Mathematical Foundations for Machine Learning I: Probability

Catalog description

This course introduces students to the mathematical foundations of the theory of probability. In addition to a host of classical domains, probability is one of the foundational elements of modern data science, machine learning, and artificial intelligence. The course begins with an exploration of combinatorial probabilities in the classical setting of games of chance, proceeds to the development of an axiomatic, fully mathematical theory of probability, and concludes with the discovery of the remarkable limit laws and the eminence grise of the classical theory, the central limit theorem. The topics covered include: discrete and continuous probability space, distributions, mass functions, densities; conditional probability; independence; the Bernoulli schema: the binomial, Poisson, and waiting time distributions; uniform, exponential, normal, and related densities; expectation, variance, moments; conditional expectation; inequalities, tail bounds, and limit laws. This material is presented in its lush and glorious historical context, the mathematical theory buttressed and made vivid by rich and beautiful applications drawn from the world around us. Students are assessed by weekly problem set assignments and a proctored exam. Prerequisite: Understanding of Calculus.