Medical Decision Making Learning: Decision Trees

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Medical Decision MakingLearning Decision Trees

• Artificial Intelligence
• CSPP 56553
• February 11, 2004

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Agenda

• Decision Trees
• Motivation Medical Experts Mycin
• Basic characteristics
• Sunburn example
• From trees to rules
• Learning by minimizing heterogeneity
• Analysis Pros Cons

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Expert Systems

• Classic example of classical AI
• Narrow but very deep knowledge of a field
• E.g. Diagnosis of bacterial infections
• Manual knowledge engineering
• Elicit detailed information from human experts

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Expert Systems

• Knowledge representation
• If-then rules
• Antecedent Conjunction of conditions
• Consequent Conclusion to be drawn
• Axioms Initial set of assertions
• Reasoning process
• Forward chaining
• From assertions and rules, generate new
  assertions
• Backward chaining
• From rules and goal assertions, derive evidence
  of assertion

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Medical Expert Systems Mycin

• Mycin
• Rule-based expert system
• Diagnosis of blood infections
• 450 rules experts, better than junior MDs
• Rules acquired by extensive expert interviews
• Captures some elements of uncertainty

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Medical Expert Systems Issues

• Works well but..
• Only diagnoses blood infections
• NARROW
• Requires extensive expert interviews
• EXPENSIVE to develop
• Difficult to update, cant handle new cases
• BRITTLE

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Modern AI Approach

• Machine learning
• Learn diagnostic rules from examples
• Use general learning mechanism
• Integrate new rules, less elicitation
• Decision Trees
• Learn rules
• Duplicate MYCIN-style diagnosis
• Automatically acquired
• Readily interpretable
• cf Neural Nets/Nearest Neighbor

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Learning Identification Trees

• (aka Decision Trees)
• Supervised learning
• Primarily classification
• Rectangular decision boundaries
• More restrictive than nearest neighbor
• Robust to irrelevant attributes, noise
• Fast prediction

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Sunburn Example
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Learning about Sunburn

• Goal
• Train on labeled examples
• Predict Burn/None for new instances
• Solution??
• Exact match same features, same output
• Problem 233 feature combinations
• Could be much worse
• Nearest Neighbor style
• Problem Whats close? Which features matter?
• Many match on two features but differ on result

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Learning about Sunburn

• Better Solution
• Identification tree
• Training
• Divide examples into subsets based on feature
  tests
• Sets of samples at leaves define classification
• Prediction
• Route NEW instance through tree to leaf based on
  feature tests
• Assign same value as samples at leaf

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Sunburn Identification Tree
Blonde
Brown
Red
Emily Burn
Alex None John None Pete None
No
Yes
Sarah Burn Annie Burn
Katie None Dana None
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Simplicity

• Occams Razor
• Simplest explanation that covers the data is best
• Occams Razor for ID trees
• Smallest tree consistent with samples will be
  best predictor for new data
• Problem
• Finding all trees finding smallest Expensive!
• Solution
• Greedily build a small tree

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Building ID Trees

• Goal Build a small tree such that all samples at
  leaves have same class
• Greedy solution
• At each node, pick test such that branches are
  closest to having same class
• Split into subsets with least disorder
• (Disorder Entropy)
• Find test that minimizes disorder

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Minimizing Disorder
Brown
Blonde
Tall
Short
Red
Average
AlexN AnnieB KatieN
Sarah B Dana N Annie B Katie N
SarahB EmilyB JohnN
Alex N Pete N John N
DanaN PeteN
Emily B
Yes
No
Heavy
Light
Average
SarahB AnnieB EmilyB PeteN JohnN
DanaN AlexN KatieN
DanaN AlexN AnnieB
EmilyB PeteN JohnN
SarahB KatieN
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Minimizing Disorder
Tall
Short
Average
AnnieB KatieN
SarahB
DanaN
Yes
No
Heavy
Light
Average
SarahB AnnieB
DanaN KatieN
DanaN AnnieB
SarahB KatieN
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Measuring Disorder

• Problem
• In general, tests on large DBs dont yield
  homogeneous subsets
• Solution
• General information theoretic measure of disorder
• Desired features
• Homogeneous set least disorder 0
• Even split most disorder 1

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Measuring Entropy

• If split m objects into 2 bins size m1 m2, what
  is the entropy?

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Measuring DisorderEntropy
the probability of being in bin i
Entropy (disorder) of a split
Assume
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Computing Disorder
N instances
Branch 2
Branch1
N2 a N2 b
N1 a N1 b
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Entropy in Sunburn Example
Hair color 4/8(-2/4 log 2/4 - 2/4log2/4)
1/80 3/8 0 0.5 Height
0.69 Weight 0.94 Lotion 0.61
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Entropy in Sunburn Example
Height 2/4(-1/2log1/2-1/2log1/2)
1/401/40 0.5 Weight 2/4(-1/2log1/2-1/2l
og1/2) 2/4(-1/2log1/2-1/2log1/2) 1 Lotion
0
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Building ID Trees with Disorder

• Until each leaf is as homogeneous as possible
• Select an inhomogeneous leaf node
• Replace that leaf node by a test node creating
  subsets with least average disorder
• Effectively creates set of rectangular regions
• Repeatedly draws lines in different axes

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Features in ID Trees Pros

• Feature selection
• Tests features that yield low disorder
• E.g. selects features that are important!
• Ignores irrelevant features
• Feature type handling
• Discrete type 1 branch per value
• Continuous type Branch on gt value
• Need to search to find best breakpoint
• Absent features Distribute uniformly

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Features in ID Trees Cons

• Features
• Assumed independent
• If want group effect, must model explicitly
• E.g. make new feature AorB
• Feature tests conjunctive

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From Trees to Rules

• Tree
• Branches from root to leaves
• Tests gt classifications
• Tests if antecedents Leaf labels consequent
• All ID trees-gt rules Not all rules as trees

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From ID Trees to Rules
Blonde
Brown
Red
Emily Burn
Alex None John None Pete None
No
Yes
Sarah Burn Annie Burn
Katie None Dana None
(if (equal haircolor blonde) (equal lotionused
yes) (then None)) (if (equal haircolor blonde)
(equal lotionused no) (then Burn)) (if (equal
haircolor red) (then Burn)) (if (equal haircolor
brown) (then None))
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Identification Trees

• Train
• Build tree by forming subsets of least disorder
• Predict
• Traverse tree based on feature tests
• Assign leaf node sample label
• Pros Robust to irrelevant features, some noise,
  fast prediction, perspicuous rule reading
• Cons Poor feature combination, dependency,
  optimal tree build intractable