Related papers: Adaptive wavelet multivariate regression with erro…
We consider non parametric estimation problem for stochastic tomography regression model, i.e. we consider the estimation problem of function of multivariate variables (image) observed through its Radon transformation calculated with the…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…
The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…
Many modern datasets consist of multiple related matrices measured on a common set of units, where the goal is to recover the shared low-dimensional subspace. While the Angle-based Joint and Individual Variation Explained (AJIVE) framework…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is…
We reveal the phenomenon that ``naive'' multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal convergence rate for nonparametric estimation of regression…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
Conformal prediction is a valuable tool for quantifying predictive uncertainty of machine learning models. However, its applicability relies on the assumption of data exchangeability, a condition which is often not met in real-world…
Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these methods by integrating convex transformations of the…
This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both…
Nonparametric estimators of a regression function with circular response and Rd-valued predictor are considered in this work. Local polynomial type estimators are proposed and studied. Expressions for their asymptotic biases and variances…
The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric…
This paper proposes an active learning (AL) algorithm to solve regression problems based on inverse-distance weighting functions for selecting the feature vectors to query. The algorithm has the following features: (i) supports both…
Estimators computed from adaptively collected data do not behave like their non-adaptive brethren. Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data…
Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
In this paper, we first discuss the optimal convergence of the adaptive finite element methods for non-self-adjoint eigenvalue problems. We present new theoretical error estimators and computable error estimators for multiple and clustered…