--Learning the structure of Bayesian networks (BNs) from data is challenging, especially for datasets involving a large number of variables. The recently proposed divide-and-conquer (D&D) strategies present a promising approach for learning large BNs. However, they still face a main issue of unstable learning accuracy across subproblems. In this work, we introduce the idea of employing structure learning ensemble (SLE), which combines multiple BN structure learning algorithms, to consistently achieve high learning accuracy. We further propose an automatic approach called Auto-SLE for learning near-optimal SLEs, addressing the challenge of manually designing high-quality SLEs. The learned SLE is then integrated into a D&D method. Extensive experiments firmly show the superiority of our method over D&D methods with single BN structure learning algorithm in learning large BNs, achieving accuracy improvement usually by 30% 225% on datasets involving 10,000 variables. These results indicate the significant potential of employing (automatic learning of) SLEs for scalable BN structure learning. Learning the structure of Bayesian networks (BNs) [1] from data has attracted much research interest, due to its wide applications in machine learning, statistical modeling, and causal inference [2]-[4].

Discrete diffusion models represent a significant advance in generative modeling, demonstrating remarkable success in synthesizing complex, high-quality discrete data. However, to avoid exponential computational costs, they typically rely on calculating per-dimension transition probabilities when learning high-dimensional distributions. In this study, we rigorously prove that this approach leads to a worst-case linear scaling of Kullback-Leibler (KL) divergence with data dimension. To address this, we propose a Quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM), which enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces, offering a theoretical pathway to faithfully capture the true joint distribution. By deriving posterior states through quantum Bayes' theorem, similar to the crucial role of posterior probabilities in classical diffusion models, and by learning the joint probability, we establish a solid theoretical foundation for quantum-enhanced diffusion models. For denoising, we design a quantum circuit that utilizes temporal information for parameter sharing and incorporates learnable classical-data-controlled rotations for encoding. Exploiting joint distribution learning, our approach enables single-step sampling from pure noise, eliminating iterative requirements of existing models. Simulations demonstrate the proposed model's superior accuracy in modeling complex distributions compared to factorization methods. Hence, this paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.

Despite AI's impressive achievements, including recent advances in generative and large language models, there remains a significant gap in the ability of AI systems to handle uncertainty and generalize beyond their training data. AI models consistently fail to make robust enough predictions when facing unfamiliar or adversarial data. Traditional machine learning approaches struggle to address this issue, due to an overemphasis on data fitting, while current uncertainty quantification approaches suffer from serious limitations. This position paper posits a paradigm shift towards epistemic artificial intelligence, emphasizing the need for models to learn from what they know while at the same time acknowledging their ignorance, using the mathematics of second-order uncertainty measures. This approach, which leverages the expressive power of such measures to efficiently manage uncertainty, offers an effective way to improve the resilience and robustness of AI systems, allowing them to better handle unpredictable real-world environments.

This research addresses critical autonomous vehicle control challenges arising from road roughness variation, which induces course deviations and potential loss of road contact during steering operations. We present a novel real-time road roughness estimation system employing Bayesian calibration methodology that processes axle accelerations to predict terrain roughness with quantifiable confidence measures. The technical framework integrates a Gaussian process surrogate model with a simulated half-vehicle model, systematically processing vehicle velocity and road surface roughness parameters to generate corresponding axle acceleration responses. The Bayesian calibration routine performs inverse estimation of road roughness from observed accelerations and velocities, yielding posterior distributions that quantify prediction uncertainty for adaptive risk management. Training data generation utilizes Latin Hypercube sampling across comprehensive velocity and roughness parameter spaces, while the calibrated model integrates seamlessly with a Simplex controller architecture to dynamically adjust velocity limits based on real-time roughness predictions. Experimental validation on stochastically generated surfaces featuring varying roughness regions demonstrates robust real-time characterization capabilities, with the integrated Simplex control strategy effectively enhancing autonomous vehicle operational safety through proactive surface condition response. This innovative Bayesian framework establishes a comprehensive foundation for mitigating roughness-related operational risks while simultaneously improving efficiency and safety margins in autonomous vehicle systems.

Modern observatories are designed to deliver increasingly detailed views of astrophysical signals. To fully realize the potential of these observations, principled data-analysis methods are required to effectively separate and reconstruct the underlying astrophysical components from data corrupted by noise and instrumental effects. In this work, we introduce a novel multi-frequency Bayesian model of the sky emission field that leverages latent-space tension as an indicator of model misspecification, enabling automated separation of diffuse, point-like, and extended astrophysical emission components across wavelength bands. Deviations from latent-space prior expectations are used as diagnostics for model misspecification, thus systematically guiding the introduction of new sky components, such as point-like and extended sources. We demonstrate the effectiveness of this method on synthetic multi-frequency imaging data and apply it to observational X-ray data from the eROSITA Early Data Release (EDR) of the SN1987A region in the Large Magellanic Cloud (LMC). Our results highlight the method's capability to reconstruct astrophysical components with high accuracy, achieving sub-pixel localization of point sources, robust separation of extended emission, and detailed uncertainty quantification. The developed methodology offers a general and well-founded framework applicable to a wide variety of astronomical datasets, and is therefore well suited to support the analysis needs of next-generation multi-wavelength and multi-messenger surveys.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

Modern cyberattacks in cyber-physical systems (CPS) rapidly evolve and cannot be deterred effectively with most current methods which focused on characterizing past threats. Adaptive anomaly detection (AAD) is among the most promising techniques to detect evolving cyberattacks focused on fast data processing and model adaptation. AAD has been researched in the literature extensively; however, to the best of our knowledge, our work is the first systematic literature review (SLR) on the current research within this field. We present a comprehensive SLR, gathering 397 relevant papers and systematically analyzing 65 of them (47 research and 18 survey papers) on AAD in CPS studies from 2013 to 2023 (November). We introduce a novel taxonomy considering attack types, CPS application, learning paradigm, data management, and algorithms. Our analysis indicates, among other findings, that reviewed works focused on a single aspect of adaptation (either data processing or model adaptation) but rarely in both at the same time. We aim to help researchers to advance the state of the art and help practitioners to become familiar with recent progress in this field. We identify the limitations of the state of the art and provide recommendations for future research directions.

Despite their widespread use, large language models (LLMs) are known to hallucinate incorrect information and be poorly calibrated. This makes the uncertainty quantification of these models of critical importance, especially in high-stakes domains, such as autonomy and healthcare. Prior work has made Bayesian deep learning-based approaches to this problem more tractable by performing inference over the low-rank adaptation (LoRA) parameters of a fine-tuned model. While effective, these approaches struggle to scale to larger LLMs due to requiring further additional parameters compared to LoRA. In this work we present $\textbf{Scala}$ble $\textbf{B}$ayesian $\textbf{L}$ow-Rank Adaptation via Stochastic Variational Subspace Inference (ScalaBL). We perform Bayesian inference in an $r$-dimensional subspace, for LoRA rank $r$. By repurposing the LoRA parameters as projection matrices, we are able to map samples from this subspace into the full weight space of the LLM. This allows us to learn all the parameters of our approach using stochastic variational inference. Despite the low dimensionality of our subspace, we are able to achieve competitive performance with state-of-the-art approaches while only requiring ${\sim}1000$ additional parameters. Furthermore, it allows us to scale up to the largest Bayesian LLM to date, with four times as a many base parameters as prior work.

Current approaches for question answering (QA) over tabular data, such as NL2SQL systems, perform well for factual questions where answers are directly retrieved from tables. However, they fall short on probabilistic questions requiring reasoning under uncertainty. In this paper, we introduce a new benchmark LUCARIO and a framework for probabilistic QA over large tabular data. Our method induces Bayesian Networks from tables, translates natural language queries into probabilistic queries, and uses large language models (LLMs) to generate final answers. Empirical results demonstrate significant improvements over baselines, highlighting the benefits of hybrid symbolic-neural reasoning.

Dynamic treatment regimes (DTRs) provide a principled framework for optimizing sequential decision-making in domains where decisions must adapt over time in response to individual trajectories, such as healthcare, education, and digital interventions. However, existing statistical methods often rely on strong positivity assumptions and lack robustness under partial data coverage, while offline reinforcement learning approaches typically focus on average training performance, lack statistical guarantees, and require solving complex optimization problems. To address these challenges, we propose POLAR, a novel pessimistic model-based policy learning algorithm for offline DTR optimization. POLAR estimates the transition dynamics from offline data and quantifies uncertainty for each history-action pair. A pessimistic penalty is then incorporated into the reward function to discourage actions with high uncertainty. Unlike many existing methods that focus on average training performance, POLAR directly targets the suboptimality of the final learned policy and offers theoretical guarantees, without relying on computationally intensive minimax or constrained optimization procedures. To the best of our knowledge, POLAR is the 1 first model-based DTR method to provide both statistical and computational guarantees, including finite-sample bounds on policy suboptimality. Empirical results on both synthetic data and the MIMIC-III dataset demonstrate that POLAR outperforms state-of-the-art methods and yields near-optimal, history-aware treatment strategies.