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As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
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…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
In this paper, we focus on regression estimation in both the inductive and the transductive case. We assume that we are given a set of features (which can be a base of functions, but not necessarily). We begin by giving a deviation…
In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…
This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the…
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…
This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional…
We propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional…
In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…
We establish minimax optimal rates of convergence for nonparametric estimation in functional ANOVA models when data from first-order partial derivatives are available. Our results reveal that partial derivatives can improve convergence…
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum-free sets, $B_{h}[g]$-sets and Hilbert cubes. In…
In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…
In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks,…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…