These authors contribute to the paper equally. Abstract General purpose optimization routines such as nlminb, optim (R) or nlmixed (SAS) are frequently used to estimate model parameters in nonstandard distributions. This paper presents Particle Swarm Optimization (PSO), as an alternative to many of the current algorithms used in statistics. We find that PSO can not only reproduce the same results as the above routines, it can also produce results that are more optimal or when others cannot converge. In the latter case, it can also identify the source of the problem or problems. We highlight advantages of using PSO using four examples, where: (1) some parameters in a generalized distribution are unidentified using PSO when it is not apparent or computationally manifested using routines in R or SAS; (2) PSO can produce estimation results for the log-binomial regressions when current routines may not; (3) PSO provides flexibility in the link function for binomial regression with LASSO penalty, which is unsupported by standard packages like GLM and GENMOD in Stata and SAS, respectively, and (4) PSO provides superior MLE estimates for an EE-IW distribution compared with those from the traditional statistical methods that rely on moments. Metaheuristics, and in particular, nature-inspired metaheuristic algorithms, is increasingly used across disciplines to tackle challenging optimization problems [11]. They may be broadly categorized swarm based or evolutionary based algorithms. Some examples of the former are particle swarm optimization and competitive swarm optimizer (CSO) and examples of the latter are genetic algorithm (GA) and the differential evolution. The statistical community is probably most aware of GA and simulated annealing (SA) but they are many others that have recently proven more popular in engineering and computer science.

Range-based localization is ubiquitous: global navigation satellite systems (GNSS) power mobile phone-based navigation, and autonomous mobile robots can use range measurements from a variety of modalities including sonar, radar, and even WiFi signals. Many of these localization systems rely on fixed anchors or beacons with known positions acting as transmitters or receivers. In this work, we answer a fundamental question: given a set of positions we would like to localize, how should beacons be placed so as to minimize localization error? Specifically, we present an information theoretic method for optimally selecting an arrangement consisting of a few beacons from a large set of candidate positions. By formulating localization as maximum a posteriori (MAP) estimation, we can cast beacon arrangement as a submodular set function maximization problem. This approach is probabilistically rigorous, simple to implement, and extremely flexible. Furthermore, we prove that the submodular structure of our problem formulation ensures that a greedy algorithm for beacon arrangement has suboptimality guarantees. We compare our method with a number of benchmarks on simulated data and release an open source Python implementation of our algorithm and experiments.

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to acclerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive conditions on the accuracy of the machine learning model to facilitate more efficient hierarchical sampling. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these approaches are evaluated on the same two datasets. We find that all techniques are capable of accurately reproducing the particle-level spectra across complex observables. Given that these approaches are conceptually diverse, they offer an exciting toolkit for a new class of measurements that can probe the Standard Model with an unprecedented level of detail and may enable sensitivity to new phenomena.

Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a univariate signal deconvolution method with a wide range of applications to coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. Our multidimensional space reconstruction method from an arbitrary received signal is proven to be agnostic vis-a-vis the encoding-decoding scheme, computation model, programming language, formal theory, the computable (or semi-computable) method of approximation to algorithmic complexity, and any arbitrarily chosen (computable) probability measure of the events. The method derives from the principles of an approach to Artificial General Intelligence capable of building a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We argue that this optimal and universal method of decoding non-random data has applications to signal processing, causal deconvolution, topological and geometric properties encoding, cryptography, and bio- and technosignature detection.

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key component of this approach is a probabilistic surrogate model, typically a Gaussian Process (GP), which approximates an unknown functional relationship between control parameters and a target property. However, conventional GPs often struggle when applied to systems with discontinuities and non-stationarities, prompting the exploration of alternative models. This limitation becomes particularly relevant in physical science problems, which are often characterized by abrupt transitions between different system states and rapid changes in physical property behavior. Fully Bayesian Neural Networks (FBNNs) serve as a promising substitute, treating all neural network weights probabilistically and leveraging advanced Markov Chain Monte Carlo techniques for direct sampling from the posterior distribution. This approach enables FBNNs to provide reliable predictive distributions, crucial for making informed decisions under uncertainty in the active learning setting. Although traditionally considered too computationally expensive for 'big data' applications, many physical sciences problems involve small amounts of data in relatively low-dimensional parameter spaces. Here, we assess the suitability and performance of FBNNs with the No-U-Turn Sampler for active learning tasks in the 'small data' regime, highlighting their potential to enhance predictive accuracy and reliability on test functions relevant to problems in physical sciences.

Modern neural trajectory predictors in autonomous driving are developed using imitation learning (IL) from driving logs. Although IL benefits from its ability to glean nuanced and multi-modal human driving behaviors from large datasets, the resulting predictors often struggle with out-of-distribution (OOD) scenarios and with traffic rule compliance. On the other hand, classical rule-based predictors, by design, can predict traffic rule satisfying behaviors while being robust to OOD scenarios, but these predictors fail to capture nuances in agent-to-agent interactions and human driver's intent. In this paper, we present RuleFuser, a posterior-net inspired evidential framework that combines neural predictors with classical rule-based predictors to draw on the complementary benefits of both, thereby striking a balance between performance and traffic rule compliance. The efficacy of our approach is demonstrated on the real-world nuPlan dataset where RuleFuser leverages the higher performance of the neural predictor in in-distribution (ID) scenarios and the higher safety offered by the rule-based predictor in OOD scenarios.

We propose a new notion of uniqueness for the adversarial Bayes classifier in the setting of binary classification. Analyzing this concept produces a simple procedure for computing all adversarial Bayes classifiers for a well-motivated family of one dimensional data distributions. This characterization is then leveraged to show that as the perturbation radius increases, certain the regularity of adversarial Bayes classifiers improves. Various examples demonstrate that the boundary of the adversarial Bayes classifier frequently lies near the boundary of the Bayes classifier.

One can improve predictability in the unknown domain by combining forecasts of imperfect complex computational models using a Bayesian statistical machine learning framework. In many cases, however, the models used in the mixing process are similar. In addition to contaminating the model space, the existence of such similar, or even redundant, models during the multimodeling process can result in misinterpretation of results and deterioration of predictive performance. In this work we describe a method based on the Principal Component Analysis that eliminates model redundancy. We show that by adding model orthogonalization to the proposed Bayesian Model Combination framework, one can arrive at better prediction accuracy and reach excellent uncertainty quantification performance.

These emergencies are unexpected events that occur suddenly and result in or have the potential to result in significant casualties, property damage, ecological harm, and serious social consequences [147]. Throughout history, natural disasters (such as earthquakes, tsunamis, volcanic eruptions, storms, floods, avalanches, droughts, and wildfires) and accident disasters (including environmental disasters, traffic accidents, explosions, and gas leaks) have caused numerous fatalities, infrastructure damage, and extensive economic loss. According to the Emergencies Database (EM-DAT), between 2000 and 2023, 5,922 public emergencies occurred, leading to 480,000 casualties and 3.5 trillion in economic losses, as shown in Figure 1 [1]. Therefore, it is increasingly vital to use data, information, and various models to predict potential public emergencies that jeopardize public safety and well-being. Predicting the cascade of information in the event deduction process under public emergencies assists governments, organizations, and individuals in taking proactive measures to mitigate the impact of emergencies and minimize damage. Public emergencies are classified into different categories. The most common categories of public emergencies include (1) Natural disasters, (2) Accident disasters.