Robust Multi-Task Learning for Principal Component Analysis
Abstract
Principal component analysis (PCA) is a fundamental tool for learning low-dimensional structure from high-dimensional data. When data are collected from multiple sources, the underlying task distributions may exhibit unknown degrees of similarity, with some tasks potentially arising from arbitrary distributions. We propose new multi-task PCA procedures that exploit similarity structure across tasks to improve eigenspace estimation while remaining robust to outlier tasks. We establish non-asymptotic convergence rates and show that the proposed procedures attain minimax optimal rates in a range of regimes. One of the procedures builds on the matrix-depth notion of Chen, Gao, and Ren (2018) and can achieve the optimal dependence of the estimation error on the proportion of outlier tasks, addressing a key challenge in robust multi-task learning. Extensive simulations and real-data analyses demonstrate the effectiveness of the proposed methods.
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BibTeX
@misc{liu2026robust,
title = {{Robust Multi-Task Learning for Principal Component Analysis}},
author = {Dali Liu and Haolei Weng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20733},
eprint = {2609.20733},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20733},
}
RIS
TY - UNPB
TI - Robust Multi-Task Learning for Principal Component Analysis
AU - Dali Liu
AU - Haolei Weng
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20733
UR - https://arxiv.org/abs/2609.20733
AB - Principal component analysis (PCA) is a fundamental tool for learning low-dimensional structure from high-dimensional data. When data are collected from multiple sources, the underlying task distributions may exhibit unknown degrees of similarity, with some tasks potentially arising from arbitrary distributions. We propose new multi-task PCA procedures that exploit similarity structure across tasks to improve eigenspace estimation while remaining robust to outlier tasks. We establish non-asymptotic convergence rates and show that the proposed procedures attain minimax optimal rates in a range of regimes. One of the procedures builds on the matrix-depth notion of Chen, Gao, and Ren (2018) and can achieve the optimal dependence of the estimation error on the proportion of outlier tasks, addressing a key challenge in robust multi-task learning. Extensive simulations and real-data analyses demonstrate the effectiveness of the proposed methods.
ER -