Related papers: A New Framework for Distance and Kernel-based Metr…
This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike…
We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Sz\'{e}kely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that…
In this article a new family of tests is proposed for the comparison problem of the equality of distribution of two-sample under right censoring scheme. The tests are based on energy distance and kernels mean embedding, are calibrated by…
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…
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…
In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
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…
We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…
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…
Dimensionality reduction techniques map values from a high dimensional space to one with a lower dimension. The result is a space which requires less physical memory and has a faster distance calculation. These techniques are widely used…
Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with…
In this paper, we consider testing the correlation coefficient matrix between two subsets of high-dimensional variables. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
The multivariate Hilbert-Schmidt-Independence-Criterion (dHSIC) and distance multivariance allow to measure and test independence of an arbitrary number of random vectors with arbitrary dimensions. Here we define versions which only depend…
This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…