Machine learning continued

1. Machine learning continued Image source: https://www.coursera.org/course/ml

2. More about linear classifiers • When the data is linearly separable, there may be more than one separator (hyperplane) Which separatoris best?

3. Support vector machines • Find hyperplane that maximizes the margin between the positive and negative examples C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

4. Support vector machines • Find hyperplane that maximizes the margin between the positive and negative examples For support vectors, Distance between point and hyperplane: Therefore, the margin is 2 / ||w|| Support vectors Margin C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

5. Finding the maximum margin hyperplane • Maximize margin 2 / ||w|| • Correctly classify all training data: • Quadratic optimization problem: C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

6. Finding the maximum margin hyperplane • Solution: learnedweight Support vector C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

7. Finding the maximum margin hyperplane • Solution:b = yi – w·xi for any support vector • Classification function (decision boundary): • Notice that it relies on an inner product between the testpoint x and the support vectors xi • Solving the optimization problem also involvescomputing the inner products xi· xjbetween all pairs oftraining points C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

8. x 0 x 0 x2 Nonlinear SVMs • Datasets that are linearly separable work out great: • But what if the dataset is just too hard? • We can map it to a higher-dimensional space: 0 x Slide credit: Andrew Moore

9. Nonlinear SVMs • General idea: the original input space can always be mapped to some higher-dimensional feature space where the training set is separable Φ: x→φ(x) Slide credit: Andrew Moore

10. Nonlinear SVMs • The kernel trick: instead of explicitly computing the lifting transformation φ(x), define a kernel function K such thatK(x,y) = φ(x)· φ(y) • (to be valid, the kernel function must satisfy Mercer’s condition) • This gives a nonlinear decision boundary in the original feature space: C. Burges, A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 1998

11. x2 Nonlinear kernel: Example • Consider the mapping

12. Polynomial kernel:

13. Gaussian kernel • Also known as the radial basis function (RBF) kernel: • The corresponding mapping φ(x)is infinite-dimensional! • What is the role of parameter σ? • What if σ is close to zero? • What if σ is very large?

14. Gaussian kernel SV’s

15. What about multi-class SVMs? • Unfortunately, there is no “definitive” multi-class SVM formulation • In practice, we have to obtain a multi-class SVM by combining multiple two-class SVMs • One vs. others • Traning: learn an SVM for each class vs. the others • Testing: apply each SVM to test example and assign to it the class of the SVM that returns the highest decision value • One vs. one • Training: learn an SVM for each pair of classes • Testing: each learned SVM “votes” for a class to assign to the test example

16. SVMs: Pros and cons • Pros • Many publicly available SVM packages:http://www.kernel-machines.org/software • Kernel-based framework is very powerful, flexible • SVMs work very well in practice, even with very small training sample sizes • Cons • No “direct” multi-class SVM, must combine two-class SVMs • Computation, memory (esp. for nonlinear SVMs) • During training time, must compute matrix of kernel values for every pair of examples • Learning can take a very long time for large-scale problems

17. Beyond simple classification: Structured prediction Word Image Source: B. Taskar

18. Structured Prediction Parse tree Sentence Source: B. Taskar

19. Structured Prediction Word alignment Sentence in two languages Source: B. Taskar

20. Structured Prediction Bond structure Amino-acid sequence Source: B. Taskar

21. Structured Prediction • Many image-based inference tasks can loosely be thought of as “structured prediction” model Source: D. Ramanan

22. Unsupervised Learning • Idea: Given only unlabeled data as input, learn some sort of structure • The objective is often more vague or subjective than in supervised learning • This is more of an exploratory/descriptive data analysis

23. Unsupervised Learning • Clustering • Discover groups of “similar” data points

24. Unsupervised Learning • Quantization • Map a continuous input to a discrete (more compact) output 2 1 3

25. Unsupervised Learning • Dimensionality reduction, manifold learning • Discover a lower-dimensional surface on which the data lives

26. Unsupervised Learning • Density estimation • Find a function that approximates the probability density of the data (i.e., value of the function is high for “typical” points and low for “atypical” points) • Can be used for anomaly detection

27. Semi-supervised learning • Lots of data is available, but only small portion is labeled (e.g. since labeling is expensive) • Why is learning from labeled and unlabeled data better than learning from labeled data alone? ?

28. Active learning • The learning algorithm can choose its own training examples, or ask a “teacher” for an answer on selected inputs S. Vijayanarasimhan and K. Grauman, “Cost-Sensitive Active Visual Category Learning,” 2009

29. Lifelong learning http://rtw.ml.cmu.edu/rtw/

30. Lifelong learning http://rtw.ml.cmu.edu/rtw/

31. Xinlei Chen, AbhinavShrivastava and Abhinav Gupta. NEIL: Extracting Visual Knowledge from Web Data. In ICCV 2013