Related papers: Kernel Machines With Missing Responses
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…
The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…
The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…
In the context of multivariate nonparametric regression with missing covariates, we propose Pattern Embedded Neural Networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum…
We propose Bayesian extensions of two nonparametric regression methods which are kernel and mutual $k$-nearest neighbor regression methods. Derived based on Gaussian process models for regression, the extensions provide distributions for…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
We propose a novel approach to model selection for simulator-based statistical models. The proposed approach defines a mixture of candidate models, and then iteratively updates the weight coefficients for those models as well as the…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods…