Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis

• URL: http://arxiv.org/abs/2605.20681v1
• Date: Wed, 20 May 2026 03:48:31 GMT
• Title: Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis
• Abstract summary: We study a scale-calibrated median-of-means estimator for distributed principal component analysis.<n>A node-level PCA expansion shows that the mean component has the usual linear influence, whereas the subspace component is an eigengap spatial perturbation.<n>We propose robust block-scale and inference-optimal calibration rules, establish high-probability median-of-means bounds, characterize factorwise bad-node influence, and prove node-bootstrap validity.
• Score: 0.31727619150610836
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Distributed principal component analysis (PCA) produces node-level estimates of both a mean vector and a principal subspace. Robustly aggregating these heterogeneous objects requires a relative scale between mean error and subspace error. We study a scale-calibrated median-of-means estimator for this problem using the product geometry of Euclidean space and the Grassmann manifold. A node-level PCA expansion shows that the mean component has the usual linear influence, whereas the subspace component is an eigengap-weighted covariance perturbation. We prove a local reduction showing that the proposed product-manifold median-of-means estimator is asymptotically equivalent to a scaled spatial median of node influence errors. This yields fixed-node non-Gaussian limits, growing-node Gaussian limits with finite-block bias, and an explicit scale-dependent covariance formula. We propose robust block-scale and inference-optimal calibration rules, establish high-probability median-of-means bounds, characterize factorwise bad-node influence, and prove node-bootstrap validity. Simulations and large-scale single-cell RNA-seq data show that scale calibration adapts to eigengap-driven subspace uncertainty and provides a robust distributed PCA summary.

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