Related papers: A General Framework of Nonparametric Feature Selec…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…

Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…

Eficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as…

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…

Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…

We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is…

In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on…

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

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…

Feature selection is an essential process in machine learning, especially when dealing with high-dimensional datasets. It helps reduce the complexity of machine learning models, improve performance, mitigate overfitting, and decrease…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

Feature selection is an important task in many problems occurring in pattern recognition, bioinformatics, machine learning and data mining applications. The feature selection approach enables us to reduce the computation burden and the…

Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…

Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…

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…

A nonparametric approach for policy learning for POMDPs is proposed. The approach represents distributions over the states, observations, and actions as embeddings in feature spaces, which are reproducing kernel Hilbert spaces.…

We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional…

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…