Objectives: Metabolic Bariatric Surgery (MBS) is a critical intervention for patients living with obesity and related health issues. Accurate classification and prediction of patient outcomes are vital for optimizing treatment strategies. This study presents a novel machine learning approach to classify patients in the context of metabolic bariatric surgery, providing insights into the efficacy of different models and variable types. Methods: Various machine learning models, including GaussianNB, ComplementNB, KNN, Decision Tree, KNN with RandomOverSampler, and KNN with SMOTE, were applied to a dataset of 73 patients. The dataset, comprising psychometric, socioeconomic, and analytical variables, was analyzed to determine the most efficient predictive model. The study also explored the impact of different variable groupings and oversampling techniques. Results: Experimental results indicate average accuracy values as high as 66.7% for the best model. Enhanced versions of KNN and Decision Tree, along with variations of KNN such as RandomOverSampler and SMOTE, yielded the best results. Conclusions: The study unveils a promising avenue for classifying patients in the realm of metabolic bariatric surgery. The results underscore the importance of selecting appropriate variables and employing diverse approaches to achieve optimal performance. The developed system holds potential as a tool to assist healthcare professionals in decision-making, thereby enhancing metabolic bariatric surgery outcomes. These findings lay the groundwork for future collaboration between hospitals and healthcare entities to improve patient care through the utilization of machine learning algorithms. Moreover, the findings suggest room for improvement, potentially achievable with a larger dataset and careful parameter tuning.

Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of Bayesian nonparametrics, particularly in addressing complex challenges across various domains such as statistics, computer science, and electrical engineering. By elucidating the basic properties and theoretical foundations of these nonparametric models, this survey aims to provide a comprehensive understanding of Bayesian nonparametrics and their relevance in addressing complex problems, particularly in the domain of multi-object tracking. Through this exploration, we uncover the versatility and efficacy of Bayesian nonparametric methodologies, paving the way for innovative solutions to intricate challenges across diverse disciplines.

Lithium-ion batteries (Li-ion) have revolutionized energy storage technology, becoming integral to our daily lives by powering a diverse range of devices and applications. Their high energy density, fast power response, recyclability, and mobility advantages have made them the preferred choice for numerous sectors. This paper explores the seamless integration of Prognostics and Health Management within batteries, presenting a multidisciplinary approach that enhances the reliability, safety, and performance of these powerhouses. Remaining useful life (RUL), a critical concept in prognostics, is examined in depth, emphasizing its role in predicting component failure before it occurs. The paper reviews various RUL prediction methods, from traditional models to cutting-edge data-driven techniques. Furthermore, it highlights the paradigm shift toward deep learning architectures within the field of Li-ion battery health prognostics, elucidating the pivotal role of deep learning in addressing battery system complexities. Practical applications of PHM across industries are also explored, offering readers insights into real-world implementations.This paper serves as a comprehensive guide, catering to both researchers and practitioners in the field of Li-ion battery PHM.

This paper studies the directed graph clustering problem through the lens of statistics, where we formulate clustering as estimating underlying communities in the directed stochastic block model (DSBM). We conduct the maximum likelihood estimation (MLE) on the DSBM and thereby ascertain the most probable community assignment given the observed graph structure. In addition to the statistical point of view, we further establish the equivalence between this MLE formulation and a novel flow optimization heuristic, which jointly considers two important directed graph statistics: edge density and edge orientation. Building on this new formulation of directed clustering, we introduce two efficient and interpretable directed clustering algorithms, a spectral clustering algorithm and a semidefinite programming based clustering algorithm. We provide a theoretical upper bound on the number of misclustered vertices of the spectral clustering algorithm using tools from matrix perturbation theory. We compare, both quantitatively and qualitatively, our proposed algorithms with existing directed clustering methods on both synthetic and real-world data, thus providing further ground to our theoretical contributions. Keywords: graph clustering, directed graphs, maximum likelihood estimation, spectral methods, matrix perturbation analysis, semidefinite programming. Authors are listed in alphabetical order. This is the corresponding author.

Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition (CPD) and Tensor Train (TT)-constrained kernel machines recover a Gaussian Process (GP), which we fully characterize, when placing i.i.d. priors over their parameters. We analyze the convergence of both CPD and TT-constrained models, and show how TT yields models exhibiting more GP behavior compared to CPD, for the same number of model parameters. We empirically observe this behavior in two numerical experiments where we respectively analyze the convergence to the GP and the performance at prediction. We thereby establish a connection between TN-constrained kernel machines and GPs.

Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian counterpart. In this work we present a promising approach to address this challenge, based on the hypothesis that commonly used ML algorithms are efficient across a wide variety of tasks and may thus be near Bayes-optimal w.r.t. an unknown task distribution. We prove that it is possible to recover the Bayesian posterior defined by the task distribution, which is unknown but optimal in this setting, by building a martingale posterior using the algorithm. We further propose a practical uncertainty quantification method that apply to general ML algorithms. Experiments based on a variety of non-NN and NN algorithms demonstrate the efficacy of our method.

Industrial process optimization and control is crucial to increase economic and ecologic efficiency. However, data sovereignty, differing goals, or the required expert knowledge for implementation impede holistic implementation. Further, the increasing use of data-driven AI-methods in process models and industrial sensory often requires regular fine-tuning to accommodate distribution drifts. We propose the Artificial Neural Twin, which combines concepts from model predictive control, deep learning, and sensor networks to address these issues. Our approach introduces differentiable data fusion to estimate the state of distributed process steps and their dependence on input data. By treating the interconnected process steps as a quasi neural-network, we can backpropagate loss gradients for process optimization or model fine-tuning to process parameters or AI models respectively. The concept is demonstrated on a virtual machine park simulated in Unity, consisting of bulk material processes in plastic recycling.

University of Sussex, School of Engineering and Informatics, Chichester I, CI-128, Falmer, Brighton, BN1 9RH, United Kingdom Acknowledgement This work was supported by a European Research Council Grant (XSCAPE) ERC-2020-SyG 951631 Abstract Legal autonomy -- the lawful activity of artificial intelligence agents -- can be achieved in one of two ways. It can be achieved either by imposing constraints on AI actors such as developers, deployers and users, and on AI resources such as data, or by imposing constraints on the range and scope of the impact that AI agents can have on the environment. The latter approach involves encoding extant rules concerning AI driven devices into the software of AI agents controlling those devices (e.g., encoding rules about limitations on zones of operations into the agent software of an autonomous drone device). This is a challenge since the effectivity of such an approach requires a method of extracting, loading, transforming and computing legal information that would be both explainable and legally interoperable, and that would enable AI agents to "reason" about the law. In this paper, we sketch a proof of principle for such a method using large language models (LLMs), expert legal systems known as legal decision paths, and Bayesian networks. We then show how the proposed method could be applied to extant regulation in matters of autonomous cars, such as the California Vehicle Code. Keywords Legal Reasoning; Large Language Models; Expert System; Bayesian Network; Explanability; Interoperability; Autonomous Vehicles 1. Two paths towards legal autonomy What does it mean to regulate artificial intelligence (AI), and how should we go about it? To answer this question, one must first be clear on what artificial intelligence is--at least, for the purposes of the law-- and then ask whether existing laws are sufficient for its regulation. This consensus is that the term "AI" refers to software (i) that is developed using computational techniques, (ii) that is able to make decisions that influence an environment, (iii) that is able to make such decisions autonomously, or partly autonomously, and (iv) that makes those decisions to align with a set of human defined objectives. In AI research, decision-making typically involves the ability to evaluate options, predict outcomes, and select an optimal or satisfactory course of action based on the data available and predefined objectives. This process is crucial in distinguishing AI systems from simple automated systems that operate based on a fixed set of rules without variation or learning ((Friedman & Frank, 1983; Gupta et al., 2022). Autonomy in AI is characterized by goal-oriented behaviour, where the system is not just reacting to inputs based on fixed rules but is actively pursuing objectives.

Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is challenging because these approaches need to explore both the tree structure space and the space of decision parameters associated with each tree structure. This has been handled by using Markov Chain Monte Carlo (MCMC) methods, where a Markov Chain is constructed to provide samples from the desired Bayesian estimate. Importantly, the structure and the decision parameters are tightly coupled; small changes in the tree structure can demand vastly different decision parameters to provide accurate predictions. A challenge for existing MCMC approaches is proposing joint changes in both the tree structure and the decision parameters that result in efficient sampling. This paper takes a different approach, where each distinct tree structure is associated with a unique set of decision parameters. The proposed approach, entitled DCC-Tree, is inspired by the work in Zhou et al. [23] for probabilistic programs and Cochrane et al. [4] for Hamiltonian Monte Carlo (HMC) based sampling for decision trees. Results show that DCC-Tree performs comparably to other HMC-based methods and better than existing Bayesian tree methods while improving on consistency and reducing the per-proposal complexity.

Past decades have witnessed a great interest in the distinction and connection between neural network learning and kernel learning. Recent advancements have made theoretical progress in connecting infinite-wide neural networks and Gaussian processes. Two predominant approaches have emerged: the Neural Network Gaussian Process (NNGP) and the Neural Tangent Kernel (NTK). The former, rooted in Bayesian inference, represents a zero-order kernel, while the latter, grounded in the tangent space of gradient descents, is a first-order kernel. In this paper, we present the Unified Neural Kernel (UNK), which characterizes the learning dynamics of neural networks with gradient descents and parameter initialization. The proposed UNK kernel maintains the limiting properties of both NNGP and NTK, exhibiting behaviors akin to NTK with a finite learning step and converging to NNGP as the learning step approaches infinity. Besides, we also theoretically characterize the uniform tightness and learning convergence of the UNK kernel, providing comprehensive insights into this unified kernel. Experimental results underscore the effectiveness of our proposed method.