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Learning Probability Distributions - What Can, What Can't Be Done - Shai Ben-David
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- 1 Intro
- 2 A fundamental statistical learning problem
- 3 The most ambitious framework
- 4 Such an ambitious task is provably impossible
- 5 Talk outline
- 6 Part 1: Density estimation of a restricted family of distributions
- 7 Our main technical tool - Sample compression schemes
- 8 A General Learning Problem
- 9 Examples of EMX problems
- 10 Binary classification (-- the "clean" case) The "Fundamental Theorem of Statistical Learning"
- 11 The case of Subset Probability Maximization
- 12 Non-equivalence for EMX
- 13 More Sample Compression
- 14 Monotone compression for subset probability maximization
- 15 Examples of such compression
- 16 A Quantitative version
- 17 A model theoretic observation
- 18 Discussion
- 19 New Challenges
