Related papers: Rate-optimal nonparametric estimation for random c…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…

Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…

We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…

We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

Consider the nonparametric regression model Y=m(X)+E, where the function m is smooth but unknown, and E is independent of X. An estimator of the density of the error term E is proposed and its weak consistency is obtained. The contribution…

This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of…

We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…

We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…

We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…

Many real-world applications generate continuous data streams for regression. Hoeffding trees and their variants have a long-standing tradition due to their effectiveness, either alone or as base models in broader ensembles. Recent…

This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain…

A common bottleneck in evaluating extremal performance measures is that, due to their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric…

A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…

We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate…

A central goal of causal inference is to detect and estimate the treatment effects of a given treatment or intervention on an outcome variable of interest, where a member known as the heterogeneous treatment effect (HTE) is of growing…

Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…

When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…