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Title: Statistical guarantees for generative models without domination Authors:  Arnak Dalayan - CREST, ENSAE, IP Paris (France) [presenting]
Nicolas Schreuder - CREST (UMR 9194) (France)
Victor-Emmanuel Brunel - ENSAE ParisTech (France)
Abstract: A convenient framework is introduced 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 through an integral probability metric. In the particular case of an 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.