The best way to model, understand, and quantify the information contained in complex systems is an open question in physics, mathematics, and computer science. The uncertain relationship between entropy and complexity further complicates this question. With ideas drawn from the object-relations theory of psychology, this paper develops an object-relations model of complex systems which generalizes to systems of all types, including mathematical operations, machines, biological organisms, and social structures. The resulting Complex Information Entropy (CIE) equation is a robust method to quantify complexity across various contexts. The paper also describes algorithms to iteratively update and improve approximate solutions to the CIE equation, to recursively infer the composition of complex systems, and to discover the connections among objects across different lengthscales and timescales. Applications are discussed in the fields of engineering design, atomic and molecular physics, chemistry, materials science, neuroscience, psychology, sociology, ecology, economics, and medicine.

Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In this paper, we present application-driven learning, a new closed-loop framework in which the processes of forecasting and decision-making are merged and co-optimized through a bilevel optimization problem. We present our methodology in a general format and prove that the solution converges to the best estimator in terms of the expected cost of the selected application. Then, we propose two solution methods: an exact method based on the KKT conditions of the second-level problem and a scalable heuristic approach suitable for decomposition methods. The proposed methodology is applied to the relevant problem of defining dynamic reserve requirements and conditional load forecasts, offering an alternative approach to current \emph{ad hoc} procedures implemented in industry practices. We benchmark our methodology with the standard sequential least-squares forecast and dispatch planning process. We apply the proposed methodology to an illustrative system and to a wide range of instances, from dozens of buses to large-scale realistic systems with thousands of buses. Our results show that the proposed methodology is scalable and yields consistently better performance than the standard open-loop approach.

Choosing the values of hyper-parameters in sparse Bayesian learning (SBL) can significantly impact performance. However, the hyper-parameters are normally tuned manually, which is often a difficult task. Most recently, effective automatic hyper-parameter tuning was achieved by using an empirical auto-tuner. In this work, we address the issue of hyper-parameter auto-tuning using neural network (NN)-based learning. Inspired by the empirical auto-tuner, we design and learn a NN-based auto-tuner, and show that considerable improvement in convergence rate and recovery performance can be achieved.

Agent-based modeling (ABM) is a well-established paradigm for simulating complex systems via interactions between constituent entities. Machine learning (ML) refers to approaches whereby statistical algorithms 'learn' from data on their own, without imposing a priori theories of system behavior. Biological systems -- from molecules, to cells, to entire organisms -- consist of vast numbers of entities, governed by complex webs of interactions that span many spatiotemporal scales and exhibit nonlinearity, stochasticity and intricate coupling between entities. The macroscopic properties and collective dynamics of such systems are difficult to capture via continuum modelling and mean-field formalisms. ABM takes a 'bottom-up' approach that obviates these difficulties by enabling one to easily propose and test a set of well-defined 'rules' to be applied to the individual entities (agents) in a system. Evaluating a system and propagating its state over discrete time-steps effectively simulates the system, allowing observables to be computed and system properties to be analyzed. Because the rules that govern an ABM can be difficult to abstract and formulate from experimental data, there is an opportunity to use ML to help infer optimal, system-specific ABM rules. Once such rule-sets are devised, ABM calculations can generate a wealth of data, and ML can be applied there too -- e.g., to probe statistical measures that meaningfully describe a system's stochastic properties. As an example of synergy in the other direction (from ABM to ML), ABM simulations can generate realistic datasets for training ML algorithms (e.g., for regularization, to mitigate overfitting). In these ways, one can envision various synergistic ABM$\rightleftharpoons$ML loops. This review summarizes how ABM and ML have been integrated in contexts that span spatiotemporal scales, from cellular to population-level epidemiology.

Where am I? This is one of the most critical questions that any intelligent system should answer to decide whether it navigates to a previously visited area. This problem has long been acknowledged for its challenging nature in simultaneous localization and mapping (SLAM), wherein the robot needs to correctly associate the incoming sensory data to the database allowing consistent map generation. The significant advances in computer vision achieved over the last 20 years, the increased computational power, and the growing demand for long-term exploration contributed to efficiently performing such a complex task with inexpensive perception sensors. In this article, visual loop closure detection, which formulates a solution based solely on appearance input data, is surveyed. We start by briefly introducing place recognition and SLAM concepts in robotics. Then, we describe a loop closure detection system's structure, covering an extensive collection of topics, including the feature extraction, the environment representation, the decision-making step, and the evaluation process. We conclude by discussing open and new research challenges, particularly concerning the robustness in dynamic environments, the computational complexity, and scalability in long-term operations. The article aims to serve as a tutorial and a position paper for newcomers to visual loop closure detection.

Prediction failures of machine learning models often arise from deficiencies in training data, such as incorrect labels, outliers, and selection biases. However, such data points that are responsible for a given failure mode are generally not known a priori, let alone a mechanism for repairing the failure. This work draws on the Bayesian view of continual learning, and develops a generic framework for both, identifying training examples which have given rise to the target failure, and fixing the model through erasing information about them. This framework naturally allows leveraging recent advances in continual learning to this new problem of model repairment, while subsuming the existing works on influence functions and data deletion as specific instances. Experimentally, the proposed approach outperforms the baselines for both identification of detrimental training data and fixing model failures in a generalisable manner.

With most technical fields, there exists a delay between fundamental academic research and practical industrial uptake. Whilst some sciences have robust and well-established processes for commercialisation, such as the pharmaceutical practice of regimented drug trials, other fields face transitory periods in which fundamental academic advancements diffuse gradually into the space of commerce and industry. For the still relatively young field of Automated/Autonomous Machine Learning (AutoML/AutonoML), that transitory period is under way, spurred on by a burgeoning interest from broader society. Yet, to date, little research has been undertaken to assess the current state of this dissemination and its uptake. Thus, this review makes two primary contributions to knowledge around this topic. Firstly, it provides the most up-to-date and comprehensive survey of existing AutoML tools, both open-source and commercial. Secondly, it motivates and outlines a framework for assessing whether an AutoML solution designed for real-world application is 'performant'; this framework extends beyond the limitations of typical academic criteria, considering a variety of stakeholder needs and the human-computer interactions required to service them. Thus, additionally supported by an extensive assessment and comparison of academic and commercial case-studies, this review evaluates mainstream engagement with AutoML in the early 2020s, identifying obstacles and opportunities for accelerating future uptake.

This paper revisits the work of Rauch et al. (1965) and develops a novel method for recursive maximum likelihood particle filtering for general state-space models. The new method is based on statistical analysis of incomplete observations of the systems. Score function and conditional observed information of the incomplete observations/data are introduced and their distributional properties are discussed. Some identities concerning the score function and information matrices of the incomplete data are derived. Maximum likelihood estimation of state-vector is presented in terms of the score function and observed information matrices. In particular, to deal with nonlinear state-space, a sequential Monte Carlo method is developed. It is given recursively by an EM-gradient-particle filtering which extends the work of Lange (1995) for state estimation. To derive covariance matrix of state-estimation errors, an explicit form of observed information matrix is proposed. It extends Louis (1982) general formula for the same matrix to state-vector estimation. Under (Neumann) boundary conditions of state transition probability distribution, the inverse of this matrix coincides with the Cramer-Rao lower bound on the covariance matrix of estimation errors of unbiased state-estimator. In the case of linear models, the method shows that the Kalman filter is a fully efficient state estimator whose covariance matrix of estimation error coincides with the Cramer-Rao lower bound. Some numerical examples are discussed to exemplify the main results.

Sampling-based inference techniques are central to modern cosmological data analysis; these methods, however, scale poorly with dimensionality and typically require approximate or intractable likelihoods. In this paper we describe how Truncated Marginal Neural Ratio Estimation (TMNRE) (a new approach in so-called simulation-based inference) naturally evades these issues, improving the $(i)$ efficiency, $(ii)$ scalability, and $(iii)$ trustworthiness of the inferred posteriors. Using measurements of the Cosmic Microwave Background (CMB), we show that TMNRE can achieve converged posteriors using orders of magnitude fewer simulator calls than conventional Markov Chain Monte Carlo (MCMC) methods. Remarkably, the required number of samples is effectively independent of the number of nuisance parameters. In addition, a property called \emph{local amortization} allows the performance of rigorous statistical consistency checks that are not accessible to sampling-based methods. TMNRE promises to become a powerful tool for cosmological data analysis, particularly in the context of extended cosmologies, where the timescale required for conventional sampling-based inference methods to converge can greatly exceed that of simple cosmological models such as $\Lambda$CDM. To perform these computations, we use an implementation of TMNRE via the open-source code \texttt{swyft}.

Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer from high computational complexity due to the combinatorial nature of estimating the directed acyclic graph (DAG). Motivated by the `Cause-Effect Pair' NIPS 2013 Workshop on Causality Challenge, in this paper, we take a different approach and generate a probability distribution over all possible graphs informed by the cause-effect pair features proposed in response to the workshop challenge. The goal of the paper is to propose new methods based on this probabilistic information and compare their performance with traditional and state-of-the-art approaches. Our experiments, on both synthetic and real datasets, show that our proposed methods not only have statistically similar or better performances than some traditional approaches but also are computationally faster.