This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability distributions are developed for the new binned semiparametric Bayesian networks, the sparse binned kernel density estimation and the Fourier kernel density estimation. These two probability distributions address the curse of dimensionality, which typically impacts binned models, by using sparse tensors and restricting the number of parent nodes in conditional probability calculations. To evaluate the proposal, we perform a complexity analysis and conduct several comparative experiments using synthetic data and datasets from the UCI Machine Learning repository. The experiments include different binning rules, parent restrictions, grid sizes, and number of instances to get a holistic view of the model's behavior. As a result, our binned semiparametric Bayesian networks achieve structural learning and log-likelihood estimations with no statistically significant differences compared to the semiparametric Bayesian networks, but at a much higher speed. Thus, the new binned semiparametric Bayesian networks prove to be a reliable and more efficient alternative to their non-binned counterparts.

As autonomous agents powered by large language models (LLMs) continue to demonstrate potential across various assistive tasks, ensuring their safe and reliable behavior is crucial for preventing unintended consequences. In this work, we introduce CIP, a novel technique that leverages causal influence diagrams (CIDs) to identify and mitigate risks arising from agent decision-making. CIDs provide a structured representation of cause-and-effect relationships, enabling agents to anticipate harmful outcomes and make safer decisions. Our approach consists of three key steps: (1) initializing a CID based on task specifications to outline the decision-making process, (2) guiding agent interactions with the environment using the CID, and (3) iteratively refining the CID based on observed behaviors and outcomes. Experimental results demonstrate that our method effectively enhances safety in both code execution and mobile device control tasks.

HIV epidemiological data is increasingly complex, requiring advanced computation for accurate cluster detection and forecasting. We employed quantum-accelerated machine learning to analyze HIV prevalence at the ZIP-code level using AIDSVu and synthetic SDoH data for 2022. Our approach compared classical clustering (DBSCAN, HDBSCAN) with a quantum approximate optimization algorithm (QAOA), developed a hybrid quantum-classical neural network for HIV prevalence forecasting, and used quantum Bayesian networks to explore causal links between SDoH factors and HIV incidence. The QAOA-based method achieved 92% accuracy in cluster detection within 1.6 seconds, outperforming classical algorithms. Meanwhile, the hybrid quantum-classical neural network predicted HIV prevalence with 94% accuracy, surpassing a purely classical counterpart. Quantum Bayesian analysis identified housing instability as a key driver of HIV cluster emergence and expansion, with stigma exerting a geographically variable influence. These quantum-enhanced methods deliver greater precision and efficiency in HIV surveillance while illuminating critical causal pathways. This work can guide targeted interventions, optimize resource allocation for PrEP, and address structural inequities fueling HIV transmission.

Learning from ambiguous labels is a long-standing problem in practical machine learning applications. The purpose of \emph{partial label learning} (PLL) is to identify the ground-truth label from a set of candidate labels associated with a given instance. Inspired by the remarkable performance of diffusion models in various generation tasks, this paper explores their potential to denoise ambiguous labels through the reverse denoising process. Therefore, this paper reformulates the label disambiguation problem from the perspective of generative models, where labels are generated by iteratively refining initial random guesses. This perspective enables the diffusion model to learn how label information is generated stochastically. By modeling the generation uncertainty, we can use the maximum likelihood estimate of the label for classification inference. However, such ambiguous labels lead to a mismatch between instance and label, which reduces the quality of generated data. To address this issue, this paper proposes a \emph{diffusion disambiguation model for PLL} (DDMP), which first uses the potential complementary information between instances and labels to construct pseudo-clean labels for initial diffusion training. Furthermore, a transition-aware matrix is introduced to estimate the potential ground-truth labels, which are dynamically updated during the diffusion generation. During training, the ground-truth label is progressively refined, improving the classifier. Experiments show the advantage of the DDMP and its suitability for PLL.

Just like power, water, and transportation systems, wireless networks are a crucial societal infrastructure. As natural and human-induced disruptions continue to grow, wireless networks must be resilient. This requires them to withstand and recover from unexpected adverse conditions, shocks, unmodeled disturbances and cascading failures. Unlike robustness and reliability, resilience is based on the understanding that disruptions will inevitably happen. Resilience, as elasticity, focuses on the ability to bounce back to favorable states, while resilience as plasticity involves agents and networks that can flexibly expand their states and hypotheses through real-time adaptation and reconfiguration. This situational awareness and active preparedness, adapting world models and counterfactually reasoning about potential system failures and the best responses, is a core aspect of resilience. This article will first disambiguate resilience from reliability and robustness, before delving into key mathematical foundations of resilience grounded in abstraction, compositionality and emergence. Subsequently, we focus our attention on a plethora of techniques and methodologies pertaining to the unique characteristics of resilience, as well as their applications through a comprehensive set of use cases. Ultimately, the goal of this paper is to establish a unified foundation for understanding, modeling, and engineering resilience in wireless communication systems, while laying a roadmap for the next-generation of resilient-native and intelligent wireless systems.

Bayesian decision theory advocates the Bayes classifier as the optimal approach for minimizing the risk in machine learning problems. Current deep learning algorithms usually solve for the optimal classifier by \emph{implicitly} estimating the posterior probabilities, \emph{e.g.}, by minimizing the Softmax cross-entropy loss. This simple methodology has been proven effective for meticulously balanced academic benchmark datasets. However, it is not applicable to the long-tailed data distributions in the real world, where it leads to the gradient imbalance issue and fails to ensure the Bayes optimal decision rule. To address these challenges, this paper presents a novel approach (BAPE) that provides a more precise theoretical estimation of the data distributions by \emph{explicitly} modeling the parameters of the posterior probabilities and solving them with point estimation. Consequently, our method directly learns the Bayes classifier without gradient descent based on Bayes' theorem, simultaneously alleviating the gradient imbalance and ensuring the Bayes optimal decision rule. Furthermore, we propose a straightforward yet effective \emph{distribution adjustment} technique. This method enables the Bayes classifier trained from the long-tailed training set to effectively adapt to the test data distribution with an arbitrary imbalance factor, thereby enhancing performance without incurring additional computational costs. In addition, we demonstrate the gains of our method are orthogonal to existing learning approaches for long-tailed scenarios, as they are mostly designed under the principle of \emph{implicitly} estimating the posterior probabilities. Extensive empirical evaluations on CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist demonstrate that our method significantly improves the generalization performance of popular deep networks, despite its simplicity.

Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we study CBO in the context of closed-box adversarial attacks, which are imperceptible input perturbations that aim to fool a classifier, without accessing its gradient. Our contribution is to establish a connection between the so-called consensus hopping as introduced by Riedl et al. and natural evolution strategies (NES) commonly applied in the context of adversarial attacks and to rigorously relate both methods to gradient-based optimization schemes. Beyond that, we provide a comprehensive experimental study that shows that despite the conceptual similarities, CBO can outperform NES and other evolutionary strategies in certain scenarios.

We introduce BayesL, a novel logical framework for specifying, querying, and verifying the behaviour of Bayesian networks (BNs). BayesL (pronounced "Basil") is a structured language that allows for the creation of queries over BNs. It facilitates versatile reasoning concerning causal and evidence-based relationships, and permits comprehensive what-if scenario evaluations without the need for manual modifications to the model.

In this paper, we propose a unifying message-passing framework for training spiking neural networks (SNNs) using Expectation-Propagation. Our gradient-free method is capable of learning the marginal distributions of network parameters and simultaneously marginalizes nuisance parameters, such as the outputs of hidden layers. This framework allows for the first time, training of discrete and continuous weights, for deterministic and stochastic spiking networks, using batches of training samples. Although its convergence is not ensured, the algorithm converges in practice faster than gradient-based methods, without requiring a large number of passes through the training data. The classification and regression results presented pave the way for new efficient training methods for deep Bayesian networks.

We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang et al., 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds, surpassing existing guarantees (Fan et al., 2019; Kang et al., 2022), and reveal a novel experimental design objective, $\mathrm{GL}(π)$. The key technical challenge is controlling bias from the nonlinear inverse link function, which we address by our two-stage approach. We prove a *local* minimax lower bound, showing that our `GL-LowPopArt` enjoys instance-wise optimality up to the condition number of the ground-truth Hessian. Applications include generalized linear matrix completion, where `GL-LowPopArt` achieves a state-of-the-art Frobenius error guarantee, and **bilinear dueling bandits**, a novel setting inspired by general preference learning (Zhang et al., 2024). Our analysis of a `GL-LowPopArt`-based explore-then-commit algorithm reveals a new, potentially interesting problem-dependent quantity, along with improved Borda regret bound than vectorization (Wu et al., 2024).