Related papers: On the Complexity of the Conditional Independence …
We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…
The implication problem for conditional independence (CI) asks whether the fact that a probability distribution obeys a given finite set of CI relations implies that a further CI statement also holds in this distribution. This problem has 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 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…
We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditions on a matrix whose entries are probabilities of events…
Drawbacks of ignoring the causal mechanisms when performing imitation learning have recently been acknowledged. Several approaches both to assess the feasibility of imitation and to circumvent causal confounding and causal misspecifications…
We study the validity problem for propositional dependence logic, modal dependence logic and extended modal dependence logic. We show that the validity problem for propositional dependence logic is NEXPTIME-complete. In addition, we…
Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…
We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are…
Conditional independence provides a way to understand causal relationships among the variables of interest. An underlying system may exhibit more fine-grained causal relationships especially between a variable and its parents, which will be…
The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions…
In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the…
We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C^2, the two variable…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
We show that the finite satisfiability problem for the unary negation fragment with arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require…
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal…
We show that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables. To do this, we construct, for each $n> 3$ a family of $n$…
Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…