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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…

This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random…

Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…

We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…

Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle…

Stable Logic Programming (SLP) is an emergent, alternative style of logic programming: each solution to a problem is represented by a stable model of a deductive database/function-free logic program encoding the problem itself. Several…

Prediction-based decision-making systems are becoming increasingly prevalent in various domains. Previous studies have demonstrated that such systems are vulnerable to runaway feedback loops, e.g., when police are repeatedly sent back to…

Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete…

This paper introduces the Quantified Boolean Bayesian Network (QBBN), which provides a unified view of logical and probabilistic reasoning. The QBBN is meant to address a central problem with the Large Language Model (LLM), which has become…

This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…

The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training examples and background knowledge (BK). To improve performance, we introduce an approach that, before searching for a hypothesis, first…

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs,…

We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…

A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

Sequential neuronal activity underlies a wide range of processes in the brain. Neuroscientific evidence for neuronal sequences has been reported in domains as diverse as perception, motor control, speech, spatial navigation and memory.…

We define a context-sensitive temporal probability logic for representing classes of discrete-time temporal Bayesian networks. Context constraints allow inference to be focused on only the relevant portions of the probabilistic knowledge.…

Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…

We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint…

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…