Continuous-time reinforcement learning (CTRL) provides a natural framework for sequential decision-making in dynamic environments where interactions evolve continuously over time. While CTRL has shown growing empirical success, its ability to adapt to varying levels of problem difficulty remains poorly understood. In this work, we investigate the instance-dependent behavior of CTRL and introduce a simple, model-based algorithm built on maximum likelihood estimation (MLE) with a general function approximator. Unlike existing approaches that estimate system dynamics directly, our method estimates the state marginal density to guide learning. We establish instance-dependent performance guarantees by deriving a regret bound that scales with the total reward variance and measurement resolution. Notably, the regret becomes independent of the specific measurement strategy when the observation frequency adapts appropriately to the problem's complexity. To further improve performance, our algorithm incorporates a randomized measurement schedule that enhances sample efficiency without increasing measurement cost. These results highlight a new direction for designing CTRL algorithms that automatically adjust their learning behavior based on the underlying difficulty of the environment.

Deep learning has revolutionized modern data science. However, how to accurately quantify the uncertainty of predictions from large-scale deep neural networks (DNNs) remains an unresolved issue. To address this issue, we introduce a novel post-processing approach. This approach feeds the output from the last hidden layer of a pre-trained large-scale DNN model into a stochastic neural network (StoNet), then trains the StoNet with a sparse penalty on a validation dataset and constructs prediction intervals for future observations. We establish a theoretical guarantee for the validity of this approach; in particular, the parameter estimation consistency for the sparse StoNet is essential for the success of this approach. Comprehensive experiments demonstrate that the proposed approach can construct honest confidence intervals with shorter interval lengths compared to conformal methods and achieves better calibration compared to other post-hoc calibration techniques. Additionally, we show that the StoNet formulation provides us with a platform to adapt sparse learning theory and methods from linear models to DNNs.

Learning causal structure in complex systems is a fundamental challenge across a broad range of disciplines, from traditional scientific fields to modern engineering and technology. Unlike conventional statistical methods that focus merely on correlation, the field of causal discovery primarily considers the problem of discovering the directionality and strength of causal relationships between variables, often from observational data. Thus, it has become a critical tool for researchers aiming to predict the effects of interventions on the systems, especially where controlled experimentation may be expensive, unethical, or even infeasible. Such necessities arise not only in various areas of natural science, such as epidemiology [56], public health [65], genomics [14], neuroscience [86], and climate and environmental science [60], but also in numerous domains in social science, such as psychology [50], philosophy [26], and economics [37]. Moreover, with recent advances in science and technology and the increase in size and complexity of data generation processes, causal discovery has acquired significant relevance in the fields of machine learning [63] and artificial intelligence [81, 82] through various emerging areas such as causal representation learning [64, 85], causal transfer learning [83], causal algorithmic fairness [84], and causal reinforcement learning [5]. This work focuses on learning causal structures from purely observational data within the framework of causal Bayesian networks, which are widely used to represent causal relationships among variables through directed acyclic graphs (DAGs). This is, in general, a nontrivial and difficult task due to the vast number of potential DAG structures and multiple DAGs representing the same set of conditional independence relationships. In fact, DAGs are generally identifiable only up to their corresponding Markov equivalence class, in which all DAGs encode the same conditional independencies [31].

The use of machine learning tools has given causal inference a new lease of life, enabling complex models to be used with principled causal estimators and guarantees about statistically important quantities (Wager and Athey, 2018; Chernozhukov et al., 2018; Hahn et al., 2020). To build trustworthy causal models, however, we also need to understand when these methods may be more or less reliable, or perhaps fail completely. This implies that causal inference needs a set of good benchmarking tools. Unfortunately, real-world datasets are not ideal for this task, because they cannot give us access to the ground truth other than in a few very special circumstances. In particular, they rarely provide the counterfactual outcomes we care about, and the distribution we want to evaluate often differs from the one that produced the observations. Well-designed simulations can address this discrepancy (Neal et al., 2020; Parikh et al., 2022); they allow us to choose a ground truth, stress-test new methods, compare their generalizability and stability, and expose failure modes before deployment.

We develop a central limit theorem (CLT) for the non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under which the estimator is asymptotically normal, and reveal settings in which no CLT can exist. We then build upon it to derive CLTs for the value, Q-, and advantage functions of any stationary stochastic policy, including the optimal policy recovered from the estimated model. Goodness-of-fit tests are derived as a corollary, which enable us to test whether the logged data is stochastic. These results provide new statistical tools for offline policy evaluation and optimal policy recovery, and enable hypothesis tests for transition probabilities.

Multi-class classification annotations have significantly advanced AI applications, with truth inference serving as a critical technique for aggregating noisy and biased annotations. Existing state-of-the-art methods typically model each annotator's expertise using a confusion matrix. However, these methods suffer from two widely recognized issues: 1) when most annotators label only a few tasks, or when classes are imbalanced, the estimated confusion matrices are unreliable, and 2) a single confusion matrix often remains inadequate for capturing each annotator's full expertise patterns across all tasks. To address these issues, we propose a novel confusion-matrix-based method, PTBCC (ProtoType learning-driven Bayesian Classifier Combination), to introduce a reliable and richer annotator estimation by prototype learning. Specifically, we assume that there exists a set $S$ of prototype confusion matrices, which capture the inherent expertise patterns of all annotators. Rather than a single confusion matrix, the expertise per annotator is extended as a Dirichlet prior distribution over these prototypes. This prototype learning-driven mechanism circumvents the data sparsity and class imbalance issues, ensuring a richer and more flexible characterization of annotators. Extensive experiments on 11 real-world datasets demonstrate that PTBCC achieves up to a 15% accuracy improvement in the best case, and a 3% higher average accuracy while reducing computational cost by over 90%.

Counterfactual explanations study what should have changed in order to get an alternative result, enabling end-users to understand machine learning mechanisms with counterexamples. Actionability is defined as the ability to transform the original case to be explained into a counterfactual one. We develop a method for actionable counterfactual explanations that, unlike predecessors, does not directly leverage training data. Rather, data is only used to learn a density estimator, creating a search landscape in which to apply path planning algorithms to solve the problem and masking the endogenous data, which can be sensitive or private. We put special focus on estimating the data density using Bayesian networks, demonstrating how their enhanced interpretability is useful in high-stakes scenarios in which fairness is raising concern. Using a synthetic benchmark comprised of 15 datasets, our proposal finds more actionable and simpler counterfactuals than the current state-of-the-art algorithms. We also test our algorithm with a real-world Environmental Protection Agency dataset, facilitating a more efficient and equitable study of policies to improve the quality of life in United States of America counties. Our proposal captures the interaction of variables, ensuring equity in decisions, as policies to improve certain domains of study (air, water quality, etc.) can be detrimental in others. In particular, the sociodemographic domain is often involved, where we find important variables related to the ongoing housing crisis that can potentially have a severe negative impact on communities.

The exponential growth of scientific knowledge has made the automated generation of scientific hypotheses that combine novelty, feasibility, and research value a core challenge. Existing methods based on large language models fail to systematically model the inherent in hypotheses or incorporate the closed-loop feedback mechanisms crucial for refinement. This paper proposes a multi-agent collaborative framework called HypoAgents, which for the first time integrates Bayesian reasoning with an information entropy-driven search mechanism across three stages-hypotheses generation, evidence validation, and hypotheses Refinement-to construct an iterative closed-loop simulating scientists' cognitive processes. Specifically, the framework first generates an initial set of hypotheses through diversity sampling and establishes prior beliefs based on a composite novelty-relevance-feasibility (N-R-F) score. It then employs etrieval-augmented generation (RAG) to gather external literature evidence, updating the posterior probabilities of hypotheses using Bayes' theorem. Finally, it identifies high-uncertainty hypotheses using information entropy $H = - \sum {{p_i}\log {p_i}}$ and actively refines them, guiding the iterative optimization of the hypothesis set toward higher quality and confidence. Experimental results on the ICLR 2025 conference real-world research question dataset (100 research questions) show that after 12 optimization iterations, the average ELO score of generated hypotheses improves by 116.3, surpassing the benchmark of real paper abstracts by 17.8, while the framework's overall uncertainty, as measured by Shannon entropy, decreases significantly by 0.92. This study presents an interpretable probabilistic reasoning framework for automated scientific discovery, substantially improving the quality and reliability of machine-generated research hypotheses.

The rise of Generative AI (GenAI) in recent years has catalyzed transformative advances in wireless communications and networks. Among the members of the GenAI family, Diffusion Models (DMs) have risen to prominence as a powerful option, capable of handling complex, high-dimensional data distribution, as well as consistent, noise-robust performance. In this survey, we aim to provide a comprehensive overview of the theoretical foundations and practical applications of DMs across future communication systems. We first provide an extensive tutorial of DMs and demonstrate how they can be applied to enhance optimizers, reinforcement learning and incentive mechanisms, which are popular approaches for problems in wireless networks. Then, we review and discuss the DM-based methods proposed for emerging issues in future networks and communications, including channel modeling and estimation, signal detection and data reconstruction, integrated sensing and communication, resource management in edge computing networks, semantic communications and other notable issues. We conclude the survey with highlighting technical limitations of DMs and their applications, as well as discussing future research directions.

-- While much research explores improving robot capabilities, there is a deficit in researching how robots are expected to perform tasks safely, especially in high-risk problem domains. Robots must earn the trust of human operators in order to be effective collaborators in safety-critical tasks, specifically those where robots operate in human environments. We propose the human-robot red teaming paradigm for safety-aware reasoning . We expect humans and robots to work together to challenge assumptions about an environment and explore the space of hazards that may arise. This exploration will enable robots to perform safety-aware reasoning, specifically hazard identification, risk assessment, risk mitigation, and safety reporting. We demonstrate that: (a) human-robot red teaming allows human-robot teams to plan to perform tasks safely in a variety of domains, and (b) robots with different embodiments can learn to operate safely in two different environments--a lunar habitat and a household--with varying definitions of safety. T aken together, our work on human-robot red teaming for safety-aware reasoning demonstrates the feasibility of this approach for safely operating and promoting trust on human-robot teams in safety-critical problem domains. I. INTRODUCTION Enabling robots to reason over risks is a crucial capability of performing collaborative assistive tasks in safety-critical domains.