Related papers: Towards a Unified Analysis of Kernel-based Methods…
Probabilistic classification of unassociated Fermi-LAT sources using machine learning methods has an implicit assumption that the distributions of associated and unassociated sources are the same as a function of source parameters, which is…
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…
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…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…
Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are…
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
A mathematical model for variable selection in functional regression models with scalar response is proposed. By "variable selection" we mean a procedure to replace the whole trajectories of the functional explanatory variables with their…
The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…
This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…
Learning models whose predictions are invariant under multiple environments is a promising approach for out-of-distribution generalization. Such models are trained to extract features $X_{\text{inv}}$ where the conditional distribution $Y…
In this paper, we study two general classes of optimization algorithms for kernel methods with convex loss function and quadratic norm regularization, and analyze their convergence. The first approach, based on fixed-point iterations, is…
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the…
Consider a scenario where we have access to train data with both covariates and outcomes while test data only contains covariates. In this scenario, our primary aim is to predict the missing outcomes of the test data. With this objective in…
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…
For a certain scaling of the initialization of stochastic gradient descent (SGD), wide neural networks (NN) have been shown to be well approximated by reproducing kernel Hilbert space (RKHS) methods. Recent empirical work showed that, for…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
In this paper, we introduce a new distribution regression model for probability distributions. This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework, where universal kernels are built using Wasserstein…