Statistical guarantees for generative models without domination
This work provides theoretical guarantees for generative models, addressing a foundational problem in machine learning for researchers and practitioners.
The authors introduced a statistical framework for analyzing adversarial generative models by modeling them as smooth transformations from a low-dimensional hypercube and measuring quality with integral probability metrics. They derived a risk bound that quantifies the impact of dimension reduction on the generative model's error.
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.