Medical Decision Making Learning: Decision Trees Artificial - PowerPoint PPT Presentation

Medical Decision Making Learning: Decision Trees Artificial Intelligence CSPP 56553 February 11, 2004

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

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

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

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

Medical Expert Systems: Issues • Works well but.. – Only diagnoses blood infections • NARROW – Requires extensive expert interviews • EXPENSIVE to develop – Difficult to update, can’t handle new cases • BRITTLE

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

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

Sunburn Example Name Hair Height Weight Lotion Result Sarah Blonde Average Light No Burn Dana Blonde Tall Average Yes None Alex Brown Short Average Yes None Annie Blonde Short Average No Burn Emily Red Average Heavy No Burn Pete Brown Tall Heavy No None John Brown Average Heavy No None Katie Blonde Short Light Yes None

Learning about Sunburn • Goal: – Train on labeled examples – Predict Burn/None for new instances • Solution?? – Exact match: same features, same output • Problem: 2*3^3 feature combinations – Could be much worse – Nearest Neighbor style • Problem: What’s close? Which features matter? – Many match on two features but differ on result

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

Sunburn Identification Tree Hair Color Blonde Brown Red Emily: Burn Lotion Used Alex: None John: None No Yes Pete: None Sarah: Burn Katie: None Annie: Burn Dana: None

Simplicity • Occam’s Razor: – Simplest explanation that covers the data is best • Occam’s Razor for ID trees: – Smallest tree consistent with samples will be best predictor for new data • Problem: – Finding all trees & finding smallest: Expensive! • Solution:

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

Minimizing Disorder Hair Color Height Brown Blonde Tall Short Red Average Alex:N Sarah:B Sarah: B Alex: N Dana:N Emily: B Annie:B Emily:B Dana: N Pete: N Pete:N John:N Katie:N Annie: B John: N Katie: N Lotion Weight Yes No Heavy Light Average Sarah:B Dana:N Annie:B Dana:N Emily:B Alex:N Sarah:B Emily:B Alex:N Pete:N Katie:N Katie:N Pete:N Annie:B John:N John:N

Minimizing Disorder Height Tall Short Average Annie:B Sarah:B Dana:N Katie:N Lotion Weight Yes No Heavy Light Average Sarah:B Dana:N Annie:B Dana:N Katie:N Sarah:B Annie:B Katie:N

Measuring Disorder • Problem: – In general, tests on large DB’s don’t yield homogeneous subsets • Solution: – General information theoretic measure of disorder – Desired features: • Homogeneous set: least disorder = 0 • Even split: most disorder = 1

Measuring Entropy • If split m objects into 2 bins size m1 & m2, what is the entropy? 1.2 1 0.8 Disorder m m log − = 0.6 i i 2 ∑ m m i 0.4 m m m m 0.2 log log − − 1 1 2 2 2 2 m m m m 0 0 0.2 0.4 0.6 0.8 1 1.2 m1/m

Measuring Disorder Entropy / = p m m the probability of being in bin i i i 1 = p 0 1 ≤ ≤ p ∑ i i i log ∑ − p p Entropy (disorder) of a split 2 i i 0 log 0 0 = Assume i 2 p 1 p 2 Entropy 1 0 -1log 2 1 - 0log 2 0 = 0 - 0 = 0 ½ ½ -½ log 2 ½ - ½ log 2 ½ = ½ +½ = 1 -¼ log 2 ¼ - ¾ log 2 ¾ = 0.5 + 0.311 = ¼ ¾ 0.811

Computing Disorder N instances Branch 2 Branch1 N2 a N1 a N2 b N1 b n n n k , log   = − , AvgDisorde r i c i c i   2 ∑ ∑ n n n   = 1 ∈ i c class t i i   Fraction of samples Disorder of class down branch i distribution on branch i

Entropy in Sunburn Example n n n k , log   = − , i c i c AvgDisorde r i   2 ∑ ∑ n n n   1 = ∈ i c class t i i   Hair color = 4/8(-2/4 log 2/4 - 2/4log2/4) + 1/8*0 + 3/8 *0 = 0.5 Height = 0.69 Weight = 0.94 Lotion = 0.61

Entropy in Sunburn Example n n n k , log   = − , i c i c AvgDisorde r i   2 ∑ ∑ n n n   1 = ∈ i c class t i i   Height = 2/4(-1/2log1/2-1/2log1/2) + 1/4*0+1/4*0 = 0.5 Weight = 2/4(-1/2log1/2-1/2log1/2) +2/4(-1/2log1/2-1/2log1/2) = 1 Lotion = 0

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

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 >= value • Need to search to find best breakpoint • Absent features: Distribute uniformly

Features in ID Trees: Cons • Features – Assumed independent – If want group effect, must model explicitly • E.g. make new feature AorB • Feature tests conjunctive

From Trees to Rules • Tree: – Branches from root to leaves = – Tests => classifications – Tests = if antecedents; Leaf labels= consequent – All ID trees-> rules; Not all rules as trees

From ID Trees to Rules Hair Color Blonde Brown Red Emily: Burn Lotion Used Alex: None John: None No Yes Pete: None Sarah: Burn Katie: None Annie: Burn 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))

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