Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely observational data. Under the assumptions of acyclicity, causal sufficiency, and a uniform model prior, Markov equivalence classes are known to be small on average. In this paper, we show that this is no longer the case when any of these assumptions is relaxed. Specifically, we prove exponentially large lower bounds for the expected size of Markov equivalence classes in three settings: sparse random directed acyclic graphs, uniformly random acyclic directed mixed graphs, and uniformly random directed cyclic graphs.

Budget planning and maintenance optimization are crucial for infrastructure asset management, ensuring cost-effectiveness and sustainability. However, the complexity arising from combinatorial action spaces, diverse asset deterioration, stringent budget constraints, and environmental uncertainty significantly limits existing methods' scalability. This paper proposes a Hierarchical Deep Reinforcement Learning methodology specifically tailored to multi-year infrastructure planning. Our approach decomposes the problem into two hierarchical levels: a high-level Budget Planner allocating annual budgets within explicit feasibility bounds, and a low-level Maintenance Planner prioritizing assets within the allocated budget. By structurally separating macro-budget decisions from asset-level prioritization and integrating linear programming projection within a hierarchical Soft Actor-Critic framework, the method efficiently addresses exponential growth in the action space and ensures rigorous budget compliance. A case study evaluating sewer networks of varying sizes (10, 15, and 20 sewersheds) illustrates the effectiveness of the proposed approach. Compared to conventional Deep Q-Learning and enhanced genetic algorithms, our methodology converges more rapidly, scales effectively, and consistently delivers near-optimal solutions even as network size grows.

As demand for high-purity lithium surges with the growth of the electric vehicle (EV) industry, cost-effective extraction from lower-grade North American sources like the Smackover Formation is critical. These resources, unlike high-purity South American brines, require innovative purification techniques to be economically viable. Continuous crystallization is a promising method for producing battery-grade lithium carbonate, but its optimization is challenged by a complex parameter space and limited data. This study introduces a Human-in-the-Loop (HITL) assisted active learning framework to optimize the continuous crystallization of lithium carbonate. By integrating human expertise with data-driven insights, our approach accelerates the optimization of lithium extraction from challenging sources. Our results demonstrate the framework's ability to rapidly adapt to new data, significantly improving the process's tolerance to critical impurities like magnesium from the industry standard of a few hundred ppm to as high as 6000 ppm. This breakthrough makes the exploitation of low-grade, impurity-rich lithium resources feasible, potentially reducing the need for extensive pre-refinement processes. By leveraging artificial intelligence, we have refined operational parameters and demonstrated that lower-grade materials can be used without sacrificing product quality. This advancement is a significant step towards economically harnessing North America's vast lithium reserves, such as those in the Smackover Formation, and enhancing the sustainability of the global lithium supply chain.

We investigate lifted inference on ordered domains with predecessor relations, where the elements of the domain respect a total (cyclic) order, and every element has a distinct (clockwise) predecessor. Previous work has explored this problem through weighted first-order model counting (WFOMC), which computes the weighted sum of models for a given first-order logic sentence over a finite domain. In WFOMC, the order constraint is typically encoded by the linear order axiom introducing a binary predicate in the sentence to impose a linear ordering on the domain elements. The immediate and second predecessor relations are then encoded by the linear order predicate. Although WFOMC with the linear order axiom is theoretically tractable, existing algorithms struggle with practical applications, particularly when the predecessor relations are involved. In this paper, we treat predecessor relations as a native part of the axiom and devise a novel algorithm that inherently supports these relations. The proposed algorithm not only provides an exponential speedup for the immediate and second predecessor relations, which are known to be tractable, but also handles the general k -th predecessor relations. The extensive experiments on lifted inference tasks and combinatorics math problems demonstrate the efficiency of our algorithm, achieving speedups of a full order of magnitude.

Ensuring privacy in large-scale open datasets is increasingly challenging under regulations such as the General Data Protection Regulation (GDPR). While differential privacy (DP) provides strong theoretical guarantees, it primarily focuses on noise injection during model training, neglecting privacy preservation at the data publishing stage. Existing privacy-preserving data publishing (PPDP) approaches struggle to balance privacy and utility, particularly when data publishers and users are distinct entities. To address this gap, we focus on the graph recovery problem and propose a novel privacy-preserving estimation framework for open graph data, leveraging Gaussian DP (GDP) with a structured noise-injection mechanism. Unlike traditional methods that perturb gradients or model updates, our approach ensures unbiased graph structure recovery while enforcing DP at the data publishing stage. Moreover, we provide theoretical guarantees on estimation accuracy and extend our method to discrete-variable graphs, a setting often overlooked in DP research. Experimental results in graph learning demonstrate robust performance, offering a viable solution for privacy-conscious graph analysis.

Differentiated thyroid cancer DTC recurrence is a major public health concern, requiring classification and predictive models that are not only accurate but also interpretable and uncertainty aware. This study introduces a comprehensive framework for DTC recurrence classification using a dataset containing 383 patients and 16 clinical and pathological variables. Initially, 11 machine learning ML models were employed using the complete dataset, where the Support Vector Machines SVM model achieved the highest accuracy of 0.9481. To reduce complexity and redundancy, feature selection was carried out using the Boruta algorithm, and the same ML models were applied to the reduced dataset, where it was observed that the Logistic Regression LR model obtained the maximum accuracy of 0.9611. However, these ML models often lack uncertainty quantification, which is critical in clinical decision making. Therefore, to address this limitation, the Bayesian Neural Networks BNN with six varying prior distributions, including Normal 0,1, Normal 0,10, Laplace 0,1, Cauchy 0,1, Cauchy 0,2.5, and Horseshoe 1, were implemented on both the complete and reduced datasets. The BNN model with Normal 0,10 prior distribution exhibited maximum accuracies of 0.9740 and 0.9870 before and after feature selection, respectively.

NLP models often rely on human-labeled data for training and evaluation. Many approaches crowdsource this data from a large number of annotators with varying skills, backgrounds, and motivations, resulting in conflicting annotations. These conflicts have traditionally been resolved by aggregation methods that assume disagreements are errors. Recent work has argued that for many tasks annotators may have genuine disagreements and that variation should be treated as signal rather than noise. However, few models separate signal and noise in annotator disagreement. In this work, we introduce NUTMEG, a new Bayesian model that incorporates information about annotator backgrounds to remove noisy annotations from human-labeled training data while preserving systematic disagreements. Using synthetic data, we show that NUTMEG is more effective at recovering ground-truth from annotations with systematic disagreement than traditional aggregation methods. We provide further analysis characterizing how differences in subpopulation sizes, rates of disagreement, and rates of spam affect the performance of our model. Finally, we demonstrate that downstream models trained on NUTMEG-aggregated data significantly outperform models trained on data from traditionally aggregation methods. Our results highlight the importance of accounting for both annotator competence and systematic disagreements when training on human-labeled data.

Reinforcement learning has been widely applied to robotic control, but effective policy learning under partial observability remains a major challenge, especially in high-dimensional tasks like humanoid locomotion. To date, no prior work has demonstrated stable training of humanoid policies with incomplete state information in the benchmark Gymnasium Humanoid-v4 environment. The objective in this environment is to walk forward as fast as possible without falling, with rewards provided for staying upright and moving forward, and penalties incurred for excessive actions and external contact forces. This research presents the first successful instance of learning under partial observability in this environment. The learned policy achieves performance comparable to state-of-the-art results with full state access, despite using only one-third to two-thirds of the original states. Moreover, the policy exhibits adaptability to robot properties, such as variations in body part masses. The key to this success is a novel history encoder that processes a fixed-length sequence of past observations in parallel. Integrated into a standard model-free algorithm, the encoder enables performance on par with fully observed baselines. We hypothesize that it reconstructs essential contextual information from recent observations, thereby enabling robust decision-making.

-- Efficient exploration in multi-agent reinforcement learning (MARL) is a challenging problem when receiving only a team reward, especially in environments with sparse rewards. A powerful method to mitigate this issue involves crafting dense individual rewards to guide the agents toward efficient exploration. However, individual rewards generally rely on manually engineered shaping-reward functions that lack high-order intelligence, thus it behaves ineffectively than humans regarding learning and generalization in complex problems. T o tackle these issues, we combine the above two paradigms and propose a novel framework, LIGHT (Learning Individual Intrinsic reward via Incorporating Generalized Human experTise), which can integrate human knowledge into MARL algorithms in an end-to-end manner . LIGHT guides each agent to avoid unnecessary exploration by considering both individual action distribution and human expertise preference distribution. Then, LIGHT designs individual intrinsic rewards for each agent based on actionable representational transformation relevant to Q-learning so that the agents align their action preferences with the human expertise while maximizing the joint action value. Experimental results demonstrate the superiority of our method over representative baselines regarding performance and better knowledge reusability across different sparse-reward tasks on challenging scenarios. Cooperative multi-agent reinforcement learning (MARL) is an important branch in the field of artificial intelligence (AI), playing a crucial role in sequential challenging decision-making problems, such as in autonomous driving [1], sensor networks [2], [3] and robotics control [4]. Centralized training with decentralized execution (CTDE) paradigm has gained substantial attention in cooperative MARL that aims to facilitate agent cooperation by providing global state information during training and executing only based on local observations during execution [5], [6], [7].

Background: Hypertensive kidney disease (HKD) patients in intensive care units (ICUs) face high short-term mortality, but tailored risk prediction tools are lacking. Early identification of high-risk individuals is crucial for clinical decision-making. Methods: We developed a machine learning framework to predict 30-day in-hospital mortality among ICU patients with HKD using early clinical data from the MIMIC-IV v2.2 database. A cohort of 1,366 adults was curated with strict criteria, excluding malignancy cases. Eighteen clinical features-including vital signs, labs, comorbidities, and therapies-were selected via random forest importance and mutual information filtering. Several models were trained and compared with stratified five-fold cross-validation; CatBoost demonstrated the best performance. Results: CatBoost achieved an AUROC of 0.88 on the independent test set, with sensitivity of 0.811 and specificity of 0.798. SHAP values and Accumulated Local Effects (ALE) plots showed the model relied on meaningful predictors such as altered consciousness, vasopressor use, and coagulation status. Additionally, the DREAM algorithm was integrated to estimate patient-specific posterior risk distributions, allowing clinicians to assess both predicted mortality and its uncertainty. Conclusions: We present an interpretable machine learning pipeline for early, real-time risk assessment in ICU patients with HKD. By combining high predictive performance with uncertainty quantification, our model supports individualized triage and transparent clinical decisions. This approach shows promise for clinical deployment and merits external validation in broader critical care populations.