
Aug 23: Introduction slides [pdf]

Aug 25: Statistical distances and concentration
[pdf]

Aug 30: Minimax setting, learning discrete distributions, lowerbound for learning Bernoulli distributions
[pdf]

Sep 01: Lower bound for general discrete distribution learning, basic information theory
[pdf]
Elements of Information Theory. T. Cover, J. Thomas
Assouad, Fano, and Le Cam. B. Yu

Sep 06: Information theory basics, metric entropy
[pdf]
Elements of Information Theory. T. Cover, J. Thomas. Chapter 2.
Combinatorial Methods in Density Estimation. L. Devroye, G. Lugosi

Sep 08: Metric entropy, Gaussian mixtures
[pdf]
Combinatorial Methods in Density Estimation. L. Devroye, G. Lugosi
Faster and Sample NearOptimal Algorithms for Proper Learning Mixtures of Gaussians. C. Daskalakis, G. Kamath.
NearOptimalSample Estimators For Spherical Gaussian Mixtures. J. Acharya, A. Jafarpour, A. Orlitsky, and A. Suresh

Sep 13: Learning monotone and other shape restricted distributions

Sep 15: Robust Learning of distributions
[pdf]
Robust Statistics. P. Huber, E. Ronchetti
Robust Estimators in High Dimensions without the Computational Intractability. I. Diakonikolas, G. Kamath, D. Kane, J. Li, A. Moitra, A. Stewart.

Sep 20: Missing mass and GoodTuring probability estimation
[pdf]
On the convergence of Good Turing Estimators. D. McAllester, R. Schapire
Concentration Bounds for Unigram Language Models. E. Drukh, Y. Mansour

Sep 22: Universal Compression and Competitive Distribution Estimation
Unit 2
References:

A Survey on Distribution Testing, Clement Canonne [pdf]
A nice survey covering a lot of the testing related developments in recent years.

Testing random variables for independence and identity. T. Batu, E. Fischer, L. Fortnow, R. Kumar, R. Rubinfeld, and P. White.
 A coincidencebased test for uniformity given very sparselysampled discrete data. L. Paninski
 Testing Shape Restrictions of Discrete Distributions. C. Canonne, I. Diakonikolas, T. Gouleakis, R. Rubinfeld
 Optimal Testing for Properties of Distributions. J. Acharya C. Daskalakis, G. Kamath
 A New Approach for Testing Properties of Discrete Distributions, I. Diakonikolas, D. Kane
A beautiful paper providing a unified approach to testing many properties, and a nice informationtheoretic lower bound!

Sep 27, 29: Distribution Property Testing, Uniformity
[pdf]