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C3.4.1
1.
Machine Learning Specialization Overfitting in
decision trees Emily Fox & Carlos Guestrin Machine Learning Specialization University of Washington ©2015-2016 Emily Fox & Carlos Guestrin
2.
Machine Learning Specialization3 Review
of loan default prediction ©2015-2016 Emily Fox & Carlos Guestrin Safe ✓ Risky ✘ Risky ✘ Intelligent loan application review system Loan Applications
3.
Machine Learning Specialization4
©2015-2016 Emily Fox & Carlos Guestrin Decision tree review T(xi) = Traverse decision tree Loan Application Input: xi ŷi Credit? Safe Term? Risky Safe Income? Term? Risky Safe Risky start excellent poor fair 5 years 3 years Low high 5 years 3 years
4.
Machine Learning Specialization Overfitting
review ©2015-2016 Emily Fox & Carlos Guestrin
5.
Machine Learning Specialization8 Overfitting
in logistic regression ©2015-2016 Emily Fox & Carlos Guestrin Model complexity Error= ClassificationError Overfitting if there exists w*: • training_error(w*) > training_error(ŵ) • true_error(w*) < true_error(ŵ) True error Training error
6.
Machine Learning Specialization9 Overfitting
è Overconfident predictions ©2015-2016 Emily Fox & Carlos Guestrin Logistic Regression (Degree 6) Logistic Regression (Degree 20)
7.
Machine Learning Specialization Overfitting
in decision trees ©2015-2016 Emily Fox & Carlos Guestrin
8.
Machine Learning Specialization13 Decision
stump (Depth 1): Split on x[1] ©2015-2016 Emily Fox & Carlos Guestrin Root 18 13 x[1] < -0.07 13 3 x[1] >= -0.07 4 11 x[1] y values - +
9.
Machine Learning Specialization14 Tree
depth depth = 1 depth = 2 depth = 3 depth = 5 depth = 10 Training error 0.22 0.13 0.10 0.03 0.00 Decision boundary ©2015-2016 Emily Fox & Carlos Guestrin Training error reduces with depth What happens when we increase depth?
10.
Machine Learning Specialization16 Deeper
trees è lower training error ©2015-2016 Emily Fox & Carlos Guestrin Tree depth TrainingError Depth 10 (training error = 0.0)
11.
Machine Learning Specialization17 Training
error = 0: Is this model perfect? ©2015-2016 Emily Fox & Carlos Guestrin Depth 10 (training error = 0.0) NOT PERFECT
12.
Machine Learning Specialization18 Why
training error reduces with depth? ©2015-2016 Emily Fox & Carlos Guestrin Root 22 18 excellent 9 0 good 9 4 fair 4 14 Loan status: Safe Risky Credit? Tree Training error (root) 0.45 split on credit 0.20 Safe Safe Risky Training error improved by 0.25 because of the split Split on credit
13.
Machine Learning Specialization19 Feature
split selection algorithm ©2015-2016 Emily Fox & Carlos Guestrin • Given a subset of data M (a node in a tree) • For each feature hi(x): 1. Split data of M according to feature hi(x) 2. Compute classification error split • Chose feature h*(x) with lowest classification error By design, each split reduces training error
14.
Machine Learning Specialization21 Decision
trees overfitting on loan data ©2015-2016 Emily Fox & Carlos Guestrin
15.
Machine Learning Specialization Principle
of Occam’s razor: Simpler trees are better ©2015-2016 Emily Fox & Carlos Guestrin
16.
Machine Learning Specialization25 Principle
of Occam’s Razor ©2015-2016 Emily Fox & Carlos Guestrin “Among competing hypotheses, the one with fewest assumptions should be selected”, William of Occam, 13th Century OR Diagnosis 1: 2 diseases Two diseases D1 and D2 where D1 explains S1, D2 explains S2 Diagnosis 2: 1 disease Disease D3 explains both symptoms S1 and S2 Symptoms: S1 and S2 SIMPLER
17.
Machine Learning Specialization26 Occam’s
Razor for decision trees ©2015-2016 Emily Fox & Carlos Guestrin When two trees have similar classification error on the validation set, pick the simpler one Complexity Train error Validation error Simple 0.23 0.24 Moderate 0.12 0.15 Complex 0.07 0.15 Super complex 0 0.18 Overfit Same validation error
18.
Machine Learning Specialization27 Which
tree is simpler? ©2015-2016 Emily Fox & Carlos Guestrin OR SIMPLER
19.
Machine Learning Specialization29 Modified
tree learning problem ©2015-2016 Emily Fox & Carlos Guestrin T1(X) T2(X) T4(X) Find a “simple” decision tree with low classification error Complex treesSimple trees
20.
Machine Learning Specialization30 How
do we pick simpler trees? ©2015-2016 Emily Fox & Carlos Guestrin 1. Early Stopping: Stop learning algorithm before tree become too complex 2. Pruning: Simplify tree after learning algorithm terminates
21.
Machine Learning Specialization Early
stopping for learning decision trees ©2015-2016 Emily Fox & Carlos Guestrin
22.
Machine Learning Specialization33 Deeper
trees è Increasing complexity ©2015-2016 Emily Fox & Carlos Guestrin Model complexity increases with depth Depth = 1 Depth = 2 Depth = 10
23.
Machine Learning Specialization Early
stopping condition 1: Limit the depth of a tree ©2015-2016 Emily Fox & Carlos Guestrin
24.
Machine Learning Specialization36 Restrict
tree learning to shallow trees? ©2015-2016 Emily Fox & Carlos Guestrin ClassificationError Complex trees True error Training error Simple trees Tree depth max_depth
25.
Machine Learning Specialization37 Early
stopping condition 1: Limit depth of tree ©2015-2016 Emily Fox & Carlos Guestrin ClassificationError Stop tree building when depth = max_depth max_depth Tree depth
26.
Machine Learning Specialization38 Picking
value for max_depth??? ©2015-2016 Emily Fox & Carlos Guestrin ClassificationError Validation set or cross-validation max_depth Tree depth
27.
Machine Learning Specialization Early
stopping condition 2: Use classification error to limit depth of tree ©2015-2016 Emily Fox & Carlos Guestrin
28.
Machine Learning Specialization40 Decision
tree recursion review ©2015-2016 Emily Fox & Carlos Guestrin Loan status: Safe Risky Credit? Safe Root 22 18 excellent 16 0 fair 1 2 poor 5 16 Build decision stump with subset of data where Credit = poor Build decision stump with subset of data where Credit = fair
29.
Machine Learning Specialization42 Split
selection for credit=poor ©2015-2016 Emily Fox & Carlos Guestrin No split improves classification error è Stop! Splits for credit=poor Classification error (no split) 0.45 split on term 0.24 split on income 0.24 Credit? Safe Root 22 18 excellent 16 0 fair 1 2 poor 5 16 Loan status: Safe Risky Splits for credit=poor Classification error (no split) 0.24
30.
Machine Learning Specialization43 Early
stopping condition 2: No split improves classification error ©2015-2016 Emily Fox & Carlos Guestrin Credit? Safe Risky Early stopping condition 2 Root 22 18 excellent 16 0 fair 1 2 poor 5 16 Splits for credit=poor Classification error (no split) 0.24 split on term 0.24 split on income 0.24 Build decision stump with subset of data where Credit = fair Loan status: Safe Risky
31.
Machine Learning Specialization45 Practical
notes about stopping when classification error doesn’t decrease 1. Typically, add magic parameter ε - Stop if error doesn’t decrease by more than ε 2. Some pitfalls to this rule (see pruning section) 3. Very useful in practice ©2015-2016 Emily Fox & Carlos Guestrin
32.
Machine Learning Specialization Early
stopping condition 3: Stop if number of data points contained in a node is too small ©2015-2016 Emily Fox & Carlos Guestrin
33.
Machine Learning Specialization47 Can
we trust nodes with very few points? ©2015-2016 Emily Fox & Carlos Guestrin Root 22 18 excellent 16 0 fair 1 2 poor 5 16 Loan status: Safe Risky Credit? Safe Stop recursing Only 3 data points! Risky
34.
Machine Learning Specialization48 Early
stopping condition 3: Stop when data points in a node <= Nmin ©2015-2016 Emily Fox & Carlos Guestrin Root 22 18 excellent 16 0 fair 1 2 poor 5 16 Credit? Safe Risky Example: Nmin = 10 Risky Early stopping condition 3 Loan status: Safe Risky
35.
Machine Learning Specialization Summary
of decision trees with early stopping ©2015-2016 Emily Fox & Carlos Guestrin
36.
Machine Learning Specialization50 Early
stopping: Summary ©2015-2016 Emily Fox & Carlos Guestrin 1. Limit tree depth: Stop splitting after a certain depth 2. Classification error: Do not consider any split that does not cause a sufficient decrease in classification error 3. Minimum node “size”: Do not split an intermediate node which contains too few data points
37.
Machine Learning Specialization52 Recursion Stopping conditions
1 & 2 or Early stopping conditions 1, 2 & 3 Greedy decision tree learning ©2015-2016 Emily Fox & Carlos Guestrin • Step 1: Start with an empty tree • Step 2: Select a feature to split data • For each split of the tree: • Step 3: If nothing more to, make predictions • Step 4: Otherwise, go to Step 2 & continue (recurse) on this split
38.
Machine Learning Specialization Overfitting
in Decision Trees: Pruning ©2015-2016 Emily Fox & Carlos Guestrin OPTIONAL
39.
Machine Learning Specialization55 Stopping
condition summary • Stopping condition: 1. All examples have the same target value 2. No more features to split on • Early stopping conditions: 1. Limit tree depth 2. Do not consider splits that do not cause a sufficient decrease in classification error 3. Do not split an intermediate node which contains too few data points ©2015-2016 Emily Fox & Carlos Guestrin
40.
Machine Learning Specialization Exploring
some challenges with early stopping conditions ©2015-2016 Emily Fox & Carlos Guestrin
41.
Machine Learning Specialization57 Challenge
with early stopping condition 1 ©2015-2016 Emily Fox & Carlos Guestrin ClassificationError Complex trees True error Training error Simple trees Tree depth max_depth Hard to know exactly when to stop
42.
Machine Learning Specialization58 Is
early stopping condition 2 a good idea? ©2015-2016 Emily Fox & Carlos Guestrin Tree depth ClassificationError Stop because of zero decrease in classification error
43.
Machine Learning Specialization60 Early
stopping condition 2: Don’t stop if error doesn’t decrease??? ©2015-2016 Emily Fox & Carlos Guestrin y values True False Root 2 2 Error = . = Tree Classification error (root) 0.5 x[1] x[2] y False False False False True True True False True True True False y = x[1] xor x[2]
44.
Machine Learning Specialization61 Consider
split on x[1] ©2015-2016 Emily Fox & Carlos Guestrin y values True False Root 2 2 Error = . = Tree Classification error (root) 0.5 Split on x[1] 0.5 True 1 1 False 1 1 x[1] x[1] x[2] y False False False False True True True False True True True False y = x[1] xor x[2]
45.
Machine Learning Specialization62 Consider
split on x[2] ©2015-2016 Emily Fox & Carlos Guestrin y values True False Root 2 2 Error = . = Tree Classification error (root) 0.5 Split on x[1] 0.5 Split on x[2] 0.5 True 1 1 False 1 1 x[2] Neither features improve training error… Stop now??? x[1] x[2] y False False False False True True True False True True True False y = x[1] xor x[2]
46.
Machine Learning Specialization63 Final
tree with early stopping condition 2 ©2015-2016 Emily Fox & Carlos Guestrin y values True False Root 2 2 True x[1] x[2] y False False False False True True True False True True True False y = x[1] xor x[2] Tree Classification error with early stopping condition 2 0.5
47.
Machine Learning Specialization64 Without
early stopping condition 2 ©2015-2016 Emily Fox & Carlos Guestrin y values True False Root 2 2 True 1 1 False 1 1 x[1] True 0 1 x[2] True 1 0 False 1 0 x[2] False 0 1 True FalseFalse True Tree Classification error with early stopping condition 2 0.5 without early stopping condition 2 0.0 x[1] x[2] y False False False False True True True False True True True False y = x[1] xor x[2]
48.
Machine Learning Specialization66 Early
stopping condition 2: Pros and Cons • Pros: - A reasonable heuristic for early stopping to avoid useless splits • Cons: - Too short sighted: We may miss out on “good” splits may occur right after “useless” splits ©2015-2016 Emily Fox & Carlos Guestrin
49.
Machine Learning Specialization Tree
pruning ©2015-2016 Emily Fox & Carlos Guestrin
50.
Machine Learning Specialization68 Two
approaches to picking simpler trees ©2015-2016 Emily Fox & Carlos Guestrin 1. Early Stopping: Stop the learning algorithm before the tree becomes too complex 2. Pruning: Simplify the tree after the learning algorithm terminates Complements early stopping
51.
Machine Learning Specialization70 Pruning:
Intuition Train a complex tree, simplify later ©2015-2016 Emily Fox & Carlos Guestrin Complex Tree Simplify Simpler Tree
52.
Machine Learning Specialization71 Pruning
motivation ©2015-2016 Emily Fox & Carlos Guestrin ClassificationError True Error Training Error Tree depth Don’t stop too early Complex tree Simplify after tree is built Simple tree
53.
Machine Learning Specialization72 Example
1: Which tree is simpler? ©2015-2016 Emily Fox & Carlos Guestrin OR Credit? Term? Risky Start fair 3 years Safe Safe Income? Term? Risky Safe Risky excellent poor 5 years low high 5 years 3 years Credit? Start Safe Safe excellent poor Risky fair SIMPLER
54.
Machine Learning Specialization73 Example
2: Which tree is simpler??? ©2015-2016 Emily Fox & Carlos Guestrin ORCredit? Start Safe Risky excellent poor bad SafeSafe Risky good fair Term? Start 3 years 5 years Risky Safe
55.
Machine Learning Specialization74 Simple
measure of complexity of tree ©2015-2016 Emily Fox & Carlos Guestrin Credit? Start Safe Risky excellent poor bad SafeSafe Risky good fair L(T) = # of leaf nodes
56.
Machine Learning Specialization75 Which
tree has lower L(T)? ©2015-2016 Emily Fox & Carlos Guestrin ORCredit? Start Safe Risky excellent poor bad SafeSafe Risky good fair Term? Start 3 years 5 years Risky Safe L(T1) = 5 L(T2) = 2 SIMPLER
57.
Machine Learning Specialization76
©2015-2016 Emily Fox & Carlos Guestrin Balance simplicity & predictive power Credit? Term? Risky Start fair 3 years Safe Safe Income? Term? Risky Safe Risky excellent poor 5 years low high 5 years 3 years Risky Start Too complex, risk of overfitting Too simple, high classification error
58.
Machine Learning Specialization78 Want
to balance: i. How well tree fits data ii. Complexity of tree Total cost = measure of fit + measure of complexity ©2015-2016 Emily Fox & Carlos Guestrin (classification error) Large # = bad fit to training data Large # = likely to overfit want to balance Desired total quality format
59.
Machine Learning Specialization79 Consider
specific total cost Total cost = classification error + number of leaf nodes ©2015-2016 Emily Fox & Carlos Guestrin Error(T) L(T)
60.
Machine Learning Specialization81 Balancing
fit and complexity Total cost C(T) = Error(T) + λ L(T) ©2015-2016 Emily Fox & Carlos Guestrin tuning parameter If λ=0: If λ=∞: If λ in between:
61.
Machine Learning Specialization82 Use
total cost to simplify trees ©2015-2016 Emily Fox & Carlos Guestrin Total quality based pruning Complex tree Simpler tree
62.
Machine Learning Specialization Tree
pruning algorithm ©2015-2016 Emily Fox & Carlos Guestrin
63.
Machine Learning Specialization85
©2015-2016 Emily Fox & Carlos Guestrin Credit? Term? Risky Start fair 3 years Safe Safe Income? Risky excellent poor 5 years low high Pruning Intuition Tree T Term? Risky Safe 5 years 3 years
64.
Machine Learning Specialization86
©2015-2016 Emily Fox & Carlos Guestrin Credit? Term? Risky Start fair 3 years Safe Safe Income? Risky excellent poor 5 years low high Term? Risky Safe 5 years 3 years Step 1: Consider a split Tree T Candidate for pruning
65.
Machine Learning Specialization88
©2015-2016 Emily Fox & Carlos Guestrin Credit? Term? Risky Start fair 3 years Safe Safe Income? Risky excellent poor 5 years low high Step 2: Compute total cost C(T) of split C(T) = Error(T) + λ L(T) Tree Error #Leaves Total T 0.25 λ = 0.3 Tree T Term? Risky Safe 5 years 3 years Candidate for pruning
66.
Machine Learning Specialization89
©2015-2016 Emily Fox & Carlos Guestrin Credit? Term? Risky Start fair 3 years Safe Safe Income? Safe Risky excellent poor 5 years low high Step 2: “Undo” the splits on Tsmaller Replace split by leaf node? Tree Tsmaller C(T) = Error(T) + λ L(T) Tree Error #Leaves Total T 0.25 6 0.43 Tsmaller 0.26 λ = 0.3
67.
Machine Learning Specialization90
©2015-2016 Emily Fox & Carlos Guestrin Credit? Term? Risky Start fair 3 years Safe Safe Income? Safe Risky excellent poor 5 years low high Prune if total cost is lower: C(Tsmaller) ≤ C(T) Replace split by leaf node? Tree Tsmaller C(T) = Error(T) + λ L(T) Tree Error #Leaves Total T 0.25 6 0.43 Tsmaller 0.26 5 0.41 λ = 0.3 Worse training error but lower overall cost YES!
68.
Machine Learning Specialization92
©2015-2016 Emily Fox & Carlos Guestrin Credit? Term? Risky Start fair 3 years Safe Safe Income? Safe Risky excellent poor 5 years low high Step 5: Repeat Steps 1-4 for every split Decide if each split can be “pruned”
69.
Machine Learning Specialization93 Decision
tree pruning algorithm ©2015-2016 Emily Fox & Carlos Guestrin • Start at bottom of tree T and traverse up, apply prune_split to each decision node M • prune_split(T,M): 1. Compute total cost of tree T using C(T) = Error(T) + λ L(T) 2. Let Tsmaller be tree after pruning subtree below M 3. Compute total cost complexity of Tsmaller C(Tsmaller) = Error(Tsmaller) + λ L(Tsmaller) 4. If C(Tsmaller) < C(T), prune to Tsmaller
70.
Machine Learning Specialization Summary
of overfitting in decision trees ©2015-2016 Emily Fox & Carlos Guestrin
71.
Machine Learning Specialization95 •
Identify when overfitting in decision trees • Prevent overfitting with early stopping - Limit tree depth - Do not consider splits that do not reduce classification error - Do not split intermediate nodes with only few points • Prevent overfitting by pruning complex trees - Use a total cost formula that balances classification error and tree complexity - Use total cost to merge potentially complex trees into simpler ones ©2015-2016 Emily Fox & Carlos Guestrin What you can do now…
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Machine Learning Specialization96 Thank
you to Dr. Krishna Sridhar Dr. Krishna Sridhar Staff Data Scientist, Dato, Inc. ©2015-2016 Emily Fox & Carlos Guestrin
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