The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms proposed by Simplicity Theory, relying on the computation of two Kolmogorov complexities (here implemented as min-path searches via ASP programs) rather than probabilistic inference. The proposed system enables users to compute ex-post and ex-ante measures of unexpectedness of a certain situation, mapping respectively to posterior and prior subjective probabilities. The computation is based on the specification of world and mental models by means of causal and descriptive relations between predicates weighted by complexity. The paper illustrates a few examples of application: generating relevant descriptions, and providing alternative approaches to disjunction and to negation.

Whether and how data scientists, statisticians and modellers should be accountable for the AI systems they develop remains a controversial and highly debated topic, especially given the complexity of AI systems and the difficulties in comparing and synthesising competing claims arising from their deployment for data analysis. This paper proposes to address this issue by decreasing the opacity and heightening the accountability of decision making using AI systems, through the explicit acknowledgement of the statistical foundations that underpin their development and the ways in which these dictate how their results should be interpreted and acted upon by users. In turn, this enhances (1) the responsiveness of the models to feedback, (2) the quality and meaning of uncertainty on their outputs and (3) their transparency to evaluation. To exemplify this approach, we extend Posterior Belief Assessment to offer a route to belief ownership from complex and competing AI structures. We argue that this is a significant way to bring ethical considerations into mathematical reasoning, and to implement ethical AI in statistical practice. We demonstrate these ideas within the context of competing models used to advise the UK government on the spread of the Omicron variant of COVID-19 during December 2021.

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learnt representations meaningful. For this the typical approach is to regularize the learned representation through prior probability distributions. However such priors are usually unavailable or ad hoc. To deal with this, we propose a dynamics-constrained representation learning framework. Instead of using predefined probabilities, we restrict the latent representation to follow specific dynamics, which is a more natural constraint for representation learning in dynamical systems. Our belief stems from a fundamental observation in physics that though different systems can have different marginalized probability distributions, they typically obey the same dynamics, such as Newton's and Schrodinger's equations. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. We show that our algorithm can uniquely identify an uncorrelated, isometric and meaningful latent representation.

We conduct a detailed investigation of tempered posteriors and uncover a number of crucial and previously undiscussed points. Contrary to previous results, we first show that for realistic models and datasets and the tightly controlled case of the Laplace approximation to the posterior, stochasticity does not in general improve test accuracy. The coldest temperature is often optimal. One might think that Bayesian models with some stochasticity can at least obtain improvements in terms of calibration. However, we show empirically that when gains are obtained this comes at the cost of degradation in test accuracy. We then discuss how targeting Frequentist metrics using Bayesian models provides a simple explanation of the need for a temperature parameter $\lambda$ in the optimization objective. Contrary to prior works, we finally show through a PAC-Bayesian analysis that the temperature $\lambda$ cannot be seen as simply fixing a misspecified prior or likelihood.

We present the effect of adapting to human preferences on trust in a human-robot teaming task. The team performs a task in which the robot acts as an action recommender to the human. It is assumed that the behavior of the human and the robot is based on some reward function they try to optimize. We use a new human trust-behavior model that enables the robot to learn and adapt to the human's preferences in real-time during their interaction using Bayesian Inverse Reinforcement Learning. We present three strategies for the robot to interact with a human: a non-learner strategy, in which the robot assumes that the human's reward function is the same as the robot's, a non-adaptive learner strategy that learns the human's reward function for performance estimation, but still optimizes its own reward function, and an adaptive-learner strategy that learns the human's reward function for performance estimation and also optimizes this learned reward function. Results show that adapting to the human's reward function results in the highest trust in the robot.

Predicting traffic incident risks at granular spatiotemporal levels is challenging. The datasets predominantly feature zero values, indicating no incidents, with sporadic high-risk values for severe incidents. Notably, a majority of current models, especially deep learning methods, focus solely on estimating risk values, overlooking the uncertainties arising from the inherently unpredictable nature of incidents. To tackle this challenge, we introduce the Spatiotemporal Zero-Inflated Tweedie Graph Neural Networks (STZITD-GNNs). Our model merges the reliability of traditional statistical models with the flexibility of graph neural networks, aiming to precisely quantify uncertainties associated with road-level traffic incident risks. This model strategically employs a compound model from the Tweedie family, as a Poisson distribution to model risk frequency and a Gamma distribution to account for incident severity. Furthermore, a zero-inflated component helps to identify the non-incident risk scenarios. As a result, the STZITD-GNNs effectively capture the dataset's skewed distribution, placing emphasis on infrequent but impactful severe incidents. Empirical tests using real-world traffic data from London, UK, demonstrate that our model excels beyond current benchmarks. The forte of STZITD-GNN resides not only in its accuracy but also in its adeptness at curtailing uncertainties, delivering robust predictions over short (7 days) and extended (14 days) timeframes.

Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an integral. However, the most popular algorithm in this class, Bayesian quadrature, is based on Gaussian process models and is therefore associated with a high computational cost. To improve scalability, we propose an alternative approach based on Bayesian neural networks which we call Bayesian Stein networks. The key ingredients are a neural network architecture based on Stein operators, and an approximation of the Bayesian posterior based on the Laplace approximation. We show that this leads to orders of magnitude speed-ups on the popular Genz functions benchmark, and on challenging problems arising in the Bayesian analysis of dynamical systems, and the prediction of energy production for a large-scale wind farm.

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove quantitative convergence rates of these interacting particle systems to their mean-field limit as the number of particles tends to infinity. Furthermore, we apply these techniques and examine their effectiveness as methods of Bayesian approximation for quantifying predictive uncertainty in ReLU networks.

Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations to diffeomorphisms, NFs enjoy efficient, exact sampling and density evaluation, enabling NFs to flexibly behave as both discriminative and generative models. Their restriction to diffeomorphisms, however, enforces that input, output and all intermediary spaces share the same dimension, limiting their ability to effectively represent target distributions with complex topologies (Zhang and Chen 2021). Additionally, in cases where the prior and target distributions are not homeomorphic, Normalizing Flows can leak mass outside of the support of the target (Cornish et al. 2019; Wu et al. 2020). This survey covers a selection of recent works that combine aspects of other generative model classes, such as VAEs and diffusion, and in doing so loosen the strict bijectivity constraints of NFs to achieve a balance of expressivity, training speed, sample efficiency and likelihood tractability.

Monitoring drivers' mental workload facilitates initiating and maintaining safe interactions with in-vehicle information systems, and thus delivers adaptive human machine interaction with reduced impact on the primary task of driving. In this paper, we tackle the problem of workload estimation from driving performance data. First, we present a novel on-road study for collecting subjective workload data via a modified peripheral detection task in naturalistic settings. Key environmental factors that induce a high mental workload are identified via video analysis, e.g. junctions and behaviour of vehicle in front. Second, a supervised learning framework using state-of-the-art time series classifiers (e.g. convolutional neural network and transform techniques) is introduced to profile drivers based on the average workload they experience during a journey. A Bayesian filtering approach is then proposed for sequentially estimating, in (near) real-time, the driver's instantaneous workload. This computationally efficient and flexible method can be easily personalised to a driver (e.g. incorporate their inferred average workload profile), adapted to driving/environmental contexts (e.g. road type) and extended with data streams from new sources. The efficacy of the presented profiling and instantaneous workload estimation approaches are demonstrated using the on-road study data, showing $F_{1}$ scores of up to 92% and 81%, respectively.