4 papers
Implicit score matching meets denoising score matching: improved rates of convergence and log-density Hessian estimation
Konstantin Yakovlev, Anna Markovich, Nikita Puchkin
We study the problem of estimating the score function using both implicit score matching and denoising score matching. Assuming that the data distribution exhibiting a low-dimensio…
Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networks
Konstantin Yakovlev, Nikita Puchkin
We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbound…
Approximation Capabilities of Feedforward Neural Networks with GELU Activations
Konstantin Yakovlev, Nikita Puchkin
We derive an approximation error bound that holds simultaneously for a function and all its derivatives up to any prescribed order. The bounds apply to elementary functions, includ…
Generalization error bound for denoising score matching under relaxed manifold assumption
Konstantin Yakovlev, Nikita Puchkin
We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the s…