However, such methods are usually sensitive to environmental dynamics-irrelevant information, e.g., white-noise. To handle such dynamics-irrelevant information, we propose a Dynamic Bottleneck (DB) model, which attains a dynamics-relevant representation based on the information-bottleneck principle.

Understanding causality in event sequences with thousands of sparse event types is critical in domains such as healthcare, cybersecurity, or vehicle diagnostics, yet current methods fail to scale. We present OSCAR, a one-shot causal autoregressive method that infers per-sequence Markov Boundaries using two pretrained Transformers as density estimators. This enables efficient, parallel causal discovery without costly global CI testing. On a real-world automotive dataset with 29,100 events and 474 labels, OSCAR recovers interpretable causal structures in minutes, while classical methods fail to scale, enabling practical scientific diagnostics at production scale.

Dynamic Bayesian networks (DBNs) are compact graphical representations used to model probabilistic systems where interdependent random variables and their distributions evolve over time. In this paper, we study the verification of the evolution of conditional-independence (CI) propositions against temporal logic specifications. To this end, we consider two specification formalisms over CI propositions: linear temporal logic (LTL), and non-deterministic Büchi automata (NBAs). This problem has two variants. Stochastic CI properties take the given concrete probability distributions into account, while structural CI properties are viewed purely in terms of the graphical structure of the DBN. We show that deciding if a stochastic CI proposition eventually holds is at least as hard as the Skolem problem for linear recurrence sequences, a long-standing open problem in number theory. On the other hand, we show that verifying the evolution of structural CI propositions against LTL and NBA specifications is in PSPACE, and is NP- and coNP-hard. We also identify natural restrictions on the graphical structure of DBNs that make the verification of structural CI properties tractable.

Mission critical (MC) applications such as defense operations, energy management, cybersecurity, and aerospace control require reliable, deterministic, and low-latency decision making under uncertainty. Although the classical Machine Learning (ML) approaches are effective, they often struggle to meet the stringent constraints of robustness, timing, explainability, and safety in the MC domains. Quantum Artificial Intelligence (QAI), the fusion of machine learning and quantum computing (QC), can provide transformative solutions to the challenges faced by classical ML models. In this paper, we provide a comprehensive exploration of QAI for MC systems. We begin with a conceptual background to quantum computing, MC systems, and quantum machine learning (QAI). We then examine the core mechanisms and algorithmic principles of QAI in MC systems, including quantum-enhanced learning pipelines, quantum uncertainty quantification, and quantum explainability frameworks. Subsequently, we discuss key application areas like aerospace, defense, cybersecurity, smart grids, and disaster management, focusing on the role of QA in enhancing fault tolerance, real-time intelligence, and adaptability. We provide an exploration of the positioning of QAI for MC systems in the industry in terms of deployment. We also propose a model for management of quantum resources and scheduling of applications driven by timeliness constraints. We discuss multiple challenges, including trainability limits, data access, and loading bottlenecks, verification of quantum components, and adversarial QAI. Finally, we outline future research directions toward achieving interpretable, scalable, and hardware-feasible QAI models for MC application deployment.

Autonomous robots are increasingly deployed for information-gathering tasks in environments that vary across space and time. Planning informative and safe trajectories in such settings is challenging because information decays when regions are not revisited. Most existing planners model information as static or uniformly decaying, ignoring environments where the decay rate varies spatially; those that model non-uniform decay often overlook how it evolves along the robot's motion, and almost all treat safety as a soft penalty. In this paper, we address these challenges. We model uncertainty in the environment using clarity, a normalized representation of differential entropy from our earlier work that captures how information improves through new measurements and decays over time when regions are not revisited. Building on this, we present Stein V ariational Clarity-A ware Informative Planning, a framework that embeds clarity dynamics within trajectory optimization and enforces safety through a low-level filtering mechanism based on our earlier gatekeeper framework for safety verification. The planner performs Bayesian inference-based learning via Stein variational inference, refining a distribution over informative trajectories while filtering each nominal Stein informative trajectory to ensure safety. Hardware experiments and simulations across environments with varying decay rates and obstacles demonstrate consistent safety and reduced information deficits.

Species distribution models (SDMs), which aim to predict species occurrence based on environmental variables, are widely used to monitor and respond to biodiversity change. Recent deep learning advances for SDMs have been shown to perform well on complex and heterogeneous datasets, but their effectiveness remains limited by spatial biases in the data. In this paper, we revisit deep SDMs from a Bayesian perspective and introduce BATIS, a novel and practical framework wherein prior predictions are updated iteratively using limited observational data. Models must appropriately capture both aleatoric and epistemic uncertainty to effectively combine fine-grained local insights with broader ecological patterns. We benchmark an extensive set of uncertainty quantification approaches on a novel dataset including citizen science observations from the eBird platform. Our empirical study shows how Bayesian deep learning approaches can greatly improve the reliability of SDMs in data-scarce locations, which can contribute to ecological understanding and conservation efforts.

Missing data is a common problem across various scientific disciplines, including medical research (Bell et al., 2014), social sciences (Molenberghs et al., 2014), and astronomy (Ivezi c et al., 2020). To handle missing entries in the dataset, imputation (Grzesiak et al., 2025; Kim and Shao, 2021; Little and Rubin, 2019) is a popular approach that is widely accepted in practice. An imputation model generates plausible values for each missing entry, transforming an incomplete dataset into a complete one. The critical importance of this task has led to the development of a wide array of imputation models, grounded in various modeling assumptions. These range from traditional approaches like hot-deck imputation (Little and Rubin, 2019) to more sophisticated methods such as Multiple Imputation via Chained Equations (MICE; V an Buuren and Groothuis-Oudshoorn 2011), random forest imputation (Stekhoven and Bühlmann, 2012), techniques based on Markov assumptions on graphs (Y ang and Chen, 2025), and even generative adversarial networks (Y oon et al., 2018). Despite the proliferation of imputation models, the selection of an optimal imputation model for a given dataset remains a significant challenge, largely due to the unsupervised nature of the problem. Among the many proposed strategies for evaluating and selecting imputation models, masking has emerged as a particularly popular procedure (Gelman et al., 1998; Honaker et al., 2011; Leek et al., 2012; Qian et al., 2024; Troyanskaya et al., 2001; Wang et al., 2024). Masking involves intentionally creating missing values in observed entries to create a setting where imputation accuracy can be measured against a known ground truth. This approach has demonstrated remarkable success and power in other domains, notably in language modeling (Devlin et al., 2019; Y ang et al., 2019) and image recognition (Hondru et al., 2025; Vincent et al., 2010; Xie et al., 2022) and prediction-powered inference (Angelopoulos et al., 2023; Wang et al., 2020).

Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural setting of star-structured variational inference, where a root variable impacts all the other ones. We prove the first results for existence, uniqueness, and self-consistency of the variational approximation. In turn, we derive quantitative approximation error bounds for the variational approximation to the posterior, extending prior work from the mean-field setting to the star-structured setting. We also develop a gradient-based algorithm with provable guarantees for computing the variational approximation using ideas from optimal transport theory. We explore the implications of our results for Gaussian measures and hierarchical Bayesian models, including generalized linear models with location family priors and spike-and-slab priors with one-dimensional debiasing. As a by-product of our analysis, we develop new stability results for star-separable transport maps which might be of independent interest.