Related papers: Kernel Feature Selection via Conditional Covarianc…
We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
A data driven, kernel-based method for approximating the leading Koopman eigenvalues, eigenfunctions, and modes in problems with high dimensional state spaces is presented. This approach approximates the Koopman operator using a set of…
We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem…
A method for analyzing the feature map for the kernel-based quantum classifier is developed; that is, we give a general formula for computing a lower bound of the exact training accuracy, which helps us to see whether the selected feature…
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms…
It has been observed that Convolutional Neural Networks (CNNs) suffer from redundancy in feature maps, leading to inefficient capacity utilization. Efforts to address this issue have largely focused on kernel orthogonality method. In this…
Feature selection is a pattern recognition approach to choose important variables according to some criteria to distinguish or explain certain phenomena. There are many genomic and proteomic applications which rely on feature selection to…
Selecting an optimal subset of features or instances under an information theoretic criterion has become an effective preprocessing strategy for reducing data complexity while preserving essential information. This study investigates two…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
This paper addresses the challenge of identifying a minimal subset of discrete, independent variables that best predicts a binary class. We propose an efficient iterative method that sequentially selects variables based on which one…
We consider the problem of conditional independence (CI) testing and adopt a kernel-based approach. Kernel-based CI tests embed variables in reproducing kernel Hilbert spaces, regress their embeddings on the conditioning variables, and test…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods, nonparametric learning algorithms that can approximate any…
In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
The Naive Bayesian classifier is a popular classification method employing the Bayesian paradigm. The concept of having conditional dependence among input variables sounds good in theory but can lead to a majority vote style behaviour.…
The goal of feature selection is to identify important features that are relevant to explain an outcome variable. Most of the work in this domain has focused on identifying globally relevant features, which are features that are related to…
The Maximum Mean Discrepancy (MMD) is a cornerstone statistic for nonparametric two-sample testing, but its test power is dictated entirely by the chosen kernel. Because any fixed kernel inherently fails to distinguish certain…