CSS.207.1: Probability
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In Fall 2022, I am offering a graduate-level course on Probability Theory and its applications. This course will tentatively cover the following topics.
A. Probability Measures
- Measure Spaces, Sigma-Algebras, Probability measures
- Expectation, Convergence Theorems, Product Measures
- Conditional Expectation
B. Random Variables and Stochastic Processes
- Distribution functions, Moment Generating functions
- Multivariate Normal Distribution and its properties
- Basic Concentration Inequalities
- Convergence of random variables, Law of Large Numbers, Martingale Convergence Theorems
- Basics of Markov Chains
C. Application to Learning Theory
- Generalization bounds, symmetrization, and concentration
- Basics of High Dimensional Probability
Prerequisites
Undergraduate-level probability, basic mathematical analysis
Evaluations
Problem-solving will be our primary vehicle for learning the material. We will have bi-weekly problem sets, a mid-term and a final exam. The final grade will be a weighted average of these three components as detailed below:
- Problem Sets (50%)
- Mid-term (20%)
- Final Exam (30%)
Logistics
- Schedule: Monday (4 - 5:30 pm) and Thursday (4 - 5:30 pm)
- Venue: A-201
References
We will not follow any one particular source, in general. However, the following references will be useful