Related papers: Estimation of linear operators from scattered impu…
We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
In this paper we propose an automatic selection of the bandwidth of the semi-recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and some…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
An asymptotic theory is established for linear functionals of the predictive function given by kernel ridge regression, when the reproducing kernel Hilbert space is equivalent to a Sobolev space. The theory covers a wide variety of linear…
We discuss and compare various approaches to the problem of bandwidth selection for kernel estimators of intensity functions of spatial point processes. We also propose a new method based on the Campbell formula applied to the reciprocal…
In this paper, we will introduce a new notion, that of $K$-Integral operator frames in the set of all bounded linear operators noted $\mathcal{B}(H)$, where $H$ is a separable Hilbert space. Also, we prove some results of integral…
In this paper, we study a smoothness regularization method for a varying coefficient model based on sparse and irregularly sampled functional data which is contaminated with some measurement errors. We estimate the one-dimensional…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We propose a scalable method to find a subspace $\widehat{\mathcal{H}}$ of low-rank tensors that simultaneously approximates a set of integral operators. The method can be seen as a generalization of the Tucker-2 decomposition model, which…
Observational data are often accompanied by natural structural indices, such as time stamps or geographic locations, which are meaningful to prediction tasks but are often discarded. We leverage semantically meaningful indexing data while…
This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal discrete integral…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
We investigate the asymptotic mean squared error of kernel estimators of the intensity function of a spatial point process. We show that when $n$ independent copies of a point process in $\mathbb R^d$ are superposed, the optimal bandwidth…
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
The goal of nonparametric regression is to recover an underlying regression function from noisy observations, under the assumption that the regression function belongs to a pre-specified infinite dimensional function space. In the online…
The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more…
We develop TwinKernel methods for nonparametric estimation of intensity functions of point processes. Building on the general TwinKernel framework and combining it with martingale techniques for counting processes, we construct estimators…
We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…