Nonparametric Density Estimation and Convergence of GANs under Besov IPMs

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" summary

Generalizes nonparametric density estimation to Besov IPMs and proves new minimax convergence rates, showing certain GAN estimators are minimax optimal where classical linear estimators like kernel density become provably suboptimal and the gap grows with dimension. Builds GANs using ReLU networks depth log N and size polynomial in N to approximate Besov classes, achieves statistical rates while remaining robust to ε-contamination, but the results assume access to global optima of the GAN objective.

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" chapters (8)

1. 0:00Intro
2. 0:30Big Picture
3. 1:25Contributions
4. 3:37Integral Probability Metrics (IPMS)
5. 5:10Besov Spaces
6. 5:53Neural Network GANS
7. 7:54Optimization of GANS
8. 8:20Future Work: Data Models

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