We investigate the molecular gene expressions studies and public databases for disease modelling using Probabilistic Graphical Models and Bayesian Inference. A case study on Spinal Muscle Atrophy Genome-Wide Association Study results is modelled and analyzed. The genes up and down-regulated in two stages of the disease development are linked to prior knowledge published in the public domain and co-expressions network is created and analyzed. The Molecular Pathways triggered by these genes are identified. The Bayesian inference posteriors distributions are estimated using a variational analytical algorithm and a Markov chain Monte Carlo sampling algorithm. Assumptions, limitations and possible future work are concluded.

Rapid surrogate models derived from observational data now substantially reduce the computational cost to solve practical problems like solid mechanics [1], structural health monitoring [2, 3, 4], field problem solutions [5], fault diagnosis [6, 7], medical imaging [8, 9], autonomous driving [10], and power grid simulation [11] A significant challenge in current neural network surrogate models lies in their generalization capability. Addressing this, the foundational work [12] introduced Operator Learning, a novel method aimed at learning the mapping between different function spaces. Building on this, [13] developed the Deep Operator Neural Network (DeepONet), capable of being trained with limited datasets while minimizing generalization errors. This influential research has been applied in various domains, including the prediction of linear instability waves in high-speed boundary layers [14], forecasting power grid's post-fault trajectories [15], learning nonlinear operators in oscillatory function spaces for seismic wave responses [4], and analyzing nanoscale heat transport [16]. Additionally, several advancements of DeepONet have been proposed, such as Bayesian DeepONet [17, 18], DeepONet with proper orthogonal decomposition [19], multiscale DeepONet [4], a neural operator with coupled attention [20], physics-informed DeepONet [21, 22], and the multiple-input deep neural operators (MIONet) [23].

Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely available. In this chapter, we review theoretically principled unsupervised learning schemes for solving imaging inverse problems, with a particular focus on methods rooted in optimal transport and convex analysis. We begin by reviewing the optimal transport-based unsupervised approaches such as the cycle-consistency-based models and learned adversarial regularization methods, which have clear probabilistic interpretations. Subsequently, we give an overview of a recent line of works on provably convergent learned optimization algorithms applied to accelerate the solution of imaging inverse problems, alongside their dedicated unsupervised training schemes. We also survey a number of provably convergent plug-and-play algorithms (based on gradient-step deep denoisers), which are among the most important and widely applied unsupervised approaches for imaging problems. At the end of this survey, we provide an overview of a few related unsupervised learning frameworks that complement our focused schemes. Together with a detailed survey, we provide an overview of the key mathematical results that underlie the methods reviewed in the chapter to keep our discussion self-contained.

Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization of the latent MAP. In this work, we propose to use compressive autoencoders for latent estimation. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. We then introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs this estimation within the framework of variational inference. This allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance than state-of-the-art plug-and-play methods, while being able to quantify uncertainties faster than other existing posterior sampling techniques.

Weak supervision enables efficient development of training sets by reducing the need for ground truth labels. However, the techniques that make weak supervision attractive -- such as integrating any source of signal to estimate unknown labels -- also entail the danger that the produced pseudolabels are highly biased. Surprisingly, given everyday use and the potential for increased bias, weak supervision has not been studied from the point of view of fairness. We begin such a study, starting with the observation that even when a fair model can be built from a dataset with access to ground-truth labels, the corresponding dataset labeled via weak supervision can be arbitrarily unfair. To address this, we propose and empirically validate a model for source unfairness in weak supervision, then introduce a simple counterfactual fairness-based technique that can mitigate these biases. Theoretically, we show that it is possible for our approach to simultaneously improve both accuracy and fairness -- in contrast to standard fairness approaches that suffer from tradeoffs. Empirically, we show that our technique improves accuracy on weak supervision baselines by as much as 32\% while reducing demographic parity gap by 82.5\%. A simple extension of our method aimed at maximizing performance produces state-of-the-art performance in five out of ten datasets in the WRENCH benchmark.

We study the problem of class distribution estimation under dataset shift. On the training dataset, both features and class labels are observed while on the test dataset only the features can be observed. The task then is the estimation of the distribution of the class labels, i.e. the estimation of the class prior probabilities, in the test dataset. Assumptions of invariance between the training joint distribution of features and labels and the test distribution can considerably facilitate this task. We discuss the assumptions of covariate shift, factorizable joint shift, and sparse joint shift and their implications for class distribution estimation.

The concept of rationality is central to the field of artificial intelligence. Whether we are seeking to simulate human reasoning, or the goal is to achieve bounded optimality, we generally seek to make artificial agents as rational as possible. Despite the centrality of the concept within AI, there is no unified definition of what constitutes a rational agent. This article provides a survey of rationality and irrationality in artificial intelligence, and sets out the open questions in this area. The understanding of rationality in other fields has influenced its conception within artificial intelligence, in particular work in economics, philosophy and psychology. Focusing on the behaviour of artificial agents, we consider irrational behaviours that can prove to be optimal in certain scenarios. Some methods have been developed to deal with irrational agents, both in terms of identification and interaction, however work in this area remains limited. Methods that have up to now been developed for other purposes, namely adversarial scenarios, may be adapted to suit interactions with artificial agents. We further discuss the interplay between human and artificial agents, and the role that rationality plays within this interaction; many questions remain in this area, relating to potentially irrational behaviour of both humans and artificial agents.

This study investigated the performance, explainability, and robustness of deployed artificial intelligence (AI) models in predicting mortality during the COVID-19 pandemic and beyond. The first study of its kind, we found that Bayesian Neural Networks (BNNs) and intelligent training techniques allowed our models to maintain performance amidst significant data shifts. Our results emphasize the importance of developing robust AI models capable of matching or surpassing clinician predictions, even under challenging conditions. Our exploration of model explainability revealed that stochastic models generate more diverse and personalized explanations thereby highlighting the need for AI models that provide detailed and individualized insights in real-world clinical settings. Furthermore, we underscored the importance of quantifying uncertainty in AI models which enables clinicians to make better-informed decisions based on reliable predictions. Our study advocates for prioritizing implementation science in AI research for healthcare and ensuring that AI solutions are practical, beneficial, and sustainable in real-world clinical environments. By addressing unique challenges and complexities in healthcare settings, researchers can develop AI models that effectively improve clinical practice and patient outcomes.

Jamming and intrusion detection are critical in 5G research, aiming to maintain reliability, prevent user experience degradation, and avoid infrastructure failure. This paper introduces an anonymous jamming detection model for 5G based on signal parameters from the protocol stacks. The system uses supervised and unsupervised learning for real-time, high-accuracy detection of jamming, including unknown types. Supervised models reach an AUC of 0.964 to 1, compared to LSTM models with an AUC of 0.923 to 1. However, the need for data annotation limits the supervised approach. To address this, an unsupervised auto-encoder-based anomaly detection is presented with an AUC of 0.987. The approach is resistant to adversarial training samples. For transparency and domain knowledge injection, a Bayesian network-based causation analysis is introduced.

For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized least squares objective function where the regularization is based on a compound Gaussian prior distribution. The compound Gaussian prior subsumes many of the commonly used priors in image reconstruction, including those of sparsity-based approaches. The developed iterative algorithm gives rise to the paper's second new approach, which is a deep neural network that corresponds to an "unrolling" or "unfolding" of the iterative algorithm. Unrolled deep neural networks have interpretable layers and outperform standard deep learning methods. This paper includes a detailed computational theory that provides insight into the construction and performance of both algorithms. The conclusion is that both algorithms outperform other state-of-the-art approaches to tomographic image formation and compressive sensing, especially in the difficult regime of low training.