4 papers
A Minimax Theory of Nonparametric Regression Under Covariate Shift
Petr Zamolodtchikov
We consider nonparametric regression under covariate shift, where we observe samples from both the target distribution and a related but distinct source distribution. We introduce…
On empirical Hodge Laplacians under the manifold hypothesis
Jan-Paul Lerch, Martin Wahl, Petr Zamolodtchikov
Given i.i.d. observations uniformly distributed on a closed submanifold of the Euclidean space, we study higher-order generalizations of graph Laplacians, so-called Hodge Laplacian…
Generative Modelling via Quantile Regression
Johannes Schmidt-Hieber, Petr Zamolodtchikov
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness a…
Transfer Learning under Covariate Shift: Local -Nearest Neighbours Regression with Heavy-Tailed Design
Petr Zamolodtchikov, Hanyuan Hang
Covariate shift is a common transfer learning scenario where the marginal distributions of input variables vary between source and target data while the conditional distribution of…