Taming the Learning Zoo

1. Taming the Learning Zoo

2. Supervised Learning Zoo • Bayesian learning (find parameters of a probabilistic model) • Maximum likelihood • Maximum a posteriori • Classification • Decision trees (discrete attributes, few relevant) • Support vector machines (continuous attributes) • Regression • Least squares (known structure, easy to interpret) • Neural nets (unknown structure, hard to interpret) • Nonparametric approaches • k-Nearest-Neighbors • Locally-weighted averaging / regression

3. Very approximate “cheat-sheet” for techniques Discussed in Class

4. Very approximate “cheat-sheet” for techniques Discussed in Class • Note: we have looked at a limited subset of existing techniques in this class (typically, the “classical” versions). • Most techniques extend to: • Both C/R tasks (e.g., support vector regression) • Both continuous and discrete attributes • Better scalability for certain types of problem With “sufficiently large” data sets With “sufficiently diverse” weak leaners

5. Agenda • Quantifying learner performance • Cross validation • Error vs. loss • Precision & recall • Model selection

6. Cross-Validation

7. Assessing Performance of a Learning Algorithm • Samples from X are typically unavailable • Take out some of the training set • Train on the remaining training set • Test on the excluded instances • Cross-validation

8. - - + - + - - - - + + + + - - + + + + - - - + + Cross-Validation • Split original set of examples, train Examples D Train Hypothesis space H

9. - - - - + + + + + + - - + Cross-Validation • Evaluate hypothesis on testing set Testing set Hypothesis space H

10. Cross-Validation • Evaluate hypothesis on testing set Testing set - + + - + + + Test - + + - - - Hypothesis space H

11. - - - - + + + + + + - - + Cross-Validation • Compare true concept against prediction 9/13 correct Testing set - + + - + + + - + + - - - Hypothesis space H

12. Common Splitting Strategies • k-fold cross-validation Dataset Train Test

13. Common Splitting Strategies • k-fold cross-validation • Leave-one-out (n-fold cross validation) Dataset Train Test

14. Computational complexity • k-fold cross validation requires • k training steps on n(k-1)/k datapoints • k testing steps on n/k datapoints • (There are efficient ways of computing L.O.O. estimates for some nonparametric techniques, e.g. Nearest Neighbors) • Average results reported

15. Bootstrapping • Similar technique for estimating the confidence in the model parameters • Procedure: • Draw k hypothetical datasets from original data. Either via cross validation or sampling with replacement. • Fit the model for each dataset to compute parameters k • Return the standard deviation of 1,…,k (or a confidence interval) Can also estimate confidence in a prediction y=f(x)

16. Simple Example: average of N numbers • Data D={x(1),…,x(N)}, model is constant  • Learning: minimize E() = i(x(i)-)2=> compute average • Repeat for j=1,…,k : • Randomly sample subset x(1)’,…,x(N)’ from D • Learn j = 1/N i x(i)’ • Return histogram of 1,…,j

17. Beyond Error Rates

18. Beyond Error Rate • Predicting security risk • Predicting “low risk” for a terrorist, is far worse than predicting “high risk” for an innocent bystander (but maybe not 5 million of them) • Searching for images • Returning irrelevant images is worse than omitting relevant ones

19. Biased Sample Sets • Often there are orders of magnitude more negative examples than positive • E.g., all images of Kris on Facebook • If I classify all images as “not Kris” I’ll have >99.99% accuracy • Examples of Kris should count much more than non-Kris!

20. False Positives True concept Learned concept x2 x1

21. False Positives An example incorrectly predicted to be positive True concept Learned concept x2 New query x1

22. False Negatives An example incorrectly predicted to be negative True concept Learned concept x2 New query x1

23. Precision vs. Recall • Precision • # of relevant documents retrieved / # of total documents retrieved • Recall • # of relevant documents retrieved / # of total relevant documents • Numbers between 0 and 1

24. Precision vs. Recall • Precision • # of true positives / (# true positives + # false positives) • Recall • # of true positives / (# true positives + # false negatives) • A precise classifier is selective • A classifier with high recall is inclusive

25. Reducing False Positive Rate True concept Learned concept x2 x1

26. Reducing False Negative rate True concept Learned concept x2 x1

27. Precision-Recall curves Measure Precision vs Recall as the classification boundary is tuned Perfect classifier Recall Actual performance Precision

28. Precision-Recall curves Measure Precision vs Recall as the classification boundary is tuned Recall Penalize false negatives Equal weight Penalize false positives Precision

29. Precision-Recall curves Measure Precision vs Recall as the classification boundary is tuned Recall Precision

30. Precision-Recall curves Measure Precision vs Recall as the classification boundary is tuned Recall Better learningperformance Precision

31. Option 1: Classification Thresholds • Many learning algorithms (e.g., linear models, NNets, BNs, SVM) give real-valued output v(x) that needs thresholding for classification v(x) > t => positive label given to x v(x) < t => negative label given to x • May want to tune threshold to get fewer false positives or false negatives

32. Option 2: Loss functions & Weighted datasets • General learning problem: “Given data D and loss function L, find the hypothesis from hypothesis class H that minimizes L” • Loss functions: L may contain weights to favor accuracy on positive or negative examples • E.g., L = 10 E++ 1 E- • Weighted datasets: attach a weight w to each example to indicate how important it is • Or construct a resampled dataset D’ where each example is duplicated proportionally to its w

33. Model Selection

34. Complexity Vs. Goodness of Fit • More complex models can fit the data better, but can overfit • Model selection: enumerate several possible hypothesis classes of increasing complexity, stop when cross-validated error levels off • Regularization: explicitly define a metric of complexity and penalize it in addition to loss

35. Model Selection with k-fold Cross-Validation • Parameterize learner by a complexity level C • Model selection pseudocode: • For increasing levels of complexity C: • errT[C],errV[C] = Cross-Validate(Learner,C,examples) • If errT has converged, • Find value Cbest that minimizes errV[C] • Return Learner(Cbest,examples)

36. Regularization • Minimize: • Cost(h) = Loss(h) +  Complexity(h) • Example with linear models y = Tx: • L2 error: Loss() = i (y(i)-Tx(i))2 • Lq regularization: Complexity(): j|j|q • L2 and L1 are most popular in linear regularization • L2regularization leads to simple computation of optimal  • L1 is more complex to optimize, but produces sparse models in which many coefficients are 0!

37. Data Dredging • As the number of attributes increases, the likelihood of a learner to pick up on patterns that arise purely from chance increases • In the extreme case where there are more attributes than datapoints (e.g., pixels in a video), even very simple hypothesis classes can overfit • E.g., linear classifiers • Many opportunities for charlatans in the big data age!

38. Other topics in Machine Learning • Unsupervised learning • Dimensionality reduction • Clustering • Reinforcement learning • Agent that acts and learns how to act in an environment by observing rewards • Learning from demonstration • Agent that learns how to act in an environment by observing demonstrations from an expert

39. Issues in Practice • The distinctions between learning algorithms diminish when you have a lot of data • The web has made it much easier to gather large scale datasets than in early days of ML • Understanding data with many more attributes than examples is still a major challenge! • Do humans just have really great priors?

40. Next Lectures • Temporal sequence models (R&N 15) • Decision-theoretic planning • Reinforcement learning • Applications of AI