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The very expressiveness of Bayesian networks can introduce fresh challenges due to the large number of relationships they often model. In many domains, it is thus often essential to supplement any available data with elicited expert…

In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…

Bell's theorem, a cornerstone of quantum theory, shows that quantum correlations are incompatible with a classical theory of cause and effect. Through the lens of causal inference, it can be understood as a particular case of causal…

The causal discovery of Bayesian networks is an active and important research area, and it is based upon searching the space of causal models for those which can best explain a pattern of probabilistic dependencies shown in the data.…

Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive…

Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports…

Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not…

Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…

When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…

In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…

We present a method that allows the study of classical and quantum correlations in networks with causally-independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a…

The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in…

Causal theory is now widely developed with many applications to medicine and public health. However within the discipline of reliability, although causation is a key concept in this field, there has been much less theoretical attention. In…

From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization…

Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…

Generalizations of Bell's framework to causal networks have yielded new foundational insights and applications, including the use of interventions to enhance the detection of nonclassicality in scenarios with communication. Such…

We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multi-objective optimization problem of matching observed data while minimizing the causal effect of…