Social survey datasets, for example, are typically mixed because they include variables like age (continuous), demographic group (categorical), and Likert scales (ordinal) measuring how strongly a respondent agrees with certain stated opinions. Continuous variables are encoded as real numbers and sometimes called numeric. We refer to variables that admit a total order (e.g.

The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these mechanisms by identifying synergistic, redundant, and unique contributions to the mutual information between one and several variables. While many works have studied aspects of PID for Gaussian and discrete distributions, the case of general continuous distributions is still uncharted territory. In this work we present a method for estimating the unique information in continuous distributions, for the case of one versus two variables. Our method solves the associated optimization problem over the space of distributions with fixed bivariate marginals by combining copula decompositions and techniques developed to optimize variational autoencoders. We obtain excellent agreement with known analytic results for Gaussians, and illustrate the power of our new approach in several brain-inspired neural models. Our method is capable of recovering the effective connectivity of a chaotic network of rate neurons, and uncovers a complex trade-off between redundancy, synergy and unique information in recurrent networks trained to solve a generalized XOR~task.

Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study presents the state-of-the-art of these approaches and compares them using various simulation models. The compared methods include the distance-based approaches k-prototypes, PDQ, and convex k-means, and the probabilistic methods KAy-means for MIxed LArge data (KAMILA), the mixture of Bayesian networks (MBNs), and latent class model (LCM). The aim is to provide insights into the behavior of different methods across a wide range of scenarios by varying some experimental factors such as the number of clusters, cluster overlap, sample size, dimension, proportion of continuous variables in the dataset, and clusters' distribution. The degree of cluster overlap and the proportion of continuous variables in the dataset and the sample size have a significant impact on the observed performances. When strong interactions exist between variables alongside an explicit dependence on cluster membership, none of the evaluated methods demonstrated satisfactory performance. In our experiments KAMILA, LCM, and k-prototypes exhibited the best performance, with respect to the adjusted rand index (ARI). All the methods are available in R.

Predictive maintenance (PdM) is crucial for optimizing efficiency and minimizing downtime of electric buses. While these vehicles provide environmental benefits, they pose challenges for PdM due to complex electric transmission and battery systems. Traditional maintenance, often based on scheduled inspections, struggles to capture anomalies in multi-dimensional real-time CAN Bus data. This study employs a graph-based feature selection method to analyze relationships among CAN Bus parameters of electric buses and investigates the prediction performance of targeted alarms using artificial intelligence techniques. The raw data collected over two years underwent extensive preprocessing to ensure data quality and consistency. A hybrid graph-based feature selection tool was developed by combining statistical filtering (Pearson correlation, Cramer's V, ANOVA F-test) with optimization-based community detection algorithms (InfoMap, Leiden, Louvain, Fast Greedy). Machine learning models, including SVM, Random Forest, and XGBoost, were optimized through grid and random search with data balancing via SMOTEEN and binary search-based down-sampling. Model interpretability was achieved using LIME to identify the features influencing predictions. The results demonstrate that the developed system effectively predicts vehicle alarms, enhances feature interpretability, and supports proactive maintenance strategies aligned with Industry 4.0 principles.

Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based heuristic solutions to accelerate downstream solvers. While recent generative models have shown promise in learning powerful heuristics, they suffer from a critical limitation. That is, they model the distribution of only the integer variables and fail to capture the intricate coupling between integer and continuous variables, creating an information bottleneck and ultimately leading to suboptimal solutions. To this end, we propose Joint Continuous-Integer Flow for Mixed-Integer Linear Programming (FMIP), which is the first generative framework that models the joint distribution of both integer and continuous variables for MILP solutions. Built upon the joint modeling paradigm, a holistic guidance mechanism is designed to steer the generative trajectory, actively refining solutions toward optimality and feasibility during the inference process. Extensive experiments on eight standard MILP benchmarks demonstrate the superior performance of FMIP against existing baselines, reducing the primal gap by 41.34% on average. Moreover, we show that FMIP is fully compatible with arbitrary backbone networks and various downstream solvers, making it well-suited for a broad range of real-world MILP applications.

We address the problem of learning a sparse Bayesian network structure for continuous variables in a high-dimensional space. The constraint that the estimated Bayesian network structure must be a directed acyclic graph (DAG) makes the problem challenging because of the huge search space of network structures. Most previous methods were based on a two-stage approach that prunes the search space in the first stage and then searches for a network structure that satisfies the DAG constraint in the second stage. Although this approach is effective in a low-dimensional setting, it is difficult to ensure that the correct network structure is not pruned in the first stage in a high-dimensional setting. In this paper, we propose a single-stage method, called A* lasso, that recovers the optimal sparse Bayesian network structure by solving a single optimization problem with A* search algorithm that uses lasso in its scoring system. Our approach substantially improves the computational efficiency of the well-known exact methods based on dynamic programming. We also present a heuristic scheme that further improves the efficiency of A* lasso without significantly compromising the quality of solutions and demonstrate this on benchmark Bayesian networks and real data.

Background: Heart failure (HF) research is constrained by limited access to large, shareable datasets due to privacy regulations and institutional barriers. Synthetic data generation offers a promising solution to overcome these challenges while preserving patient confidentiality. Methods: We generated synthetic HF datasets from institutional data comprising 12,552 unique patients using five deep learning models: tabular variational autoencoder (TVAE), normalizing flow, ADSGAN, SurvivalGAN, and tabular denoising diffusion probabilistic models (TabDDPM). We comprehensively evaluated synthetic data utility through statistical similarity metrics, survival prediction using machine learning and privacy assessments. Results: SurvivalGAN and TabDDPM demonstrated high fidelity to the original dataset, exhibiting similar variable distributions and survival curves after applying histogram equalization. SurvivalGAN (C-indices: 0.71-0.76) and TVAE (C-indices: 0.73-0.76) achieved the strongest performance in survival prediction evaluation, closely matched real data performance (C-indices: 0.73-0.76). Privacy evaluation confirmed protection against re-identification attacks. Conclusions: Deep learning-based synthetic data generation can produce high-fidelity, privacy-preserving HF datasets suitable for research applications. This publicly available synthetic dataset addresses critical data sharing barriers and provides a valuable resource for advancing HF research and predictive modeling.