# Stochastic diagonal estimation with adaptive parameter selection

arXiv: https://arxiv.org/abs/2410.11613 · HTML: https://mlsanity.com/paper/2410.11613/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 15 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Large-scale Log-determinant Computation through Stochastic Chebyshev Expansions](https://mlsanity.com/paper/1503.06394/) (2015)
- [Stochastic diagonal estimation: probabilistic bounds and an improved algorithm](https://mlsanity.com/paper/2201.10684/) (2022)
- [A Tight Analysis of Hutchinson's Diagonal Estimator](https://mlsanity.com/paper/2208.03268/) (2022)
- [Estimating leverage scores via rank revealing methods and randomization](https://mlsanity.com/paper/2105.11004/) (2021)
- [Sketching and Embedding are Equivalent for Norms](https://mlsanity.com/paper/1411.2577/) (2014)
- [Algorithm-agnostic low-rank approximation of operator monotone matrix functions](https://mlsanity.com/paper/2311.14023/) (2023)

## Built on by (most cited first, 1 of 1)

- [Matrix-Free Two-to-Infinity and One-to-Two Norms Estimation](https://mlsanity.com/paper/2508.04444/) (2025)

## Abstract (arXiv)

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.