Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then, we show that an estimator of a parameter for each edge in a directed acyclic graph (DAG) is distributed normally. We end this paper with computational experiments with the expectation and maximization (EM) algorithm and quadratic optimization.

In response to the lack of trust in Artificial Intelligence (AI) for sequential planning, we design a Computational Tree Logic-guided large language model (LLM)-based natural language explanation framework designed for the Monte Carlo Tree Search (MCTS) algorithm. MCTS is often considered challenging to interpret due to the complexity of its search trees, but our framework is flexible enough to handle a wide range of free-form post-hoc queries and knowledge-based inquiries centered around MCTS and the Markov Decision Process (MDP) of the application domain. By transforming user queries into logic and variable statements, our framework ensures that the evidence obtained from the search tree remains factually consistent with the underlying environmental dynamics and any constraints in the actual stochastic control process. We evaluate the framework rigorously through quantitative assessments, where it demonstrates strong performance in terms of accuracy and factual consistency.

Deterministic partially observable Markov decision processes (DetPOMDPs) often arise in planning problems where the agent is uncertain about its environmental state but can act and observe de-terministically. In this paper, we propose DetM-CVI, an adaptation of the Monte Carlo V alue Iteration (MCVI) algorithm for DetPOMDPs, which builds policies in the form of finite-state controllers (FSCs). DetMCVI solves large problems with a high success rate, outperforming existing baselines for DetPOMDPs. We also verify the performance of the algorithm in a real-world mobile robot forest mapping scenario.

Parkinsons Disease (PD) is a progressive neurological disorder that primarily affects motor functions and can lead to mild cognitive impairment (MCI) and dementia in its advanced stages. With approximately 10 million people diagnosed globally 1 to 1.8 per 1,000 individuals, according to reports by the Japan Times and the Parkinson Foundation early and accurate diagnosis of PD is crucial for improving patient outcomes. While numerous studies have utilized machine learning (ML) and deep learning (DL) techniques for PD recognition, existing surveys are limited in scope, often focusing on single data modalities and failing to capture the potential of multimodal approaches. To address these gaps, this study presents a comprehensive review of PD recognition systems across diverse data modalities, including Magnetic Resonance Imaging (MRI), gait-based pose analysis, gait sensory data, handwriting analysis, speech test data, Electroencephalography (EEG), and multimodal fusion techniques. Based on over 347 articles from leading scientific databases, this review examines key aspects such as data collection methods, settings, feature representations, and system performance, with a focus on recognition accuracy and robustness. This survey aims to serve as a comprehensive resource for researchers, providing actionable guidance for the development of next generation PD recognition systems. By leveraging diverse data modalities and cutting-edge machine learning paradigms, this work contributes to advancing the state of PD diagnostics and improving patient care through innovative, multimodal approaches.

Collaborative robots must continually adapt to novel tasks and user preferences without overburdening the user. While prior interactive robot learning methods aim to reduce human effort, they are typically limited to single-task scenarios and are not well-suited for sustained, multi-task collaboration. We propose COIL (Cost-Optimal Interactive Learning) -- a multi-task interaction planner that minimizes human effort across a sequence of tasks by strategically selecting among three query types (skill, preference, and help). When user preferences are known, we formulate COIL as an uncapacitated facility location (UFL) problem, which enables bounded-suboptimal planning in polynomial time using off-the-shelf approximation algorithms. We extend our formulation to handle uncertainty in user preferences by incorporating one-step belief space planning, which uses these approximation algorithms as subroutines to maintain polynomial-time performance. Simulated and physical experiments on manipulation tasks show that our framework significantly reduces the amount of work allocated to the human while maintaining successful task completion.

The sharing of external data has become a strong demand of financial institutions, but the privacy issue has led to the difficulty of interconnecting different platforms and the low degree of data openness. To effectively solve the privacy problem of financial data in trans-border flow and sharing, to ensure that the data is'available but not visible', to realize the joint portrait of all kinds of heterogeneous data of business organizations in different industries, we propose a Heterogeneous Federated Graph Neural Network (HFGNN) approach. In this method, the distribution of heterogeneous business data of trans-border organizations is taken as subgraphs, and the sharing and circulation process among subgraphs is constructed as a statistically heterogeneous global graph through a central server. Each subgraph learns the corresponding personalized service model through local training to select and update the relevant subset of sub-graphs with aggregated parameters, and effectively separates and combines topological and feature information among subgraphs. Finally, our simulation experimental results show that the proposed method has higher accuracy performance and faster convergence speed than existing methods. 1 Introduction With the continuous advancement of financial technology's profound empowerment of business, the shared application of external data (such as Internet companies, insurance companies, and other third-party data providers) has become a strong demand for financial institutions. Financial risk control and customer acquisition based on privacy computing have become the most important privacy computing implementation scenario at present [ Oyewole et al., 2024; Farayola et al., 2024 ] . However, there are three main risks in the current cooperation process between financial institutions and external data sources: first, it involves a large amount of personal user information and is subject to strict regulatory requirements; second, the data assets and trade secrets Corresponding author accumulated by the institution's own business are easy to be leaked; Third, because the data itself can be copied and easily spread, and once shared cannot be traced, the confirmation of data assets is difficult, and commercialization is seriously restricted[ Christian, 2024 ] .

Satellite-based estimates of greenhouse gas (GHG) properties from observations of reflected solar spectra are integral for understanding and monitoring complex terrestrial systems and their impact on the carbon cycle due to their near global coverage. Known as retrieval, making GHG concentration estimations from these observations is a non-linear Bayesian inverse problem, which is operationally solved using a computationally expensive algorithm called Optimal Estimation (OE), providing a Gaussian approximation to a non-Gaussian posterior. This leads to issues in solver algorithm convergence, and to unrealistically confident uncertainty estimates for the retrieved quantities. Upcoming satellite missions will provide orders of magnitude more data than the current constellation of GHG observers. Development of fast and accurate retrieval algorithms with robust uncertainty quantification is critical. Doing so stands to provide substantial climate impact of moving towards the goal of near continuous real-time global monitoring of carbon sources and sinks which is essential for policy making. To achieve this goal, we propose a diffusion-based approach to flexibly retrieve a Gaussian or non-Gaussian posterior, for NASA's Orbiting Carbon Observatory-2 spectrometer, while providing a substantial computational speed-up over the current operational state-of-the-art.

With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the benefit of simplicity, and work reasonably well in low dimensions, but as the number of variables increases, they can lack the required flexibility and scalability. Classical parametric models for angular variables, such as the von Mises-Fisher (vMF) distribution, provide an alternative. Exploiting mixtures of vMF distributions increases their flexibility, but there are cases where even this is not sufficient to capture the intricate features that can arise in data. Owing to their flexibility, generative deep learning methods are able to capture complex data structures; they therefore have the potential to be useful in the simulation of angular variables. In this paper, we explore a range of deep learning approaches for this task, including generative adversarial networks, normalizing flows and flow matching. We assess their performance via a range of metrics and make comparisons to the more classical approach of using a mixture of vMF distributions. The methods are also applied to a metocean data set, demonstrating their applicability to real-world, complex data structures.

Aiming at the group decision - making problem with multi - objective attributes, this study proposes a group decision - making system that integrates fuzzy inference and Bayesian network. A fuzzy rule base is constructed by combining threshold values, membership functions, expert experience, and domain knowledge to address quantitative challenges such as scale differences and expert linguistic variables. A hierarchical Bayesian network is designed, featuring a directed acyclic graph with nodes selected by experts, and maximum likelihood estimation is used to dynamically optimize the conditional probability table, modeling the nonlinear correlations among multidimensional indices for posterior probability aggregation. In a comprehensive student evaluation case, this method is compared with the traditional weighted scoring approach. The results indicate that the proposed method demonstrates effectiveness in both rule criterion construction and ranking consistency, with a classification accuracy of 86.0% and an F1 value improvement of 53.4% over the traditional method. Additionally, computational experiments on real - world datasets across various group decision scenarios assess the method's performance and robustness, providing evidence of its reliability in diverse contexts.

Artificial Intelligence (AI) models deployed in production frequently face challenges in maintaining their performance in non-stationary environments. This issue is particularly noticeable in medical settings, where temporal dataset shifts often occur. These shifts arise when the distributions of training data differ from those of the data encountered during deployment over time. Further, new labeled data to continuously retrain AI is not typically available in a timely manner due to data access limitations. To address these challenges, we propose a proactive self-adaptive AI approach, or pro-adaptive, where we model the temporal trajectory of AI parameters, allowing us to short-term forecast parameter values. To this end, we use polynomial spline bases, within an extensible Functional Data Analysis framework. We validate our methodology with a logistic regression model addressing prior probability shift, covariate shift, and concept shift. This validation is conducted on both a controlled simulated dataset and a publicly available real-world COVID-19 dataset from Mexico, with various shifts occurring between 2020 and 2024. Our results indicate that this approach enhances the performance of AI against shifts compared to baseline stable models trained at different time distances from the present, without requiring updated training data. This work lays the foundation for pro-adaptive AI research against dynamic, non-stationary environments, being compatible with data protection, in resilient AI production environments for health.