Related papers: A Test for Independence Via Bayesian Nonparametric…
There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…
We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized…
Mutual information (MI) is a fundamental measure of statistical dependence, with a myriad of applications to information theory, statistics, and machine learning. While it possesses many desirable structural properties, the estimation of…
The aim of this paper is to provide a new method for learning the relationships between data that have been obtained independently. Unlike existing methods like matching, the proposed technique does not require any contextual information,…
The partial copula provides a method for describing the dependence between two random variables $X$ and $Y$ conditional on a third random vector $Z$ in terms of nonparametric residuals $U_1$ and $U_2$. This paper develops a nonparametric…
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the…
We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they…
Estimating mutual correlations between random variables or data streams is essential for intelligent behavior and decision-making. As a fundamental quantity for measuring statistical relationships, mutual information has been extensively…
Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…
Most existing works on disentangled representation learning are solely built upon an marginal independence assumption: all factors in disentangled representations should be statistically independent. This assumption is necessary but…
The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…
For a continuous random variable $Z$, testing conditional independence $X \perp\!\!\!\perp Y |Z$ is known to be a particularly hard problem. It constitutes a key ingredient of many constraint-based causal discovery algorithms. These…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
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…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
We develop a new statistical procedure to test whether the dependence structure is identical between two groups. Rather than relying on a single index such as Pearson's correlation coefficient or Kendall's Tau, we consider the entire…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…