5 papers
Tight Bounds for Schrödinger Potential Estimation in Unpaired Data Translation
Nikita Puchkin, Denis Suchkov, Alexey Naumov +1
Modern methods of generative modelling and unpaired data translation based on Schrödinger bridges and stochastic optimal control theory aim to transform an initial density to a ta…
Schrödinger bridge problem via empirical risk minimization
Denis Belomestny, Alexey Naumov, Nikita Puchkin +1
We study the Schrödinger bridge problem when the endpoint distributions are available only through samples. Classical computational approaches estimate Schrödinger potentials via…
Sample complexity of Schrödinger potential estimation
Nikita Puchkin, Iurii Pustovalov, Yuri Sapronov +3
We address the problem of Schrödinger potential estimation, which plays a crucial role in modern generative modelling approaches based on Schrödinger bridges and stochastic optim…
Dimension-free Structured Covariance Estimation
Nikita Puchkin, Maxim Rakhuba
Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix with an additional assumption that can b…
Rates of convergence for density estimation with generative adversarial networks
Nikita Puchkin, Sergey Samsonov, Denis Belomestny +2
In this work we undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We prove an oracle inequality for the Jensen-Shan…