Related papers: On the Conditional Independence Implication Proble…
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…
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 introduce an algebraic concept of the frame for abstract conditional independence (CI) models, together with basic operations with respect to which such a frame should be closed: copying and marginalization. Three standard examples of…
Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditional Independence…
Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple…
Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such…
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 show that the conditional independence (CI) implication problem with bounded cardinalities, which asks whether a given CI implication holds for all discrete random variables with given cardinalities, is co-NEXPTIME-hard. The problem…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic…
Given independent samples generated from the joint distribution $p(\mathbf{x},\mathbf{y},\mathbf{z})$, we study the problem of Conditional Independence (CI-Testing), i.e., whether the joint equals the CI distribution…
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models in order to improve efficiency of…
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…
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…
We study the problem of learning multivariate dependencies in nonparametric and high-dimensional settings. This includes but is not limited to graphical models. Our approach effectively combines several features that are missing from…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…