CS 294 - The Mathematics of Information and Data

This course will explore the foundations of an emerging discipline: the mathematics of information and data. Through recent and classic texts in mathematical statistics, optimization, and computer science, we will find unifying themes in these three disciplinary approaches. We will draw connections between how we analyze running time, statistical accuracy, and implementation of data-driven computations. We will focus in particular on large deviation inequalities, convex analysis and their applications in minimax statistics; sparse and stochastic optimization; and discrete and convex geometry. This course is ideal for advanced graduate students who would like to apply these theoretical and algorithmic developments to their own research.

Consent of the instructor is required. Graduate level courses in probability and optimization will be necessary.

The current list of topics (which will change depending on the course we chart) is:

1. Stochastic Optimization
   • stochastic gradients, online learning, and the Kaczmarz algorithm
   • core sets and importance sampling
   • randomized algorithms for linear systems
2. Random Matrices
   • Elementary analysis of random matrices
   • Graph sparsification, frames, and matrix approximation
   • Noncommutative Chernoff Bounds
3. Average Case Analysis of Optimization Problems
   • covering numbers, VC dimension, rademacher complexity
   • metric embedding and restricted isometries
   • compressed sensing and all that it has wrought