Statistical guarantees for generative models without domination
arXiv:2010.09237
Abstract
In this paper, we introduce a convenient framework for studying (adversarial) generative models from a statistical perspective. It consists in modeling the generative device as a smooth transformation of the unit hypercube of a dimension that is much smaller than that of the ambient space and measuring the quality of the generative model by means of an integral probability metric. In the particular case of integral probability metric defined through a smoothness class, we establish a risk bound quantifying the role of various parameters. In particular, it clearly shows the impact of dimension reduction on the error of the generative model.
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- Some Theoretical Insights into Wasserstein GANs
- A likelihood approach to nonparametric estimation of a singular distribution using deep generative models
- Rates of convergence for density estimation with generative adversarial networks
- Optimal 1-Wasserstein Distance for WGANs
- Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution