Related papers: From Conditional to Unconditional Independence: Te…
Computing observables from conditioned dynamics is typically computationally hard, because, although obtaining independent samples efficiently from the unconditioned dynamics is usually feasible, generally most of the samples must be…
The paper gives a general condition on permutations, condition under which a semicircular matrix is free independent, or asymptotically free independent from the semicircular matrix obtained by permuting its entries. In particular, it is…
Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
We establish a fundamental connection between optimal structure learning and optimal conditional independence testing by showing that the minimax optimal rate for structure learning problems is determined by the minimax rate for conditional…
We show that the d -separation criterion constitutes a valid test for conditional independence relationships that are induced by feedback systems involving discrete variables.
We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type I error control and…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
Independence and conditional independence are fundamental concepts for reasoning about groups of random variables in probabilistic programs. Verification methods for independence are still nascent, and existing methods cannot handle…
The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order…
Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
We theoretically introduce and experimentally demonstrate the realization of a nonclassicality test that allows for arbitrarily low detection efficiency without invoking any extra assumptions as independence of the devices. Our test and its…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…