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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
Eigenvector Spatial Filters Nuclear Norm Matrix Completio...
[Submitted on 3 Jun 2026 (v1), last revised 26 Jun 2026 (this ve · 2026-06-05 · via stat updates on arXiv.org

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Abstract:Reliable reconstruction of missing observations in environmental panel datasets is essential for accurate exposure assessment and policy analysis. Traditional nuclear norm matrix completion methods effectively impute missing entries in low-rank matrices, yet often overlook the spatial dependence inherent to air quality processes. This paper introduces the Eigenvector Spatial Filters Nuclear Norm Matrix Completion (ESFNNMC) method, an extension of nuclear norm fixed-effects matrix completion that replaces unit-specific intercepts with a set of Moran-type eigenvectors capturing the dominant spatial dependence patterns implied by a spatial weights matrix. To estimate the model, we propose a Block-Coordinate Descent approach for multiconvex optimization problems, with soft-thresholded singular value decomposition and cross-validated regularization. Through comprehensive simulations varying missingness patterns, the level of spatial and temporal autocorrelation, and dimension, shape, and rank structure of the matrices, ESFNNMC improves imputation accuracy when unit heterogeneity exhibits spatial structure, while remaining competitive under mild departures from this assumption. Furthermore, it keeps the computational cost approximately unchanged. The method is applied to impute missing entries in daily PM10 measurements in 64 monitoring stations in Lombardy, Italy, during the year 2021.

Submission history

From: Rodolfo Metulini [view email]
[v1] Wed, 3 Jun 2026 21:11:18 UTC (5,988 KB)
[v2] Sat, 6 Jun 2026 19:32:05 UTC (5,991 KB)
[v3] Fri, 26 Jun 2026 14:02:18 UTC (8,123 KB)