Probabilities or confidence values produced by artificial intelligence (AI) and machine learning (ML) models often do not reflect their true accuracy, with some models being under or over confident in their predictions. For example, if a model is 80% sure of an outcome, is it correct 80% of the time? Probability calibration metrics measure the discrepancy between confidence and accuracy, providing an independent assessment of model calibration performance that complements traditional accuracy metrics. Understanding calibration is important when the outputs of multiple systems are combined, for assurance in safety or business-critical contexts, and for building user trust in models. This paper provides a comprehensive review of probability calibration metrics for classifier and object detection models, organising them according to a number of different categorisations to highlight their relationships. We identify 82 major metrics, which can be grouped into four classifier families (point-based, bin-based, kernel or curve-based, and cumulative) and an object detection family. For each metric, we provide equations where available, facilitating implementation and comparison by future researchers.

We fully characterize a large class of feedforward neural networks in terms of truncation maps. As an application, we show how a ReLU neural network can implement a feature map which separates concentric data.

Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns. However, conventional density estimators based on uniform histograms often fail to capture local variations, especially when the underlying distribution is highly nonuniform. Furthermore, the inherent discontinuity of histograms poses challenges for tasks requiring smooth derivatives, such as gradient-based optimization, clustering, and nonparametric discriminant analysis. In this work, we present a novel non-parametric approach for multivariate probability density function (PDF) estimation that utilizes minimum description length (MDL)-based binning with quantile cuts. Our approach builds upon tensor factorization techniques, leveraging the canonical polyadic decomposition (CPD) of a joint probability tensor. We demonstrate the effectiveness of our method on synthetic data and a challenging real dry bean classification dataset.

Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models capture the reality in the observations better. In this project, Generalized Randomized Hamiltonian Monte Carlo (GRHMC) processes for sampling continuous densities with discontinuous gradient and piecewise smooth targets are proposed. The methods combine the advantages of Hamiltonian Monte Carlo methods with the nature of continuous time processes in the form of piecewise deterministic Markov processes to sample from such distributions. It is argued that the techniques lead to GRHMC processes that admit the desired target distribution as the invariant distribution in both scenarios. Simulation experiments verifying this fact and several relevant real-life models are presented, including a new parameterization of the spike and slab prior for regularized linear regression that returns sparse coefficient estimates and a regime switching volatility model.

In social learning, a network of agents assigns probability scores (beliefs) to some hypotheses of interest, which rule the generation of local streaming data observed by each agent. Belief formation takes place by means of an iterative two-step procedure where: i) the agents update locally their beliefs by using some likelihood model; and ii) the updated beliefs are combined with the beliefs of the neighboring agents, using a pooling rule. This procedure can fail to perform well in the presence of dynamic drifts, leading the agents to incorrect decision making. Here, we focus on the fully online setting where both the true hypothesis and the likelihood models can change over time. This goal is achieved by exploiting two adaptation stages: i) a stochastic gradient descent update to learn and track the drifts in the decision model; ii) and an adaptive belief update to track the true hypothesis changing over time. These stages are controlled by two adaptation parameters that govern the evolution of the error probability for each agent. We show that all agents learn consistently for sufficiently small adaptation parameters, in the sense that they ultimately place all their belief mass on the true hypothesis. Index T erms Social learning, belief formation, decision making, distributed optimization, online leaerning, opinion diffusion over graphs. Marco Carpentiero and Vincenzo Matta are with the Department of Information and Electrical Engineering and Applied Mathematics (DIEM), University of Salerno, via Giovanni Paolo II, I-84084, Fisciano (SA), Italy, and Vincenzo Matta is also with the National Inter-University Consortium for Telecommunications (CNIT), Italy (e-mails: { mcarpentiero, vmatta }@unisa.it). Matta was partially supported by the European Union under the Italian National Recovery and Resilience Plan (NRRP) of NextGenerationEU, partnership on "Telecommunications of the Future" (PE00000001 - program "REST ART"). This work was produced while Virginia Bordignon was a post-doc with the Ecole Polytechnique F ed erale de Lausanne EPFL, School of Engineering, CH-1015 Lausanne, Switzerland (e-mail: virginia.bordignon@alumni.epfl.ch).

Unresolved questions about how autonomous vehicles (AVs) should meet the informational needs of riders hinder real-world adoption. Complicating our ability to satisfy rider needs is that different people, goals, and driving contexts have different criteria for what constitutes interaction success. Unfortunately, most human-AV research and design today treats all people and situations uniformly. It is crucial to understand how an AV should communicate to meet rider needs, and how communications should change when the human-AV complex system changes. I argue that understanding the relationships between different aspects of the human-AV system can help us build improved and adaptable AV communications. I support this argument using three empirical studies. First, I identify optimal communication strategies that enhance driving performance, confidence, and trust for learning in extreme driving environments. Findings highlight the need for task-sensitive, modality-appropriate communications tuned to learner cognitive limits and goals. Next, I highlight the consequences of deploying faulty communication systems and demonstrate the need for context-sensitive communications. Third, I use machine learning (ML) to illuminate personal factors predicting trust in AVs, emphasizing the importance of tailoring designs to individual traits and concerns. Together, this dissertation supports the necessity of transparent, adaptable, and personalized AV systems that cater to individual needs, goals, and contextual demands. By considering the complex system within which human-AV interactions occur, we can deliver valuable insights for designers, researchers, and policymakers. This dissertation also provides a concrete domain to study theories of human-machine joint action and situational awareness, and can be used to guide future human-AI interaction research. [shortened for arxiv]

This paper develops a model-based framework for continuous-time policy evaluation (CTPE) in reinforcement learning, incorporating both Brownian and L evy noise to model stochastic dynamics influenced by rare and extreme events. Our approach formulates the policy evaluation problem as solving a partial integro-differential equation (PIDE) for the value function with unknown coefficients. A key challenge in this setting is accurately recovering the unknown coefficients in the stochastic dynamics, particularly when driven by L evy processes with heavy tail effects. To address this, we propose a robust numerical approach that effectively handles both unbiased and censored trajectory datasets. This method combines maximum likelihood estimation with an iterative tail correction mechanism, improving the stability and accuracy of coefficient recovery. Additionally, we establish a theoretical bound for the policy evaluation error based on coefficient recovery error. Through numerical experiments, we demonstrate the effectiveness and robustness of our method in recovering heavy-tailed L evy dynamics and verify the theoretical error analysis in policy evaluation.

--We propose an automated approach to bug assignment to developers in large open-source software projects. This way, we assist human bug triagers who are in charge of finding the best developer with the right level of expertise in a particular area to be assigned to a newly reported issue. Our approach is based on the history of software development as documented in the issue tracking systems. Our approach works based on the bug reports' features, such as the corresponding products and components, as well as their priority and severity levels. We sort developers based on their experience with specific combinations of new reports. The evaluation is performed using T op-k accuracy, and the results are compared with the reported results in prior work, namely T opicMiner MTM, BUGZIE, Bug triaging via deep Reinforcement Learning BT -RL, and LDA-SVM. The evaluation data come from various Eclipse and Mozilla projects, such as JDT, Firefox, and Thunderbird. Large open-source projects offer an issue tracking system or open bug repository, where developers and users can report the software defects they find or any new feature requests they may have. These reports are called bug reports or issues . In some cases, developers can volunteer to work on the reported issues they find interesting or relevant to their field of expertise. Additionally, they sometimes report issues and assign them to themselves. However, in many cases, particularly in large open-source projects, a group of developers, called bug triagers, decide who should process and fix a newly reported issue.

Energy-based models (EBMs) are a powerful class of probabilistic generative models due to their flexibility and interpretability. However, relationships between potential flows and explicit EBMs remain underexplored, while contrastive divergence training via implicit Markov chain Monte Carlo (MCMC) sampling is often unstable and expensive in high-dimensional settings. In this paper, we propose Variational Potential Flow Bayes (VPFB), a new energy-based generative framework that eliminates the need for implicit MCMC sampling and does not rely on auxiliary networks or cooperative training. VPFB learns an energy-parameterized potential flow by constructing a flow-driven density homotopy that is matched to the data distribution through a variational loss minimizing the Kullback-Leibler divergence between the flow-driven and marginal homotopies. This principled formulation enables robust and efficient generative modeling while preserving the interpretability of EBMs. Experimental results on image generation, interpolation, out-of-distribution detection, and compositional generation confirm the effectiveness of VPFB, showing that our method performs competitively with existing approaches in terms of sample quality and versatility across diverse generative modeling tasks. 1 1 Introduction

We develop a methodology for constructing confidence sets for parameters of statistical models via a reduction to sequential prediction. Our key observation is that for any generalized linear model (GLM), one can construct an associated game of sequential probability assignment such that achieving low regret in the game implies a high-probability upper bound on the excess likelihood of the true parameter of the GLM. This allows us to develop a scheme that we call online-to-confidence-set conversions, which effectively reduces the problem of proving the desired statistical claim to an algorithmic question. We study two varieties of this conversion scheme: 1) analytical conversions that only require proving the existence of algorithms with low regret and provide confidence sets centered at the maximum-likelihood estimator 2) algorithmic conversions that actively leverage the output of the online algorithm to construct confidence sets (and may be centered at other, adaptively constructed point estimators). The resulting methodology recovers all state-of-the-art confidence set constructions within a single framework, and also provides several new types of confidence sets that were previously unknown in the literature.