Related papers: Kernel-based guarantees for nonlinear parametric m…

When concept shifts and sample scarcity are present in the target domain of interest, nonparametric regression learners often struggle to generalize effectively. The technique of transfer learning remedies these issues by leveraging data or…

We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…

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…

Kernel-based feature selection is an important tool in nonparametric statistics. Despite many practical applications of kernel-based feature selection, there is little statistical theory available to support the method. A core challenge is…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernel-based specification test of a…

Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc…

Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

Kernel ridge regression (KRR) is widely used for nonparametric regression over reproducing kernel Hilbert spaces. It offers powerful modeling capabilities at the cost of significant computational costs, which typically require $O(n^3)$…

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…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…

Current methods for regularization in machine learning require quite specific model assumptions (e.g. a kernel shape) that are not derived from prior knowledge about the application, but must be imposed merely to make the method work. We…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…

Finding optimal parameter configurations for tunable GPU kernels is a non-trivial exercise for large search spaces, even when automated. This poses an optimization task on a non-convex search space, using an expensive to evaluate function…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…