Related papers: Independence Concepts for Convex Sets of Probabili…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and…
We introduce the concept of numeraires of convex sets in the nonnegative orthant of the topological vector space of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set to…
An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball…
We formulate and explore two basic axiomatic systems of typefree subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that…
Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related…
In this paper, we propose to learn sources independence in order to choose the appropriate type of combination rules when aggregating their beliefs. Some combination rules are used with the assumption of their sources independence whereas…
We give conditions under which a scalar random variable T can be coupled to a random scaling factor $\xi$ such that T and $\xi$T are rendered stochastically independent. A similar result is obtained for random measures. One consequence is a…
Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations in free probability to random variables with unbounded…
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 .,…
Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley's theory of imprecise previsions. We show that convex previsions are related with a concept of…
In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible…
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some…
This is a non-technical introduction into theory of contextuality. More precisely, it presents the basics of a theory of contextuality called Contextuality-by-Default (CbD). One of the main tenets of CbD is that the identity of a random…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
We count the number and patterns of pairs and tuples of independent events in a simple random experiment: first a fair coin is flipped and then a fair die is tossed. The first number, equal to 888,888, suggest that there are some open…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To…