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CSIT 5220
Example: Sore Throat
Check conditional independence
Fever independent of Spots given Angina?
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Example: Infected MilkPage 5
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Example: Infected MilkPage 6
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Example: Infected MilkPage 7
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Example: Insemination of a cowPage 8
Insemination is the process of impregnating the femalemale
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Example: Insemination of a cowPage 9
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Why Mediating VariablesPage 10
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Example: Simplified Poker GamePage 11
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Example: Simplified Poker GamePage 12
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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)
Will see later
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SummaryPage 14
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Outline
Outline Catching the structure Determining probabilities Reducing the number of parameters Other Issues
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CSIT 5220
P(Test|Inf) from Sensitivity & Specificity of Test
P( Test=y | Inf=y ) = sensitivity
P( Test=y| inf=n) = 1-specificity
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CSIT 5220
Stud Farm Inference Results
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CSIT 5220
Outline
Outline Catching the structure Determining probabilities Reducing the number of parameters Other Issues
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CSIT 5220
Outline
Outline Catching the structure Determining probabilities Reducing the number of parameters Other issues
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CSIT 5220
Logical Constraints
Sometimes relationships among variables are undirected
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Logical ConstraintsPage 41
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Probabilities need not be exact to be useful
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.
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.
Often the combination of several strands of imperfect knowledge can allow us
to make surprisingly strong conclusions.
In some cases, we have no choice but trust judgments by experts
If we can trust decisions by experts, then we can trust the probability
assessments by experts
Bayes nets can help experts make better decisions, albeit subjective.
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Causal Conditional Probabilities are easier to estimate than the reverse
Studies have shown people are better at estimating probabilities "in
the forward direction".
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?",
rather than the reverse, "if the X-ray is abnormal, what are the
chances of lung cancer being the cause?" (Jensen96)
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