Related papers: Conditional Independence in Uncertainty Theories
We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for…
Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing universal properties of conditional independence. Categoroids are…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…
An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…
We do the error analysis in reliability measures due to the assumption of independence amongst the component lifetimes. In reliability theory, we come across different n-component structures like series, parallel, and k-out-of-n systems. A…
Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach…
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…
I introduce a temporal belief-network representation of causal independence that a knowledge engineer can use to elicit probabilistic models. Like the current, atemporal belief-network representation of causal independence, the new…
In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. In high dimension, vine copulas offer greater flexibility compared…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems,…
We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information…
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
We study extremal conditional independence for H\"{u}sler-Reiss distributions, which is a parametric subclass of multivariate Pareto distributions. As the main contribution, we introduce two set functions, i.e.~functions which assign a…
Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of…