Related papers: High-Dimensional Independence Testing via Maximum …
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…
In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
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…
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of…
Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…
This paper proposes a new statistic to test independence between two high dimensional random vectors ${\mathbf{X}}:p_1\times1$ and ${\mathbf{Y}}:p_2\times1$. The proposed statistic is based on the sum of regularized sample canonical…
We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…
This paper develops a novel unified framework for testing mutual independence among random objects residing in possibly different metric spaces. The framework generalizes existing methodologies and introduces new measures of mutual…
Testing for pairwise independence for the case where the number of variables may be of the same size or even larger than the sample size has received increasing attention in the recent years. We contribute to this branch of the literature…
Let $(Y,(X_i)_{i\in\mathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $\mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propose a new test for testing that $Y$ is independent of…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to…
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…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
Quantum correlations in Bell and prepare-and-measure experiments are central resources for probing nonclassicality and enabling device-based quantum information protocols. In the absence of shared public randomness (i.e., without run-to-run…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
This article considers change point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on $U$-statistic in Chen…