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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Kernel Regression for Spatial and Spatio-Temporal Residua...
[Submitted on 28 May 2026 (v1), last revised 2 Aug 2026 (this ve · 2026-06-01 · via stat updates on arXiv.org

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Abstract:School gun violence in the United States is a complex phenomenon spanning social, epidemiological, demographic, and political dimensions. It remains unclear where incidents are unusually concentrated nationally after accounting for the distribution and characteristics of schools. Using a newly linked case-control dataset comprising 959 gun-violence incidents at public K-12 schools in the contiguous United States during 2000-2024, we develop a semiparametric kernel-regression framework combining school-level predictors with spatial and continuously evolving spatio-temporal residual structure. Fisher-weighted orthogonalisation defines how predictor-aligned variation is allocated between fixed and smooth components, while repeated control sampling and Monte Carlo reassignment support stable mapping and local exceedance assessment. The models identify stable school-level associations, including substantially higher adjusted odds for larger, middle, and high schools, while revealing residual structure beyond the background distribution of schools. Elevated residual odds become concentrated in a broad central-eastern corridor from the mid-2010s onward, with the strongest evidence in recent years. The analysis offers both statistical and application-specific insights. Statistically, it shows how covariate-adjusted residual surfaces can characterise local departures in case-control processes evolving over space and time. For the application, it provides epidemiological clues identifying regions in which broader social, policy, and environmental conditions may warrant targeted investigation.

Submission history

From: Tilman Davies [view email]
[v1] Thu, 28 May 2026 21:59:53 UTC (8,717 KB)
[v2] Sun, 2 Aug 2026 02:38:36 UTC (9,179 KB)