Office hours: After class and by appointment
Office hours: TBD
Class email list: cse599s_wi16 [click the link to sign up]
Homeworks: Homework policy will be discussed in class.
class  topic  notes  related material 
6Jan  Entropy and relative entropy. Optimality conditions in convex optimization. Matrix scaling.  pdf
06Apr2018  
8Jan  Multiplicativeweights update. The SinkhornKnopp scaling algorithm.  pdf
06Apr2018 

13Jan  Mirror descent and density approximation.  pdf
06Apr2018  
15Jan  Discrete Fourier analysis. Chang's Lemma and generalizations  pdf
06Apr2018  
20Jan  Lifts of polytopes and nonnegative rank  pdf
06Apr2018 

22Jan  Junta degree and hardness amplification  pdf
06Apr2018 

27Jan  From junta degree to nonnegative rank  pdf
06Apr2018  
29Jan  Spectrahedral lifts and positive semidefinite rank  pdf
06Apr2018  
10Feb  Bregman divergences and mirror descent [again] 
see Lec. 3 for now; these notes will be merged 

12Feb  Quantum entropy maximization (and hyperbolic cones)  pdf
06Apr2018  
17Feb  The Schrodinger problem and entropic interpolation  
19Feb  Mixing times and convergence to equlibrium  Chapter 1 of MontenegroTetali 

24Feb  Entropytransport and discrete curvature [live stream @ 10:25am]  powerpoint  pdf  video  
26Feb  LogSobolev inequalities, hypercontractivity, and localitysensitive hashing  pdf
06Apr2018 

2Mar  [continued]  
4Mar  Entropic interpolation over Brownian motion and BrascampLieb inequalities  notes  
9Mar  No class: Grad student visit days  
11Mar  FollmerBorell interpolation  notes 
Consider the set of all probability distributions on a finite set that satisfy a given collection of linear inequalities. For instance, we might specify various linear marginals or bounds on the probabilities of certain events. This set of distributions is a finitedimensional polytope, and we can choose a distinguished element from that polytope by picking the one of maximum (Shannon) entropy. This course concerns the remarkable properties of such maximizers, along with a host of applications in computer science and mathematics. Every topic is teeming with fantastic open problems.