Related papers: Kernel Feature Selection via Conditional Covarianc…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
Relevant and high-quality data are critical to successful development of machine learning applications. For machine learning applications on dynamic systems equipped with a large number of sensors, such as connected vehicles and robots, how…
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original…
We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…
Feature screening is an important method to reduce the dimension and capture informative variables in ultrahigh-dimensional data analysis. Many methods have been developed for feature screening. These methods, however, are challenged by…
We describe and analyze a simple random feature scheme (RFS) from prescribed compositional kernels. The compositional kernels we use are inspired by the structure of convolutional neural networks and kernels. The resulting scheme yields…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…
Variable screening has been a useful research area that deals with ultrahigh-dimensional data. When there exist both marginally and jointly dependent predictors to the response, existing methods such as conditional screening or iterative…
Feature selection plays a pivotal role in learning, particularly in areas were parsimonious features can provide insight into the underlying process, such as biology. Recent approaches for non-linear feature selection employing greedy…
We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint…
Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…
We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…