Related papers: Data-Driven Representations for Testing Independen…
Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these…
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…
Suppose that we observe a short time series where each time-t-specific data-structure consists of many slightly dependent data indexed by a and that we want to estimate a feature of the law of the experiment that depends neither on t nor on…
We study the identity testing problem for high-dimensional distributions. Given as input an explicit distribution $\mu$, an $\varepsilon>0$, and access to sampling oracle(s) for a hidden distribution $\pi$, the goal in identity testing is…
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.…
One important obstacle in applying Dempster-Shafer Theory (DST) is its relationship to frequencies. In particular, there exist serious difficulties in finding factorizations of belief functions from data. In probability theory…
Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…
The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…
In this paper we develop a novel nonparametric framework to test the independence of two random variables $\mathbf{X}$ and $\mathbf{Y}$ with unknown respective marginals $H(dx)$ and $G(dy)$ and joint distribution $F(dx dy)$, based on {\it…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…
We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…
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 exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker, less interesting ones. This can be accomplished by computing a measure of dependence on…
Independence analysis is an indispensable step before regression analysis to find out essential factors that influence the objects. With many applications in machine Learning, medical Learning and a variety of disciplines, statistical…
When the underlying probability distribution in a stochastic optimization is observed only through data, various data-driven formulations have been studied to obtain approximate optimal solutions. We show that no such formulations can, in a…
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…
Randomness or mutual independence is a fundamental assumption forming the basis of statistical inference across disciplines such as economics, finance, and management. Consequently, validating this assumption is essential for the reliable…
We study here the topology of information on the space of probability measures over Polish spaces that was defined in [1]. We show that under this topology, a convergent sequence of probability measures satisfying a conditional independence…