Related papers: BMT Independence

We develop a theory of formal multivariate polynomials over commutative rings by treating them as ring terms. Our main result is that two ring terms are s-equivalent (when expanded they yield the same standard polynomial) iff they are…

Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…

We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…

This paper proposes a mixed variational formulation for the problem of two coupled plates with a rigid {junction}. The proposed mixed {formulation} introduces {the union of} stresses and moments as {an auxiliary variable}, which {are}…

We establish a bijection between marginal independence models on $n$ random variables and split closed order ideals in the poset of partial set partitions. We also establish that every discrete marginal independence model is toric in cdf…

Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs…

We establish two theorems for assessing the accuracy in total variation of multivariate discrete normal approximation to the distribution of an integer valued random vector $W$. The first is for sums of random vectors whose dependence…

We study the multiplicative convolution for c-monotone independence. This convolution unifies the monotone, Boolean and orthogonal multiplicative convolutions. We characterize convolution semigroups for the c-monotone multiplicative…

Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…

This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…

In the Method of Multiple-Time-Scales (MMTS), the introduction of independent time scales and the elimination of secular terms in the fast time variable, T0 = t, lead to the well-known solvability conditions. Starting from first order, free…

In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how…

We study mixtures of free, monotone, and Boolean independence described by a directed graph $G = (V,E)$ in the context of $\mathcal{T}$-free convolutions of Jekel and Liu. We prove general limit theorems for the associated additive…

Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…

The sum of $n$ {non-independent} Bernoulli random variables could be modeled in several different ways. One of these is the Multiplicative Binomial Distribution (MBD), introduced by Altham (1978) and revised by Lovison (1998). In this work,…

We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…

We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…

Bounded-rate multi-mode systems are hybrid systems that can switch among a finite set of modes. Its dynamics is specified by a finite number of real-valued variables with mode-dependent rates that can vary within given bounded sets. Given…

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…

When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…