Statistics and Learning Theory for Computer Scientists

Undergraduate

This course explores the basic mathematical foundation of learning theory and statistics from a computer science perspective. This is a proof based course and mathematical maturity is necessary to follow the material of the course. The course is divided in three parts. The first part covers the basic mathematical theory of that is used in statistical analysis and includes: (a) log-likelihood estimation for parametric models, (b) density estimation, (c) hypothesis testing, p-values and confidence intervals. The second part covers statistical learning theory: (i) definition of PAC learning and agnostic learning, (ii) uniform convergence, (iii) learnability via VC dimension and Rademacher complexity, (iv) computational aspects of learning theory. The final part is related to modern challenges in statistics and learning theory from a computational perspective and includes: (1) statistical analysis with corrupted data, (2) missing data and causal inference, (3) computationally efficient methods for learning theory, and (4) statistical analysis while preserving privacy, i.e., the notion of differential privacy and its applications. This is an advanced course, which requires mathematical maturity and comfort with multivariate calculus, linear algebra, and probability theory. The course also assumes prior knowledge of discrete mathematics and algorithms (CPSC 202 and CPSC 365 or equivalent). TTh 2:35pm-3:50pm