Related papers: Large-Scale Kernel Methods for Independence Testin…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
Large scale online kernel learning aims to build an efficient and scalable kernel-based predictive model incrementally from a sequence of potentially infinite data points. A current key approach focuses on ways to produce an approximate…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive…
Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…
We discuss how MultiFIT, the Multiscale Fisher's Independence Test for Multivariate Dependence proposed by Gorsky and Ma (2022), compares to existing linear-time kernel tests based on the Hilbert-Schmidt independence criterion (HSIC). We…
Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…
We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…