1. Learning Algorithm Evaluation

2. Algorithm evaluation: Outline
Why?
Overfitting
How?
Train/Test vs Cross-validation
What?
Evaluation measures
Who wins?
Statistical significance

3. Introduction

4. Introduction
A model should perform well on unseen data drawn from the same distribution

5. Classification accuracy
performance measure
Success: instance’s class is predicted correctly
Error: instance’s class is predicted incorrectly
Error rate: #errors/#instances
Accuracy: #successes/#instances
Quiz
50 examples, 10 classified incorrectly
Accuracy? Error rate?

6. Evaluation
Rule #1
Never evaluate on training data!

7. Train and Test
Step 1: Randomly split data into training and test set (e.g. 2/3-1/3)
a.k.a. holdout set

8. Train and Test
Step 2: Train model on training data

9. Train and Test
Step 3: Evaluate model on test data

10. Train and Test
Quiz: Can I retry with other parameter settings?

11. Evaluation Rule #1 Rule #2 Never evaluate on training data!
Never train on test data!
(that includes parameter setting or feature selection)

12. Train and Test Step 4: Optimize parameters on separate validation set
testing

13. Test data leakage Never use test data to create the classifier
Can be tricky: e.g. social network
Proper procedure uses three sets
training set: train models
validation set: optimize algorithm parameters
test set: evaluate final model

14. Making the most of the data
Once evaluation is complete, all the data can be used to build the final classifier
Trade-off: performance  evaluation accuracy
More training data, better model (but returns diminish)
More test data, more accurate error estimate

15. Train and Test
Step 5: Build final model on ALL data (more data, better model)

16. Cross-Validation

17. k-fold Cross-validation
Split data (stratified) in k-folds
Use (k-1) for training, 1 for testing
Repeat k times
Average results
train
test
Original Fold Fold Fold 3

18. Cross-validation Standard method: 10? Enough to reduce sampling bias
Stratified ten-fold cross-validation
10? Enough to reduce sampling bias
Experimentally determined

19. Leave-One-Out Cross-validation
100
Original Fold Fold 100
………
A particular form of cross-validation:
#folds = #instances
n instances, build classifier n times
Makes best use of the data, no sampling bias
Computationally expensive

20. ROC Analysis

21. ROC Analysis Stands for “Receiver Operating Characteristic”
From signal processing: tradeoff between hit rate and false alarm rate over noisy channel
Compute FPR, TPR and plot them in ROC space
Every classifier is a point in ROC space
For probabilistic algorithms
Collect many points by varying prediction threshold
Or, make cost sensitive and vary costs (see below)

22. TPrate (sensitivity):
Confusion Matrix
actual + - TP FP +
true positive
false positive
predicted FN TN -
false negative
true negative
TP+FN
FP+TN
P(TP): % true positives: sensitivity
P(FP): % false positives: 1 – specificity
TPrate (sensitivity):
FPrate (fall-out):

23. ROC space classifiers J48 parameters fitted J48 OneR
P(TP): % true positives: sensitivity
P(FP): % false positives: 1 – specificity

24. ROC curves Area Under Curve (AUC) =0.75 Change prediction threshold:
Threshold t: (P(+) > t)
P(TP): % true positives: sensitivity
P(FP): % false positives: 1 – specificity
Area Under Curve (AUC)
=0.75

25. ROC curves Alternative method (easier, but less intuitive)
Rank probabilities
Start curve in (0,0), move down probability list
If positive, move up. If negative, move right
Jagged curve—one set of test data
Smooth curve—use cross-validation

26. ROC curves Method selection
Overall: use method with largest Area Under ROC curve (AUROC)
If you aim to cover just 40% of true positives in a sample: use method A
Large sample: use method B
In between: choose between A and B with appropriate probabilities

27. ROC Space and Costs equal costs skewed costs
P(TP): % true positives: sensitivity
P(FP): % false positives: 1 – specificity

28. Different Costs In practice, TP and FN errors incur different costs
Examples:
Medical diagnostic tests: does X have leukemia?
Loan decisions: approve mortgage for X?
Promotional mailing: will X buy the product?
Add cost matrix to evaluation that weighs TP,FP,...
pred +
pred -
actual +
cTP = 0
cFN = 1
actual -
cFP = 1
cTN = 0

29. Statistical Significance

30. Comparing data mining schemes
Which of two learning algorithms performs better?
Note: this is domain dependent!
Obvious way: compare 10-fold CV estimates
Problem: variance in estimate
Variance can be reduced using repeated CV
However, we still don’t know whether results are reliable

31. Significance tests
Significance tests tell us how confident we can be that there really is a difference
Null hypothesis: there is no “real” difference
Alternative hypothesis: there is a difference
A significance test measures how much evidence there is in favor of rejecting the null hypothesis
E.g. 10 cross-validation scores: B better than A?
mean A
mean B
P(perf)
Algorithm A
Algorithm B
perf
x x x xxxxx x x
x x x xxxx x x x

32. 32
Paired t-test
P(perf)
Algorithm A
Algorithm B
perf
Student’s t-test tells whether the means of two samples (e.g., 10 cross-validation scores) are significantly different
Use a paired t-test when individual samples are paired
i.e., they use the same randomization
Same CV folds are used for both algorithms
William Gosset
Born: 1876 in Canterbury; Died: 1937 in Beaconsfield, England
Worked as chemist in the Guinness brewery in Dublin in Invented the t-test to handle small samples for quality control in brewing. Wrote under the name "Student".

33. Performing the test Fix a significance level 
P(perf)
Algoritme A
Algoritme B
Fix a significance level 
Significant difference at % level implies (100-)% chance that there really is a difference
Scientific work: 5% or smaller (>95% certainty)
Divide  by two (two-tailed test)
Look up the z-value corresponding to /2:
If t  –z or t  z: difference is significant
null hypothesis can be rejected
perf α z
0.1%
4.3
0.5%
3.25 1%
2.82 5%
1.83
10%
1.38
20%
0.88