Statistical leverage scores emerged as a fundamental tool for matrix sketching and column sampling with applications to low rank approximation, regression, random feature learning and quadrature. Yet, the very nature of this quantity is barely understood. Borrowing ideas from the orthogonal polynomial literature, we introduce the regularized Christoffel function associated to a positive definite kernel. This uncovers a variational formulation for leverage scores for kernel methods and allows to elucidate their relationships with the chosen kernel as well as population density. Our main result quantitatively describes a decreasing relation between leverage score and population density for a broad class of kernels on Euclidean spaces. Numerical simulations support our findings.

Author ordering is determined by coin flip. For what purpose was the dataset created? Was there a specific task in mind? In order to systematically compare the location encoders' performance and their impact on the Who created the dataset (e.g., which team, research group) and on behalf of which entity (e.g., Who funded the creation of the dataset? Dr. Gengchen Mai acknowledges the Microsoft Research What do the instances that comprise the dataset represent (e.g., documents, photos, people, The instances in all 17 datasets represent images.

Statistical leverage scores emerged as a fundamental tool for matrix sketching and column sampling with applications to low rank approximation, regression, random feature learning and quadrature.

Statistical leverage scores emerged as a fundamental tool for matrix sketching and column sampling with applications to low rank approximation, regression, random feature learning and quadrature. Yet, the very nature of this quantity is barely understood. Borrowing ideas from the orthogonal polynomial literature, we introduce the regularized Christoffel function associated to a positive definite kernel. This uncovers a variational formulation for leverage scores for kernel methods and allows to elucidate their relationships with the chosen kernel as well as population density. Our main result quantitatively describes a decreasing relation between leverage score and population density for a broad class of kernels on Euclidean spaces. Numerical simulations support our findings.

Cultural infrastructures, such as libraries, museums, theaters, and galleries, support learning, civic life, health, and local economies, yet access is uneven across cities. We present a novel, scalable, and open-data framework to measure spatial equity in cultural access. We map cultural infrastructures and compute a metric called Cultural Infrastructure Accessibility Score (CIAS) using exponential distance decay at fine spatial resolution, then aggregate the score per capita and integrate socio-demographic indicators. Interpretable tree-ensemble models with SHapley Additive exPlanation (SHAP) are used to explain associations between accessibility, income, density, and tract-level racial/ethnic composition. Results show a pronounced core-periphery gradient, where non-library cultural infrastructures cluster near urban cores, while libraries track density and provide broader coverage. Non-library accessibility is modestly higher in higher-income tracts, and library accessibility is slightly higher in denser, lower-income areas.

Monitoring household water use in rapidly urbanizing regions is hampered by costly, time-intensive enumeration methods and surveys. We investigate whether publicly available imagery-satellite tiles, Google Street View (GSV) segmentation-and simple geospatial covariates (nightlight intensity, population density) can be utilized to predict household water consumption in Hubballi-Dharwad, India. We compare four approaches: survey features (benchmark), CNN embeddings (satellite, GSV, combined), and GSV semantic maps with auxiliary data. Under an ordinal classification framework, GSV segmentation plus remote-sensing covariates achieves 0.55 accuracy for water use, approaching survey-based models (0.59 accuracy). Error analysis shows high precision at extremes of the household water consumption distribution, but confusion among middle classes is due to overlapping visual proxies. We also compare and contrast our estimates for household water consumption to that of household subjective income. Our findings demonstrate that open-access imagery, coupled with minimal geospatial data, offers a promising alternative to obtaining reliable household water consumption estimates using surveys in urban analytics.

The reliability of routine health data in low and middle-income countries (LMICs) is often constrained by reporting delays and incomplete coverage, necessitating the exploration of novel data sources and analytics. Geospatial Foundation Models (GeoFMs) offer a promising avenue by synthesizing diverse spatial, temporal, and behavioral data into mathematical embeddings that can be efficiently used for downstream prediction tasks. This study evaluated the predictive performance of three GeoFM embedding sources - Google Population Dynamics Foundation Model (PDFM), Google AlphaEarth (derived from satellite imagery), and mobile phone call detail records (CDR) - for modeling 15 routine health programmatic outputs in Malawi, and compared their utility to traditional geospatial interpolation methods. We used XGBoost models on data from 552 health catchment areas (January 2021-May 2023), assessing performance with R2, and using an 80/20 training and test data split with 5-fold cross-validation used in training. While predictive performance was mixed, the embedding-based approaches improved upon baseline geostatistical methods in 13 of 15 (87%) indicators tested. A Multi-GeoFM model integrating all three embedding sources produced the most robust predictions, achieving average 5-fold cross validated R2 values for indicators like population density (0.63), new HIV cases (0.57), and child vaccinations (0.47) and test set R2 of 0.64, 0.68, and 0.55, respectively. Prediction was poor for prediction targets with low primary data availability, such as TB and malnutrition cases. These results demonstrate that GeoFM embeddings imbue a modest predictive improvement for select health and demographic outcomes in an LMIC context. We conclude that the integration of multiple GeoFM sources is an efficient and valuable tool for supplementing and strengthening constrained routine health information systems.

Author ordering is determined by coin flip. For what purpose was the dataset created? Was there a specific task in mind? In order to systematically compare the location encoders' performance and their impact on the Who created the dataset (e.g., which team, research group) and on behalf of which entity (e.g., Who funded the creation of the dataset? Dr. Gengchen Mai acknowledges the Microsoft Research What do the instances that comprise the dataset represent (e.g., documents, photos, people, The instances in all 17 datasets represent images.

This is the preprint version of the article published in IEEE Access vol. 13, pp. 146503--146526, 2025, doi:10.1109/ACCESS.2025.3599541. Please cite the published version. Urban air pollution remains a pressing global concern, particularly in densely populated and traffic-intensive metropolitan areas like Delhi, where exposure to harmful pollutants severely impacts public health. Delhi, being one of the most polluted cities globally, experiences chronic air quality issues due to vehicular emissions, industrial activities, and construction dust, which exacerbate its already fragile atmospheric conditions. Traditional pollution mitigation strategies, such as static air purifying installations, often fail to maximize their impact due to suboptimal placement and limited adaptability to dynamic urban environments. This study presents a novel deep reinforcement learning (DRL) framework to optimize the placement of air purification booths to improve the air quality index (AQI) in the city of Delhi. We employ Proximal Policy Optimization (PPO), a state-of-the-art reinforcement learning algorithm, to iteratively learn and identify high-impact locations based on multiple spatial and environmental factors, including population density, traffic patterns, industrial influence, and green space constraints. Our approach is benchmarked against conventional placement strategies, including random and greedy AQI-based methods, using multi-dimensional performance evaluation metrics such as AQI improvement, spatial coverage, population and traffic impact, and spatial entropy.

This study presents an integrated approach to understanding epidemic dynamics through a stochastic spatio-temporal simulation model on a multiplex network, blending physical and informational layers. The physical layer maps the geographic movement of individuals, while the information layer tracks the spread of knowledge and health behavior via social interactions. We explore the interplay between physical mobility, information flow, and epidemic outcomes by simulating disease spread within this dual-structured network. Our model employs stochastic elements to mirror human behavior, mobility, and information dissemination uncertainties. Through simulations, we assess the impact of network structure, mobility patterns, and information spread speed on epidemic dynamics. The findings highlight the crucial role of effective communication in curbing disease transmission, even in highly mobile societies. Additionally, our agent-based simulation allows for real-time scenario analysis through a user interface, offering insights into leveraging physical and informational networks for epidemic control. This research sheds light on designing strategic interventions in complex social systems to manage disease outbreaks.