Additionally, experiments have shown that depersonalization symptoms can arise as a reaction to alcohol consumption (Raimo et al., 1999), and they are increasingly recognized as a significant prognostic factor in the course of depression (Michal et al., 2024). Despite these findings, little research has explored the mediating role of depersonalization symptoms in the causal pathway from alcohol consumption to depression. In this paper, we propose a methodological framework to evaluate the indirect effect of alcohol consumption on depression, with depersonalization acting as a mediator. To ground our analysis, we use data from a cross-sectional survey conducted during the COVID-19 pandemic by Dom ınguez-Espinosa et al. (2023) as a running example. In observational studies, the population average causal effect (ACE) and the natural indirect effect (NIE) are the most commonly used measures of total and mediation effects, respectively, to compare the outcomes of different intervention policies. For instance, in our running example, these two measures compare the depression outcomes between individuals engaging in hazardous versus non-hazardous alcohol consumption. However, clinical practice imposes ethical constraints, as healthcare professionals would not prescribe harmful levels of alcohol consumption. As a result, hypothetical interventions involving dangerous exposure levels are unrealistic. To address this situation with potentially harmful exposure, Hubbard and Van der Laan (2008) propose the population intervention effect (PIE), which contrasts outcomes between the natural population and a hypothetical population where no one is exposed to the harmful exposure level.

We explore the approximation capabilities of Transformer networks for H\"older and Sobolev functions, and apply these results to address nonparametric regression estimation with dependent observations. First, we establish novel upper bounds for standard Transformer networks approximating sequence-to-sequence mappings whose component functions are H\"older continuous with smoothness index $\gamma \in (0,1]$. To achieve an approximation error $\varepsilon$ under the $L^p$-norm for $p \in [1, \infty]$, it suffices to use a fixed-depth Transformer network whose total number of parameters scales as $\varepsilon^{-d_x n / \gamma}$. This result not only extends existing findings to include the case $p = \infty$, but also matches the best known upper bounds on number of parameters previously obtained for fixed-depth FNNs and RNNs. Similar bounds are also derived for Sobolev functions. Second, we derive explicit convergence rates for the nonparametric regression problem under various $\beta$-mixing data assumptions, which allow the dependence between observations to weaken over time. Our bounds on the sample complexity impose no constraints on weight magnitudes. Lastly, we propose a novel proof strategy to establish approximation bounds, inspired by the Kolmogorov-Arnold representation theorem. We show that if the self-attention layer in a Transformer can perform column averaging, the network can approximate sequence-to-sequence H\"older functions, offering new insights into the interpretability of self-attention mechanisms.

Moran Eigenvector Spatial Filtering (ESF) approaches have shown promise in accounting for spatial effects in statistical models. Can this extend to machine learning? This paper examines the effectiveness of using Moran Eigenvectors as additional spatial features in machine learning models. We generate synthetic datasets with known processes involving spatially varying and nonlinear effects across two different geometries. Moran Eigenvectors calculated from different spatial weights matrices, with and without a priori eigenvector selection, are tested. We assess the performance of popular machine learning models, including Random Forests, LightGBM, XGBoost, and TabNet, and benchmark their accuracies in terms of cross-validated R2 values against models that use only coordinates as features. We also extract coefficients and functions from the models using GeoShapley and compare them with the true processes. Results show that machine learning models using only location coordinates achieve better accuracies than eigenvector-based approaches across various experiments and datasets. Furthermore, we discuss that while these findings are relevant for spatial processes that exhibit positive spatial autocorrelation, they do not necessarily apply when modeling network autocorrelation and cases with negative spatial autocorrelation, where Moran Eigenvectors would still be useful.

In many applications, especially those involving prediction, models may yield near-optimal performance yet significantly disagree on individual-level outcomes. This phenomenon, known as predictive multiplicity, has been formally defined in binary, probabilistic, and multi-target classification, and undermines the reliability of predictive systems. However, its implications remain unexplored in the context of survival analysis, which involves estimating the time until a failure or similar event while properly handling censored data. We frame predictive multiplicity as a critical concern in survival-based models and introduce formal measures -- ambiguity, discrepancy, and obscurity -- to quantify it. This is particularly relevant for downstream tasks such as maintenance scheduling, where precise individual risk estimates are essential. Understanding and reporting predictive multiplicity helps build trust in models deployed in high-stakes environments. We apply our methodology to benchmark datasets from predictive maintenance, extending the notion of multiplicity to survival models. Our findings show that ambiguity steadily increases, reaching up to 40-45% of observations; discrepancy is lower but exhibits a similar trend; and obscurity remains mild and concentrated in a few models. These results demonstrate that multiple accurate survival models may yield conflicting estimations of failure risk and degradation progression for the same equipment. This highlights the need to explicitly measure and communicate predictive multiplicity to ensure reliable decision-making in process health management.

This paper presents a novel computational approach for evaluating urban metrics through density gradient analysis using multi-modal satellite imagery, with applications including public transport and other urban systems. By combining optical and Synthetic Aperture Radar (SAR) data, we develop a method to segment urban areas, identify urban centers, and quantify density gradients. Our approach calculates two key metrics: the density gradient coefficient ($α$) and the minimum effective distance (LD) at which density reaches a target threshold. We further employ machine learning techniques, specifically K-means clustering, to objectively identify uniform and high-variability regions within density gradient plots. We demonstrate that these metrics provide an effective screening tool for public transport analyses by revealing the underlying urban structure. Through comparative analysis of two representative cities with contrasting urban morphologies (monocentric vs polycentric), we establish relationships between density gradient characteristics and public transport network topologies. Cities with clear density peaks in their gradient plots indicate distinct urban centers requiring different transport strategies than those with more uniform density distributions. This methodology offers urban planners a cost-effective, globally applicable approach to preliminary public transport assessment using freely available satellite data. The complete implementation, with additional examples and documentation, is available in an open-source repository under the MIT license at https://github.com/nexri/Satellite-Imagery-Urban-Analysis.

Risk-averse reinforcement learning (RARL) is critical for decision-making under uncertainty, which is especially valuable in high-stake applications. However, most existing works focus on risk measures, e.g., conditional value-at-risk (CVaR), while measures of variability remain underexplored. In this paper, we comprehensively study nine common measures of variability, namely Variance, Gini Deviation, Mean Deviation, Mean-Median Deviation, Standard Deviation, Inter-Quantile Range, CVaR Deviation, Semi_Variance, and Semi_Standard Deviation. Among them, four metrics have not been previously studied in RARL. We derive policy gradient formulas for these unstudied metrics, improve gradient estimation for Gini Deviation, analyze their gradient properties, and incorporate them with the REINFORCE and PPO frameworks to penalize the dispersion of returns. Our empirical study reveals that variance-based metrics lead to unstable policy updates. In contrast, CVaR Deviation and Gini Deviation show consistent performance across different randomness and evaluation domains, achieving high returns while effectively learning risk-averse policies. Mean Deviation and Semi_Standard Deviation are also competitive across different scenarios. This work provides a comprehensive overview of variability measures in RARL, offering practical insights for risk-aware decision-making and guiding future research on risk metrics and RARL algorithms.

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This problem, known as network alignment, holds significant importance. It enhances our understanding of complex system structures and behaviours, facilitates the validation and extension of theoretical physics research about studying complex systems, and fosters diverse practical applications across various fields. However, due to variations in the structure, characteristics, and properties of complex networks across different fields, the study of network alignment is often isolated within each domain, with even the terminologies and concepts lacking uniformity. This review comprehensively summarizes the latest advancements in network alignment research, focusing on analyzing network alignment characteristics and progress in various domains such as social network analysis, bioinformatics, computational linguistics and privacy protection. It provides a detailed analysis of various methods' implementation principles, processes, and performance differences, including structure consistency-based methods, network embedding-based methods, and graph neural network-based (GNN-based) methods. Additionally, the methods for network alignment under different conditions, such as in attributed networks, heterogeneous networks, directed networks, and dynamic networks, are presented. Furthermore, the challenges and the open issues for future studies are also discussed.

Motivation: Network-based analyses of omics data are widely used, and while many of these methods have been adapted to single-cell scenarios, they often remain memory- and space-intensive. As a result, they are better suited to batch data or smaller datasets. Furthermore, the application of network-based methods in multi-omics often relies on similarity-based networks, which lack structurally-discrete topologies. This limitation may reduce the effectiveness of graph-based methods that were initially designed for topologies with better defined structures. Results: We propose Subset-Contrastive multi-Omics Network Embedding (SCONE), a method that employs contrastive learning techniques on large datasets through a scalable subgraph contrastive approach. By exploiting the pairwise similarity basis of many network-based omics methods, we transformed this characteristic into a strength, developing an approach that aims to achieve scalable and effective analysis. Our method demonstrates synergistic omics integration for cell type clustering in single-cell data. Additionally, we evaluate its performance in a bulk multi-omics integration scenario, where SCONE performs comparable to the state-of-the-art despite utilising limited views of the original data. We anticipate that our findings will motivate further research into the use of subset contrastive methods for omics data.

Developing an understanding of high-dimensional data can be facilitated by visualizing that data using dimensionality reduction. However, the low-dimensional embeddings are often difficult to interpret. To facilitate the exploration and interpretation of low-dimensional embeddings, we introduce a new concept named partitioning with explanations. The idea is to partition the data shown through the embedding into groups, each of which is given a sparse explanation using the original high-dimensional attributes. We introduce an objective function that quantifies how much we can learn through observing the explanations of the data partitioning, using information theory, and also how complex the explanations are. Through parameterization of the complexity, we can tune the solutions towards the desired granularity. We propose InfoClus, which optimizes the partitioning and explanations jointly, through greedy search constrained over a hierarchical clustering. We conduct a qualitative and quantitative analysis of InfoClus on three data sets. We contrast the results on the Cytometry data with published manual analysis results, and compare with two other recent methods for explaining embeddings (RVX and VERA). These comparisons highlight that InfoClus has distinct advantages over existing procedures and methods. We find that InfoClus can automatically create good starting points for the analysis of dimensionality-reduction-based scatter plots.

This systematic literature review examines the critical challenges and solutions related to scalability and maintainability in Machine Learning (ML) systems. As ML applications become increasingly complex and widespread across industries, the need to balance system scalability with long-term maintainability has emerged as a significant concern. This review synthesizes current research and practices addressing these dual challenges across the entire ML life-cycle, from data engineering to model deployment in production. We analyzed 124 papers to identify and categorize 41 maintainability challenges and 13 scalability challenges, along with their corresponding solutions. Our findings reveal intricate inter dependencies between scalability and maintainability, where improvements in one often impact the other. The review is structured around six primary research questions, examining maintainability and scalability challenges in data engineering, model engineering, and ML system development. We explore how these challenges manifest differently across various stages of the ML life-cycle. This comprehensive overview offers valuable insights for both researchers and practitioners in the field of ML systems. It aims to guide future research directions, inform best practices, and contribute to the development of more robust, efficient, and sustainable ML applications across various domains.