Introduction to Statistical Machine Learning

Part I: Introduction to Statistics and Probability 1. Random variables and probability distributions 2. Examples of discrete probability distributions 3. Examples of continuous probability distributions 4. Multi-dimensional probability distributions 5. Examples of multi-dimensional probability distributions 6. Random sample generation from arbitrary probability distributions 7. Probability distributions of the sum of independent random variables 8. Probability inequalities 9. Statistical inference 10. Hypothesis testing Part II: Generative Approach to Statistical Pattern Recognition 11. Fundamentals of statistical pattern recognition 12. Criteria for developing classifiers 13. Maximum likelihood estimation 14. Theoretical properties of maximum likelihood estimation 15. Linear discriminant analysis 16. Model selection for maximum likelihood estimation 17. Maximum likelihood estimation for Gaussian mixture model 18. Bayesian inference 19. Numerical computation in Bayesian inference 20. Model selection in Bayesian inference 21. Kernel density estimation 22. Nearest neighbor density estimation Part III: Discriminative Approach to Statistical Machine Learning 23. Fundamentals of statistical machine learning 24. Learning Models 25. Least-squares regression 26. Constrained least-squares regression 27. Sparse regression 28. Robust regression 29. Least-squares classification 30. Support vector classification 31. Ensemble classification 32. Probabilistic classification 33. Structured classification Part IV: Further Topics 34. Outlier detection 35. Unsupervised dimensionality reduction 36. Clustering 37. Online learning 38. Semi-supervised learning 39. Supervised dimensionality reduction 40. Transfer learning 41. Multi-task learning