36-700 Probability and Mathematical Statistics I
This course covers the fundamentals of theoretical statistics. Topics include: concentration of measure, basic empirical process theory, convergence, point and interval estimation, maximum likelihood, hypothesis testing, Bayesian inference, nonparametric statistics and bootstrap re-sampling. This course is excellent preparation for advanced work in Statistics and Machine Learning. See below for a detailed schedule.
Course Syllabus
The syllabus provides information on grading, class policies etc.
Lecture Notes
- Lecture 1: (8/29) Probability Review 1
- Lecture 2: (8/31) Probability Review 2
- Lecture 3: (9/2) Probability Review 3
- Lecture 4: (9/7) Expectations, Conditional Expectations and the MGF
- Lecture 5: (9/9) Concentration Inequalities
- Lecture 6: (9/12) More Concentration Inequalities, WLLN
- Lecture 7: (9/14) Stochastic Convergence, CLT
- Lecture 8: (9/16) Point Estimation
- Lecture 9: (9/19) Constructing Estimators 1
- Lecture 10: (9/21) Constructing Estimators 2
- Lecture 11: (9/23) Comparing Estimators
- Lecture 12: (9/26) MLE Asymptotics
- Lecture 13: (9/28) Estimating the CDF
- Lecture 14: (9/30) Bootstrap
- Lecture 15: (10/3) Linear Regression 1
- Lecture 16: (10/5) Linear Regression 2
- Lecture 17: (10/7) Non-Parametric Regression 1
- Lecture 18: (10/10) Non-Parametric Regression 2
- Lecture 19: (10/12) Non-Parametric Density Estimation 1
- Lecture 20: (10/14) Non-Parametric Density Estimation 2
- Lecture 21: (10/19) Cross-Validation
- Lecture 22: (10/24) Hypothesis Testing 1
- Lecture 23: (10/26) Hypothesis Testing 2
- Lecture 24: (10/28) Hypothesis Testing 3
- Lecture 25: (10/31) The Permutation Test
- Lecture 26: (11/2) Multiple Testing
- Lecture 27: (11/4) Multiple Testing 2
- Lecture 28: (11/7) Causal Inference 1
- Lecture 29: (11/14) Causal Inference 2
- Lecture 30: (11/16) Directed Graphical Models
- Lecture 31: (11/18) Directed Graphical Models
- Lecture 32: (11/28) Classification
- Lecture 33: (11/30) Logistic Regression
- Lecture 34: (12/2) Sampling and Integration
- Lecture 35: (12/5) MCMC
- Lecture 36: (12/7) Model Selection