Stochastic diagonal estimation with adaptive parameter selection

2024/10/15 by Zongyuan Han, Wenhao Li, Han, Zongyuan +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.2410.11613

openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue distributions on diagonal estimation and analyze the necessity of introducing the projection method and adaptive parameter optimization into the stochastic diagonal estimator. Based on this analysis, we derive a lower bound on the number of random query vectors needed to satisfy a given probabilistic error bound, which forms the foundation of our adaptive stochastic diagonal estimation algorithm. Finally, numerical experiments demonstrate the effectiveness of the proposed estimator for various matrix types, showcasing its efficiency and stability compared to other existing stochastic diagonal estimation methods.

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