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Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to…

Methods from statistical physics, such as those involving complex networks, have been increasingly used in quantitative analysis of linguistic phenomena. In this paper, we represented pieces of text with different levels of simplification…

Over the past several years Bayesian networks have been applied to a wide variety of problems. A central problem in applying Bayesian networks is that of finding one or more of the most probable instantiations of a network. In this paper we…

Decision tree induction systems are being used for knowledge acquisition in noisy domains. This paper develops a subjective Bayesian interpretation of the task tackled by these systems and the heuristic methods they use. It is argued that…

A core tension in models of concept learning is that the model must carefully balance the tractability of inference against the expressivity of the hypothesis class. Humans, however, can efficiently learn a broad range of concepts. We…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…

In recent years, there has been an increased need for the use of active systems - systems required to act automatically based on events, or changes in the environment. Such systems span many areas, from active databases to applications that…

Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do…

Bayesian belief networks can be used to represent and to reason about complex systems with uncertain, incomplete and conflicting information. Belief networks are graphs encoding and quantifying probabilistic dependence and conditional…

There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and…

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including…

In recent years, researchers in decision analysis and artificial intelligence (AI) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in…

Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…

Probabilistic models over strings have played a key role in developing methods allowing indels to be treated as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do…

A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…

Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…

We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

Recent advances in Bayesian probability theory and its application to cognitive science in combination with the development of a new generation of computational tools and methods for probabilistic computation have led to a 'probabilistic…