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.

Pool-based active learning (AL) is a promising technology for increasing data-efficiency of machine learning models. However, surveys show that performance of recent AL methods is very sensitive to the choice of dataset and training setting, making them unsuitable for general application. In order to tackle this problem, the field Learning Active Learning (LAL) suggests to learn the active learning strategy itself, allowing it to adapt to the given setting. In this work, we propose a novel LAL method for classification that exploits symmetry and independence properties of the active learning problem with an Attentive Conditional Neural Process model. Our approach is based on learning from a myopic oracle, which gives our model the ability to adapt to non-standard objectives, such as those that do not equally weight the error on all data points. We experimentally verify that our Neural Process model outperforms a variety of baselines in these settings. Finally, our experiments show that our model exhibits a tendency towards improved stability to changing datasets. However, performance is sensitive to choice of classifier and more work is necessary to reduce the performance the gap with the myopic oracle and to improve scalability. We present our work as a proof-of-concept for LAL on nonstandard objectives and hope our analysis and modelling considerations inspire future LAL work.

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.

Count data play a critical role in medical research, such as heart disease. The Poisson regression model is a common technique for evaluating the impact of a set of covariates on the count responses. The mixture of Poisson regression models with experts is a practical tool to exploit the covariates, not only to handle the heterogeneity in the Poisson regressions but also to learn the mixing structure of the population. Multicollinearity is one of the most common challenges with regression models, leading to ill-conditioned design matrices of Poisson regression components and expert classes. The maximum likelihood method produces unreliable and misleading estimates for the effects of the covariates in multicollinearity. In this research, we develop Ridge and Liu-type methods as two shrinkage approaches to cope with the ill-conditioned design matrices of the mixture of Poisson regression models with experts. Through various numerical studies, we demonstrate that the shrinkage methods offer more reliable estimates for the coefficients of the mixture model in multicollinearity while maintaining the classification performance of the ML method. The shrinkage methods are finally applied to a heart study to analyze the heart disease rate stages.

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.

In the simulation of physical systems, an increase in model complexity directly corresponds to an increase in the simulation time, posing substantial limitations to the use of such models for critical applications that depend on timesensitive decisions. Therefore, fast emulators learned by data-driven architectures and integrated in algorithms for the solution of forward and inverse problems are becoming increasingly successful. On one hand, several contributions in the literature have proposed architectures for physics-based emulators designed to limit the number of model evaluations during training. These include, for example, physics-informed neural networks (PINN) [1], deep operator networks (DeepONet) [2], and transformers-based architectures [3]. On the other hand, generative approaches have been the subject of significant recent research due to their flexibility to quantify uncertainty in the predicted outputs. Unlike traditional deep learning tasks, generative models focus on capturing a distributional characterization of the latent variables, providing an improved understanding, and a superior way to interact with a given system. Examples in this context include Gaussian Processes [4], Bayesian networks [5], generative adversarial networks (GAN) [6], diffusion models [7], optimal transport [8], normalizing flow [9, 10] and Variational Auto-Encoders (VAE) [11]. When using data-driven emulators in the context of inverse problems, other difficulties arise. Inverse problem are often ill-posed as a result of non-uniqueness of solutions, or of ill-conditioning due to high-dimensionality, data-sparsity, noise-corruption, and nonlinear response of the physical systems [12, 13, 14, 15, 16].

This article studies the infinite-width limit of deep feedforward neural networks whose weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden node of the network is assigned a nonnegative random variable that controls the variance of the outgoing weights of that node. We make minimal assumptions on these per-node random variables: they are iid and their sum, in each layer, converges to some finite random variable in the infinite-width limit. Under this model, we show that each layer of the infinite-width neural network can be characterised by two simple quantities: a non-negative scalar parameter and a L\'evy measure on the positive reals. If the scalar parameters are strictly positive and the L\'evy measures are trivial at all hidden layers, then one recovers the classical Gaussian process (GP) limit, obtained with iid Gaussian weights. More interestingly, if the L\'evy measure of at least one layer is non-trivial, we obtain a mixture of Gaussian processes (MoGP) in the large-width limit. The behaviour of the neural network in this regime is very different from the GP regime. One obtains correlated outputs, with non-Gaussian distributions, possibly with heavy tails. Additionally, we show that, in this regime, the weights are compressible, and some nodes have asymptotically non-negligible contributions, therefore representing important hidden features. Many sparsity-promoting neural network models can be recast as special cases of our approach, and we discuss their infinite-width limits; we also present an asymptotic analysis of the pruning error. We illustrate some of the benefits of the MoGP regime over the GP regime in terms of representation learning and compressibility on simulated, MNIST and Fashion MNIST datasets.

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.

Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic kernel machines with a flexible structure that does not scale gracefully with data or deterministic and vastly scalable automata, albeit with a restrictive parametric form and poor regularization. In this paper, we consider a probabilistic hierarchical modeling paradigm that combines the benefits of both worlds to deliver computationally efficient representations with inherent complexity regularization. The presented approaches are probabilistic interpretations of local regression techniques that approximate nonlinear functions through a set of local linear or polynomial units. Importantly, we rely on principles from Bayesian nonparametrics to formulate flexible models that adapt their complexity to the data and can potentially encompass an infinite number of components. We derive two efficient variational inference techniques to learn these representations and highlight the advantages of hierarchical infinite local regression models, such as dealing with non-smooth functions, mitigating catastrophic forgetting, and enabling parameter sharing and fast predictions. Finally, we validate this approach on large inverse dynamics datasets and test the learned models in real-world control scenarios.