IE 690: Applied Probability for Machine
Learning
Spring 2020
1 Description:
The broad goal of this course is to study recent developments in the application of proba-
bilistic tools and methods to the analysis of statistical machine learning algorithms. The
intended audience of this course are Ph.D. students who work on theoretical questions
surrounding statistical machine learning (or intend to do so).
A solid background in stochastic processes (especially Markov processes)
and real analysis is necessary. Ideal preparation includes measure theory and grad-
uate level probability.
The course will be driven by paper readings carefully chosen and assigned to each
student. There is no required textbook, but “Applied Stochastic Analysis,” by Weinan,
Li and Vanden-Eijnden is a useful resource for the basic analytical tools needed. Here
is a tentative list of topics that will be covered in this course. It should be noted that
there is significant freedom in choosing topics, depending on the class interest.
Week 1-5 Stochastic analysis of “phase-space” algorithms: we will study the asymptotics and
transient behavior of algorithms like stochastic gradient descent (SGD), Langevin
Markov chain Monte Carlo (MCMC), stochastic Langevin gradient descent (SGLD)
etc. by passing to a continuum limit. Particular focus on weak convergence to
steady state behavior, large deviations principles and metastability analyses.
Week 6-11 Stochastic analysis of “measure-space” algorithms: we will study variational ap-
proximations for Bayesian computation and distributionally robust optimization
(DRO). Particular focus on connections to gradient flow theory on Wasserstein
spaces, connections with the analysis of phase-space algorithms.
Week 12-14 Applications of the analytical tools to reinforcement learning algorithms and/or
inference of dynamical systems from time series (time permitting).
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