Related papers: BMT Independence
We study conditional independence under infinite measures on punctured product spaces, a notion recently introduced for graphical modeling in multivariate extremes and L\'evy processes. In contrast to classical probabilistic conditional…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
We develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods. One of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing…
In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph $G$ with a bounded chromatic number, in which each vertex represents a random variable.…
This paper develops sharp bounds on moments of sums of k-wise independent bounded random variables, under constrained average variance. The result closes the problem addressed in part in the previous works of Schmidt et al. and Bellare,…
We show how to reduce free independence to tensor independence in the strong sense. We construct a suitable unital *-algebra of closed operators `affiliated' with a given unital *-algebra and call the associated closure `monotone'. Then we…
We provide Berry-Esseen bounds for sums of operator-valued Boolean and monotone independent variables, in terms of the first moments of the summands. Our bounds are on the level of Cauchy transforms as well as the L\'evy distance. As…
Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by…
The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor…
We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e.,…
Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the…
We introduce the concept of mutual independence -- correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key -- it is a fully quantum and more…
This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the…
The general methods which are powerful for the necessity of bounded commutators are given. As applications, some necessary conditions for bounded commutators are first obtained in certain endpoint cases, and several new characterizations of…
Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count…
A fundamental task in AI is to assess (in)dependence between mixed-type variables (text, image, sound). We propose a Bayesian kernelised correlation test of (in)dependence using a Dirichlet process model. The new measure of (in)dependence…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…