Introduction to Statistical Machine Learning

Part I: Introduction to Statistics and Probability1. Random variables and probability distributions2. Examples of discrete probability distributions3. Examples of continuous probability distributions4. Multi-dimensional probability distributions5. Examples of multi-dimensional probability distributions6. Random sample generation from arbitrary probability distributions7. Probability distributions of the sum of independent random variables8. Probability inequalities9. Statistical inference10. Hypothesis testing

Part II: Generative Approach to Statistical Pattern Recognition11. Fundamentals of statistical pattern recognition12. Criteria for developing classifiers13. Maximum likelihood estimation14. Theoretical properties of maximum likelihood estimation15. Linear discriminant analysis16. Model selection for maximum likelihood estimation17. Maximum likelihood estimation for Gaussian mixture model18. Bayesian inference19. Numerical computation in Bayesian inference20. Model selection in Bayesian inference21. Kernel density estimation22. Nearest neighbor density estimation

Part III: Discriminative Approach to Statistical Machine Learning23. Fundamentals of statistical machine learning24. Learning Models25. Least-squares regression26. Constrained least-squares regression27. Sparse regression28. Robust regression29. Least-squares classification30. Support vector classification31. Ensemble classification32. Probabilistic classification33. Structured classification

Part IV: Further Topics34. Outlier detection35. Unsupervised dimensionality reduction36. Clustering37. Online learning38. Semi-supervised learning39. Supervised dimensionality reduction40. Transfer learning41. Multi-task learning