What makes good ensemble? CS789: Machine Learning and Neural Network. Introduction. More on diversity

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1 What makes good ensemble? CS789: Machine Learning and Neural Network Ensemble methods Jakramate Bootkrajang Department of Computer Science Chiang Mai University 1. A member of the ensemble is accurate. An accurate classifier is one that has error rate of better than random guessing ϵ < The ensemble is composed of diverse classifiers. Two classifiers are diverse if they make differrent errors on new data points. Jakramate Bootkrajang CS789: Machine Learning and Neural Network 1 / 20 Introduction Jakramate Bootkrajang CS789: Machine Learning and Neural Network 3 / 20 More on diversity We ve seen the working of a single classifier. We will now explore the possibility of combining outputs of those classifiers to make (more accurate) prediction. The method is call ensemble learning To see why diversity is important, imagine there are three classifier in the ensemble h 1, h 2, h 3 If the three classifiers predict the same thing (not diverse) then when h 1 makes a mistake the others will too. But if the classifiers are uncorrelated (diverse) when h1 makes a mistake, h 2, h 3 might not and by majority voting the final prediction is still correct. Jakramate Bootkrajang CS789: Machine Learning and Neural Network 2 / 20 Jakramate Bootkrajang CS789: Machine Learning and Neural Network 4 / 20

2 Reasons why ensemble often be more accurate [1/3] It solves statistical problem related to learning from limited number of training data. Ensemble reduces the risk of choosing wrong hypothesis. Reasons why ensemble often be more accurate [3/3] Ensemble alleviates the wrong choice of choosing hypothesis space. That is data is not linearly-separable but linear hypothesis class is chosen. An ensemble of linear classifiers can have non-linear decision boundary. Jakramate Bootkrajang CS789: Machine Learning and Neural Network 5 / 20 Reasons why ensemble often be more accurate [2/3] Jakramate Bootkrajang CS789: Machine Learning and Neural Network 7 / 20 How to construct an ensemble? Even in the abundance of data, the problem might have several local optima. Ensemble reduces the risk of stucking in local optima. Ensemble of G members in general is given by: f(x) = w i h i (x) Methods for constructing an ensemble differ in How to determine wi, the contribution of h i (x) How to get diverse set of h i (x). Introduce some randomness to the problem or learner Jakramate Bootkrajang CS789: Machine Learning and Neural Network 6 / 20 Jakramate Bootkrajang CS789: Machine Learning and Neural Network 8 / 20

3 Boostrap Aggregating: Bagging Bagging: Example (2/3) Manipulating the input data. How to get diverse h i (x)? Sample m examples from the training set randomly, with replacement. Train a classifier on the bootstrap replicate. For each boostrap, a classifier only see part of the whole data. What are the weights w i s? Classifiers are combined using identical weights. f bagging (x) = h i (x) Jakramate Bootkrajang CS789: Machine Learning and Neural Network 9 / 20 Bagging: Example (1/3) Jakramate Bootkrajang CS789: Machine Learning and Neural Network 11 / 20 Bagging: Example (3/3) Jakramate Bootkrajang CS789: Machine Learning and Neural Network 10 / 20 Jakramate Bootkrajang CS789: Machine Learning and Neural Network 12 / 20

4 Adaptive Boosting: AdaBoost AdaBoost: reweighting Place more weight on difficult examples. Instead of sampling, uses trainining set re-weighting. Place more weight on difficult examples. Classifiers are combined using f ada (x) = α i h i (x) α i is set according to h i s accuracy on the weighted training set. h i (x) is called a weak learner. D t+1 (i) = { Dt (i) exp( α t ) if y = h t (x i ) D t (i) exp(α t ) if y h t (x i ) α t is set according to h t s accuracy (1 ϵ t ) on the weighted training set. ϵ = 0.5, α = 0 ϵ = 0.4, α = 0.20 ϵ = 0.3, α = 0.42 (1) α t = 1 2 ln 1 ϵ t ϵ t (2) ϵ = 0.1, α = 1.09 Jakramate Bootkrajang CS789: Machine Learning and Neural Network 13 / 20 AdaBoost algorithm Jakramate Bootkrajang CS789: Machine Learning and Neural Network 15 / 20 Effect of ϵ on α (contribution) Data: S = {x i, y i } N, x i X and y i { 1, 1} initialization: uniform weight for initial data D 1 (i) = 1 N ; for t = 1... T do Learn a classifier h t : X { 1, 1} that minimises training error, ϵ j = N D t(i)[y i h j (x i )] ; if ϵ t > 0.5 then STOP; else Set α t = 1 2 ln 1 ϵ t ϵ t ; Reweighting by D t+1 (i) = D t(i) exp( α t y i h t (x i )) ; ( is a normaliser making N D t+1(i) = 1); end end Result: f ada (x) = T t=1 α th t (x) Contribution Error Jakramate Bootkrajang CS789: Machine Learning and Neural Network 14 / 20 Jakramate Bootkrajang CS789: Machine Learning and Neural Network 16 / 20

5 Boosting: Example (1/2) Summary Ensembles are method for obtaining highly accurate classifiers by combining less accurate ones. This is another approach to solve non-linear problem. Well known algorithms include, bagging and boosting. Jakramate Bootkrajang CS789: Machine Learning and Neural Network 17 / 20 Boosting: Example (2/2) Jakramate Bootkrajang CS789: Machine Learning and Neural Network 19 / 20 References Ensemble Methods in Machine Learning by Tom Dietterich. web.engr.oregonstate.edu/~tgd/publications/ mcs-ensembles.pdf Freund; Schapire (1999). A Short Introduction to Boosting (PDF): introduction to AdaBoost Jakramate Bootkrajang CS789: Machine Learning and Neural Network 18 / 20 Jakramate Bootkrajang CS789: Machine Learning and Neural Network 20 / 20