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Beyond Berry Esseen: Structure and Learning of Sums of Random Variables
November 7, 2014 @ 11:00 am
Constantinos Daskalakis (MIT EECS)
The celebrated Berry-Esseen theorem, and its variants, provide a useful approximation to the sum of independent random variables by a Gaussian. In this talk, I will restrict attention to the important case of sums of integer random variables, arguing that Berry-Esseen theorems fall short from characterizing their general structure. I will offer stronger finitary central limit theorems, tightly characterizing the structure of these distributions, and show their implications to learning. In particular, I will present algorithms that can learn sums of integer random variables from a number of samples that is independent of how many variables are summed over.