1. Robust Optimization and Applications in Machine Learning

2. Part 2: Robust Classification

3. Data matrix

4. Classification problems

5. What is a linear classifier?

6. Separable data

7. Non-separable data

8. Loss functions

9. Two specific loss functions

10. Generalization error and regularization

11. Regularization and Sparsity

12. Robust classification

13. Formulation of robustness approach

14. Non-separable case

15. Link with worst-case loss minimization

16. Box uncertainty model

17. Formulation

18. Link with worst-case loss minimization

19. Our findings so far

20. Part 2: Robust Classification

21. Classification with interval data

22. Robust classification: main idea

23. Main results

24. Part 2: Robust Classification

25. Robust classification with hinge loss

26. Bound on robust SVM

27. Part 2: Robust Classification

28. Robust LR classification

29. Robust LR: dual

30. Moment matching

31. Part 2: Robust Classification

32. Minimax probability machine

33. Problem statement

34. Problem formulation

35. Marhsall and Olkin’s result? ?

36. SOCP formulation

37. Dual problem

38. Geometric interpretation

39. Solving the problem

40. Robustness to estimation errors

41. Robust MPM

42. Formulation of Robust MPM
Lemma

43. R-MPM: A Specific Uncertainty Model (1)

44. R-MPM: A Specific Uncertainty Model (2)

45. Robust MPM: Estimation Errors in Means

46. Rost MPM: Estimation Errors in Covariance

47. R-MPM: putting everything together

48. Part 2: summary