Big Data Analytics. Special Topics for Computer Science CSE CSE Feb 24

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1 Big Data Analytics Special Topics for Computer Science CSE CSE Feb 24 Fei Wang Associate Professor Department of Computer Science and Engineering

2 Prediction III

3 Goal of Supervised Learning Minimize the probability of model prediction errors on future data Two Competing Methodologies Build one really good model Traditional approach Build many models and average the results Ensemble learning (more recent)

4 Single Model Philosophy Motivation: Occam s Razor one should not increase, beyond what is necessary, the number of entities required to explain anything Infinitely many models can explain any given dataset Might as well pick the smallest one

5 Support Vector Machine Minimize the number of Support Vectors! Maximized Margin

6 Support Vector Machines! The$old$formula-on:$ Find w and b such that Φ(w) =½ w T w is minimized and for all {(x i,y i )} y i (w T x i + b) 1! The$new$formula-on$incorpora-ng$slack$variables:$ Find w and b such that Φ(w) =½ w T w + CΣξ i is minimized and for all {(x i,y i )} y i (w T x i + b) 1- ξ i and ξ i 0 for all i! Parameter$C$can$be$viewed$as$a$way$to$control$overfi=ng$! A$regulariza-on$term$

7 Loss Hinge Loss Find w and b such that Φ(w) =½ w T w + CΣξ i is minimized and for all {(x i,y i )} y i (w T x i + b) 1- ξ i and ξ i 0 for all i Parameter$C$can$be$viewed$as$a$way$to$control$overfi=ng$ al SVM arises by considering the specific loss 1 n argmin (1 y i f (x i )) + + λ f V (f (x, y)) (1 yf 2 H n (x)). +, f H i=1 (k) + max(k, 0).

8 Least Square Regression

9 Ridge Regression

10 Gradient Similarly to the usual derivative, the gradient represents the slope of the tangent of the graph of the function. More precisely, the gradient points in the direction of the greatest rate of increase of the function and its magnitude is the slope of the graph in that direction.

11 Gradient

12 Ensemble Methods Learn multiple alternative definitions of a concept using different training data or different learning algorithms. Combine decisions of multiple definitions, e.g. using weighted voting. Training Data Data1 Data2 Data m Learner1 Learner2 Learner m Model1 Model2 Model m Model Combiner Final Model

13 Bootstrap! Repeatedly draw n samples from D! For each set of samples, estimate a statistic! The bootstrap estimate is the mean of the individual estimates! Used to estimate a statistic (parameter) and its variance

14 Bagging! For i = 1.. M " Draw n * <n samples from D with replacement " Learn classifier C i! Final classifier is a vote of C 1.. C M! Increases classifier stability/reduces variance

15 Bagging Example

16 Boosting An ensemble-learning method One of the most powerful learning ideas introduced in the past 10+ years A procedure that combines many weak classifiers to produce a powerful committee

17 Boosting In an ensemble, the output of an instance is computed by averaging the output of several hypothesis Choose the individual classifiers and their ensembles to get a good fit Instead of constructing the hypothesis independently, construct them such that new hypothesis focus on instance that were problematic for the previous hypothesis Boosting implements this idea!

18 Boosting New classifiers should focus on difficult cases Examine the learning set Get some rule of thumb (weak learner ideas) Reweight the examples of the training set, concentrate on hard cases for the previous rule Derive the next rule of thumb!. Build a single, accurate predictor by combining the rules of thumb Challenges: how to reweight? How to combine?

19 AdaBoost The most popular boosting algorithm Fruend and Schapire (1997) Consider a two-class problem, output variable coded as Y {-1,+1} For a predictor variable X, a classifier G(X) produces predictions that are in {-1,+1} The error rate on the training sample is 1 N err = N i= 1 I(y G(x )) i i

20 AdaBoost Sequentially apply the weak classification to repeatedly modified versions of data! produce a sequence of weak classifiers G m (x) m=1,2,..,m The predictions from all classifiers are combined via majority vote to produce the final prediction

21 AdaBoost Some slides borrowed from

22 AdaBoost

23 The Strength of Ensemble Learning

24 Source Additive Model

25 Forward Stagewise Additive Modeling An approximate solution to the minimization problem is obtained via forward stagewise additive modeling (greedy algorithm) Source

26 Why AdaBoost Works Adaboost is a forward stagewise additive algorithm using the loss function Source

27 Why AdaBoost Works

28 Loss Functions

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