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On Comparing Classifiers: Pitfalls to Avoid and Recommended Approach Published by Steven L. Salzberg Presented by Prakash Tilwani MACS 598 April 25 th 2001

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Agenda Introduction Classification basics Definitions Statistical validity Bonferroni Adjustment Statistical Accidents Repeated Tuning A Recommended Approach Conclusion

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Introduction Comparative studies – proper methodology? Public databases – relied too heavily on them? Comparison results – are they really correct or just statistical accidents?

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Definitions T-test F-test P-value Null hypothesis

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T-test The t-test assesses whether the means of two groups are statistically different from each other. Ratio of difference in means to variability of groups.

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F-test It determines whether the variances of two samples are significantly different. Ratio of variance of two datasets Basis for “Analysis of Variance” (ANOVA)

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p-value It represents probability of concluding (incorrectly) that there is a difference in samples when no true difference exists. Dependent upon the statistical test being performed. P = 0.05 means that there is 5% chance that you would be wrong if concluding the populations are different.

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NULL Hypothesis Assumption that there is no difference in two or more populations. Any observed difference in samples is due to chance or sampling error.

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Statistical Validity Tests Statistics offers many tests that are designed to measure the significance of any difference. Adaptation to classifier comparison should be done carefully.

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Bonferroni Adjustment – an example Comparison of classifier algorithms 154 datasets NULL hypothesis is true if p-value is < 0.05 (not very stringent) Differences were reported significant if a t-test produced p-value < 0.05.

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Example (cont.) This is not correct usage of p-value significance test. There were 154 experiments. Therefore, 154 chances to be significant. Actual p-value used is 154*0.05 (= 7.7).

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Example (cont.) Let the significance for each level be Chance for making right conclusion for one experiment is 1- Assuming experiments are independent of one another, chance for getting n experiments correct is (1- ) n Chances of not making correct conclusion is 1-(1- ) n

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Example (cont.) Substituting =0.05 Chances for making incorrect conclusion is 0.9996 To obtain results significant at 0.05 level with 154 tests 1-(1- ) 154 < 0.05 or < 0.003

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Example - conclusion Rough calculations but provides insight to problem The use of wrong p-value results in incorrect conclusions T-test overall is wrong test as training and test sets are not independent

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Simple Recommended Statistical Test Comparison must consider 4 numbers when a common test set to compare two algorithms (A and B) A > B A < B A = B ~A = ~B

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Simple Recommended Statistical Test (cont.) If only two algorithms compared Throw out ties. Compare A>B Vs A<B If more than two algorithms compared Use “Analysis of Variance” (ANOVA) Bonferroni adjustment for multiple test should be applied

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Statistical Accidents Suppose 100 people are studying the effect of algorithms A and B. At least 5 will get results statistically significant at p <= 0.05 (assuming independent experiments). These results are nothing but due to chance.

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Repeated Tuning Algorithms are “tuned” repeatedly on same datasets. Every “tuning” attempt should be considered as a separate experiment. For example if 10 tuning experiments were attempted, then p-value should be 0.005 instead of 0.05.

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Repeated Tuning (cont.) Datasets are not independent, therefore even Bonferroni adjustment is not very accurate. A greater problem occurs while using an algorithm that has been used before: you may not know how it was tuned (one disadvantage of using public databases).

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Repeated Tuning – Recommended approach Break dataset into k disjoint subsets of approximately equal size. K experiments are performed. After every experiment one subset is removed. Trained system is tested on held-out subsystem.

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Repeated Tuning – Recommended approach (cont.) At the end of k-fold experiment, every sample has been used in test set exactly once. Advantage: test sets are independent. Disadvantage: training sets are clearly not independent.

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A Recommended Approach Choose other algorithms to include in the comparison. Try including most similar to new algorithm. Choose datasets. Divide the data set into k subsets for cross validation. Typically k=10. For a small data set, choose larger k, since this leaves more examples in the training set.

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A Recommended Approach (cont.) Run a cross-validation For each of the k subsets of the data set D, create a training set T = D – k Divide T into T1 (training) and T2 (tuning) subsets Once tuning is done, rerun training on T Finally measure accuracy on k Overall accuracy is averaged across all k partitions.

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A Recommended Approach (cont.) Finally, compare algorithms In case of multiple data sets, Bonferroni adjustment should be applied

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Conclusion We don’t mean to discourage empirical comparisons but to provide suggestions to avoid pitfalls. Statistical tools should be used carefully. Every details of the experiment should be reported.

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