8 citations · 8 across the 6 of their papers we have counts for
6 papers
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 S…
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 tar…
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 optimal…
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 be…
Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations
Denis Belomestny, Alexey Naumov, Nikita Puchkin +1
This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a…
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…