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Register a new userRates of convergence for density estimation with GANs
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Added by
Nikita Puchkin
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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We undertake a precise study of the non-asymptotic properties of vanilla generative adversarial networks (GANs) and derive theoretical guarantees in the problem of estimating an unknown $d$-dimensional density $p^*$ under a proper choice of the class of generators and discriminators. We prove that the resulting density estimate converges to $p^*$ in terms of Jensen-Shannon (JS) divergence at the rate $(log n/n)^{2beta/(2beta+d)}$ where $n$ is the sample size and $beta$ determines the smoothness of $p^*.$ This is the first result in the literature on density estimation using vanilla GANs with JS rates faster than $n^{-1/2}$ in the regime $beta>d/2.$
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