Related papers: Detecting practically significant dependencies in …
We are concerned with the detection of associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all…
We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…
The proposal of Reshef et al. (2011) is an interesting new approach for discovering non-linear dependencies among pairs of measurements in exploratory data mining. However, it has a potentially serious drawback. The authors laud the fact…
We extend the use of Classification Without Labels for anomaly detection with a hypothesis test designed to exclude the background-only hypothesis. By testing for statistical independence of the two discriminating dataset regions, we are…
In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated…
The accurate classification of galaxies in large-sample astrophysical databases of galaxy clusters depends sensitively on the ability to distinguish between morphological types, especially at higher redshifts. This capability can be…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
Correlations obtained from sequences of measurements have been employed to distinguish among different physical theories or to witness the dimension of a system. In this work we show that they can also be used to establish semi-device…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
The concept of matching dependencies (mds) is recently pro- posed for specifying matching rules for object identification. Similar to the functional dependencies (with conditions), mds can also be applied to various data quality…
We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…
A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…
Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, this paper establishes a new central limit theorem (CLT) for a linear spectral statistic (LSS) of high dimensional…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
Several recent works [DHLNSY25, CPPS25a, CPPS25b] have studied a model of property testing of Boolean functions under a \emph{relative-error} criterion. In this model, the distance from a target function $f: \{0,1\}^n \to \{0,1\}$ that is…
The distance covariance of Sz\'ekely, et al. [23] and Sz\'ekely and Rizzo [21], a powerful measure of dependence between sets of multivariate random variables, has the crucial feature that it equals zero if and only if the sets are mutually…
Assessing whether a sample survey credibly represents the population is a critical question for ensuring the validity of downstream research. Generally, this problem reduces to estimating the distance between two high-dimensional…
We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…