The talk is based on the paper https://arxiv.org/abs/2010.09237 in which 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. Naturally, the quality of the generative model is measured 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. The obtained risk bounds are proved to be minimax rate optimal.
Personal Website of Arnak Dalalyan
The talk also can be joined online via our ZOOM MEETING
Meeting room opens at: January 16, 2023, 4.30 pm Vienna
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