相关论文: Representing Independence Models with Elementary T…

The method of imsets, introduced by Studen\'y, provides a geometric and combinatorial description of conditional independence statements. Elementary conditional independence statements over a finite set of discrete random variables…

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…

We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…

This paper discusses causal independence models and a generalization of these models called causal interaction models. Causal interaction models are models that have independent mechanisms where a mechanism can have several causes. In…

This course introduces the fruitful links between model theory and a combinatoric of sets given by independence relations. An independence relation on a set is a ternary relation between subsets. Chapter 1 should be considered as an…

Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…

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…

We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated…

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…

We define and study a metric independence notion in a homogeneous metric abstract elementary class with perturbations that is $d^p$-superstable (superstable wrt. the perturbation topology), weakly simple and has complete type spaces and we…

We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…

This note presents an analytic technique for proving the linear independence of certain small subsets of real numbers over the rational numbers. The applications of this test produce simple linear independence proofs for the subsets of…

Traditional economic models typically treat private information, or signals, as generated from some underlying state. Recent work has explicated alternative models, where signals correspond to interpretations of available information. We…

Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional…

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…

Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…

The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid…

Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…

Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models…