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.

Minimizing an adversarial surrogate risk is a common technique for learning robust classifiers. Prior work showed that convex surrogate losses are not statistically consistent in the adversarial context-- or in other words, a minimizing sequence of the adversarial surrogate risk will not necessarily minimize the adversarial classification error. We connect the consistency of adversarial surrogate losses to properties of minimizers to the adversarial classification risk, known as adversarial Bayes classifiers. Specifically, under reasonable distributional assumptions, a convex surrogate loss is statistically consistent for adversarial learning iff the adversarial Bayes classifier satisfies a certain notion of uniqueness.

Personalization is crucial for the widespread adoption of advanced driver assistance system. To match up with each user's preference, the online evolution capability is a must. However, conventional evolution methods learn from naturalistic driving data, which requires a lot computing power and cannot be applied online. To address this challenge, this paper proposes a lesson learning approach: learning from driver's takeover interventions. By leveraging online takeover data, the driving zone is generated to ensure perceived safety using Gaussian discriminant analysis. Real-time corrections to trajectory planning rewards are enacted through apprenticeship learning. Guided by the objective of optimizing rewards within the constraints of the driving zone, this approach employs model predictive control for trajectory planning. This lesson learning framework is highlighted for its faster evolution capability, adeptness at experience accumulating, assurance of perceived safety, and computational efficiency. Simulation results demonstrate that the proposed system consistently achieves a successful customization without further takeover interventions. Accumulated experience yields a 24% enhancement in evolution efficiency. The average number of learning iterations is only 13.8. The average computation time is 0.08 seconds.

The widespread integration of deep neural networks in developing data-driven surrogate models for high-fidelity simulations of complex physical systems highlights the critical necessity for robust uncertainty quantification techniques and credibility assessment methodologies, ensuring the reliable deployment of surrogate models in consequential decision-making. This study presents the Occam Plausibility Algorithm for surrogate models (OPAL-surrogate), providing a systematic framework to uncover predictive neural network-based surrogate models within the large space of potential models, including various neural network classes and choices of architecture and hyperparameters. The framework is grounded in hierarchical Bayesian inferences and employs model validation tests to evaluate the credibility and prediction reliability of the surrogate models under uncertainty. Leveraging these principles, OPAL-surrogate introduces a systematic and efficient strategy for balancing the trade-off between model complexity, accuracy, and prediction uncertainty. The effectiveness of OPAL-surrogate is demonstrated through two modeling problems, including the deformation of porous materials for building insulation and turbulent combustion flow for the ablation of solid fuels within hybrid rocket motors.

In Reinforcement Learning (RL), artificial agents are trained to maximize numerical rewards by performing tasks. Exploration is essential in RL because agents must discover information before exploiting it. Two rewards encouraging efficient exploration are the entropy of action policy and curiosity for information gain. Entropy is well-established in literature, promoting randomized action selection. Curiosity is defined in a broad variety of ways in literature, promoting discovery of novel experiences. One example, prediction error curiosity, rewards agents for discovering observations they cannot accurately predict. However, such agents may be distracted by unpredictable observational noises known as curiosity traps. Based on the Free Energy Principle (FEP), this paper proposes hidden state curiosity, which rewards agents by the KL divergence between the predictive prior and posterior probabilities of latent variables. We trained six types of agents to navigate mazes: baseline agents without rewards for entropy or curiosity, and agents rewarded for entropy and/or either prediction error curiosity or hidden state curiosity. We find entropy and curiosity result in efficient exploration, especially both employed together. Notably, agents with hidden state curiosity demonstrate resilience against curiosity traps, which hinder agents with prediction error curiosity. This suggests implementing the FEP may enhance the robustness and generalization of RL models, potentially aligning the learning processes of artificial and biological agents.

Bayesian statistics is a cornerstone of imaging sciences, underpinning many and varied approaches from Markov random fields to score-based denoising diffusion models. In addition to powerful image estimation methods, the Bayesian paradigm also provides a framework for uncertainty quantification and for using image data as quantitative evidence. These probabilistic capabilities are important for the rigorous interpretation of experimental results and for robust interfacing of quantitative imaging pipelines with scientific and decision-making processes. However, are the probabilities delivered by existing Bayesian imaging methods meaningful under replication of an experiment, or are they only meaningful as subjective measures of belief? This paper presents a Monte Carlo method to explore this question. We then leverage the proposed Monte Carlo method and run a large experiment requiring 1,000 GPU-hours to probe the accuracy of five canonical Bayesian imaging methods that are representative of some of the main Bayesian imaging strategies from the past decades (a score-based denoising diffusion technique, a plug-and-play Langevin algorithm utilising a Lipschitz-regularised DnCNN denoiser, a Bayesian method with a dictionary-based prior trained subject to a log-concavity constraint, an empirical Bayesian method with a total-variation prior, and a hierarchical Bayesian Gibbs sampler based on a Gaussian Markov random field model). We find that, a few cases, the probabilities reported by modern Bayesian imaging techniques are in broad agreement with long-term averages as observed over a large number of replication of an experiment, but existing Bayesian imaging methods are generally not able to deliver reliable uncertainty quantification results.

As the right to be forgotten has been legislated worldwide, many studies attempt to design unlearning mechanisms to protect users' privacy when they want to leave machine learning service platforms. Specifically, machine unlearning is to make a trained model to remove the contribution of an erased subset of the training dataset. This survey aims to systematically classify a wide range of machine unlearning and discuss their differences, connections and open problems. We categorize current unlearning methods into four scenarios: centralized unlearning, distributed and irregular data unlearning, unlearning verification, and privacy and security issues in unlearning. Since centralized unlearning is the primary domain, we use two parts to introduce: firstly, we classify centralized unlearning into exact unlearning and approximate unlearning; secondly, we offer a detailed introduction to the techniques of these methods. Besides the centralized unlearning, we notice some studies about distributed and irregular data unlearning and introduce federated unlearning and graph unlearning as the two representative directions. After introducing unlearning methods, we review studies about unlearning verification. Moreover, we consider the privacy and security issues essential in machine unlearning and organize the latest related literature. Finally, we discuss the challenges of various unlearning scenarios and address the potential research directions.

Conditional independence provides a way to understand causal relationships among the variables of interest. An underlying system may exhibit more fine-grained causal relationships especially between a variable and its parents, which will be called the local independence relationships. One of the most widely studied local relationships is Context-Specific Independence (CSI), which holds in a specific assignment of conditioned variables. However, its applicability is often limited since it does not allow continuous variables: data conditioned to the specific value of a continuous variable contains few instances, if not none, making it infeasible to test independence. In this work, we define and characterize the local independence relationship that holds in a specific set of joint assignments of parental variables, which we call context-set specific independence (CSSI). We then provide a canonical representation of CSSI and prove its fundamental properties. Based on our theoretical findings, we cast the problem of discovering multiple CSSI relationships in a system as finding a partition of the joint outcome space. Finally, we propose a novel method, coined neural contextual decomposition (NCD), which learns such partition by imposing each set to induce CSSI via modeling a conditional distribution. We empirically demonstrate that the proposed method successfully discovers the ground truth local independence relationships in both synthetic dataset and complex system reflecting the real-world physical dynamics.