Related papers: Asymptotic Theory for Linear Functionals of Kernel…
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
Recent advances in machine learning have inspired a surge of research into reconstructing specific quantities of interest from measurements that comply with certain physical laws. These efforts focus on inverse problems that are governed by…
We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…
We study the kernel instrumental variable (KIV) algorithm, a kernel-based two-stage least-squares method for nonparametric instrumental variable regression. We provide a convergence analysis covering both identified and non-identified…
In this work, we study the Kuelbs-Steadman-2 space (KS-2 space), a Hilbert space constructed via the Henstock-Kurzweil integral, which allows handling non-absolutely integrable functions. We present the construction of the KS-2 space over…
The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…
We analyze the prediction error of ridge regression in an asymptotic regime where the sample size and dimension go to infinity at a proportional rate. In particular, we consider the role played by the structure of the true regression…
We characterize the asymptotic behaviour of the compression associated to a uniform embedding into some Lp-space for a large class of groups including connected Lie groups with exponential growth and word-hyperbolic finitely generated…
We consider learning an unknown target function $f_*$ using kernel ridge regression (KRR) given i.i.d. data $(u_i,y_i)$, $i\leq n$, where $u_i \in U$ is a covariate vector and $y_i = f_* (u_i) +\varepsilon_i \in \mathbb{R}$. A recent string…
Learning mappings between infinite-dimensional function spaces has achieved empirical success in many disciplines of machine learning, including generative modeling, functional data analysis, causal inference, and multi-agent reinforcement…
We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an…
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…