Learning Probability Distributions - What Can, What Can't Be Done - Shai Ben-David

Explore a seminar on theoretical machine learning focusing on learning probability distributions and their limitations. Delve into the fundamental statistical learning problem, examining the most ambitious framework and its proven impossibility. Discover density estimation of restricted distribution families and sample compression schemes as key technical tools. Investigate various examples of EMX problems, including binary classification and subset probability maximization. Analyze the "Fundamental Theorem of Statistical Learning" and its implications. Examine non-equivalence for EMX, monotone compression techniques, and quantitative versions of these concepts. Gain insights into model theoretic observations and discuss new challenges in the field of probability distribution learning.

Intro
A fundamental statistical learning problem
The most ambitious framework
Such an ambitious task is provably impossible
Talk outline
Part 1: Density estimation of a restricted family of distributions
Our main technical tool - Sample compression schemes
A General Learning Problem
Examples of EMX problems
Binary classification (-- the "clean" case) The "Fundamental Theorem of Statistical Learning"
The case of Subset Probability Maximization
Non-equivalence for EMX
More Sample Compression
Monotone compression for subset probability maximization
Examples of such compression
A Quantitative version
A model theoretic observation
Discussion
New Challenges