Related papers: Statistical Inference after Kernel Ridge Regressio…

Envelope methods improve the estimation efficiency in multivariate linear regression by identifying and separating the material and immaterial parts of the responses or the predictors and estimating the regression coefficients using only…

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…

Sound field estimation methods based on kernel ridge regression have proven effective, allowing for strict enforcement of physical properties, in addition to the inclusion of prior knowledge such as directionality of the sound field. These…

It is a commonly held belief that enforcing invariance improves generalisation. Although this approach enjoys widespread popularity, it is only very recently that a rigorous theoretical demonstration of this benefit has been established. In…

General predictive models do not provide a measure of confidence in predictions without Bayesian assumptions. A way to circumvent potential restrictions is to use conformal methods for constructing non-parametric confidence regions, that…

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…

Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple…

This paper introduces a novel nonparametric framework for data imputation, coined multilinear kernel regression and imputation via the manifold assumption (MultiL-KRIM). Motivated by manifold learning, MultiL-KRIM models data features as a…

Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…

We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of…

We study the problem of estimating the effect function for a continuous treatment, which maps each treatment value to a population-averaged outcome. A central challenge in this setting is confounding: treatment assignment often depends on…

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth…

The anisotropic kernel ridge regression (AKRR) approach in nuclear mass predictions is developed by introducing the anisotropic kernel function into the kernel ridge regression (KRR) approach, without introducing new weight parameter or…

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…

Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…

Numerical data imputation algorithms replace missing values by estimates to leverage incomplete data sets. Current imputation methods seek to minimize the error between the unobserved ground truth and the imputed values. But this strategy…

Data imputation, the process of filling in missing feature elements for incomplete data sets, plays a crucial role in data-driven learning. A fundamental belief is that data imputation is helpful for learning performance, and it follows…

This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…