Related papers: On the Independencies Hidden in the Structure of a…

This paper aims to motivate Bell's notion of local causality by means of Bayesian networks. In a locally causal theory any superluminal correlation should be screened off by atomic events localized in any so-called \textit{shielder-off…

Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly…

Probabilistic logic reasoning is a central component of such cognitive architectures as OpenCog. However, as an integrative architecture, OpenCog facilitates cognitive synergy via hybridization of different inference methods. In this paper,…

Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…

We present Polaris, a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs…

Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose…

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…

We study the following independence testing problem: given access to samples from a distribution $P$ over $\{0,1\}^n$, decide whether $P$ is a product distribution or whether it is $\varepsilon$-far in total variation distance from any…

Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…

The self-rationalising capabilities of LLMs are appealing because the generated explanations can give insights into the plausibility of the predictions. However, how faithful the explanations are to the predictions is questionable, raising…

Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…

We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal…

We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…

In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…

Separation logic's compositionality and local reasoning properties have led to significant advances in scalable static analysis. But program analysis has new challenges -- many programs display computational effects and, orthogonally,…

In recent years, there has been extensive research on how to extend general-purpose programming language semantics with domain-specific modeling constructs. Two areas of particular interest are (i) universal probabilistic programming where…

We study the algebraic varieties defined by the conditional independence statements of Bayesian Networks. A complete algebraic classification is given for Bayesian Networks on at most five random variables. Hidden variables are related to…

In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped…

One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be…