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**Learning Algorithm Evaluation**

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**Algorithm evaluation: Outline**

Why? Overfitting How? Train/Test vs Cross-validation What? Evaluation measures Who wins? Statistical significance

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Introduction

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

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**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?

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Evaluation Rule #1 Never evaluate on training data!

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

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Train and Test Step 2: Train model on training data

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Train and Test Step 3: Evaluate model on test data

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

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**Evaluation Rule #1 Rule #2 Never evaluate on training data!**

Never train on test data! (that includes parameter setting or feature selection)

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**Train and Test Step 4: Optimize parameters on separate validation set**

testing

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**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

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**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

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

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Cross-Validation

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**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

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**Cross-validation Standard method: 10? Enough to reduce sampling bias**

Stratified ten-fold cross-validation 10? Enough to reduce sampling bias Experimentally determined

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**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

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ROC Analysis

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**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)

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**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):

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**ROC space classifiers J48 parameters fitted J48 OneR**

P(TP): % true positives: sensitivity P(FP): % false positives: 1 – specificity

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**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

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**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

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**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

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**ROC Space and Costs equal costs skewed costs**

P(TP): % true positives: sensitivity P(FP): % false positives: 1 – specificity

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**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

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**Statistical Significance**

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**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

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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

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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".

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**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

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