# Communication-efficient distributed eigenspace estimation with arbitrary node failures

arXiv: https://arxiv.org/abs/2206.00127 · HTML: https://mlsanity.com/paper/2206.00127/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 17 of 17)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Byzantine-Robust Learning on Heterogeneous Datasets via Bucketing](https://mlsanity.com/paper/2006.09365/) (2020)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [Byzantine Stochastic Gradient Descent](https://mlsanity.com/paper/1803.08917/) (2018)
- [Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers](https://mlsanity.com/paper/1703.04940/) (2017)
- [Outlier-robust moment-estimation via sum-of-squares](https://mlsanity.com/paper/1711.11581/) (2017)
- [Outlier-Robust High-Dimensional Sparse Estimation via Iterative Filtering](https://mlsanity.com/paper/1911.08085/) (2019)
- [Is Network the Bottleneck of Distributed Training?](https://mlsanity.com/paper/2006.10103/) (2020)
- [Faster Eigenvector Computation via Shift-and-Invert Preconditioning](https://mlsanity.com/paper/1605.08754/) (2016)
- [Byzantine-Resilient SGD in High Dimensions on Heterogeneous Data](https://mlsanity.com/paper/2005.07866/) (2020)
- [Improved Distributed Principal Component Analysis](https://mlsanity.com/paper/1408.5823/) (2014)
- [A Unified Approach to Robust Mean Estimation](https://mlsanity.com/paper/1907.00927/) (2019)
- [Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysis](https://mlsanity.com/paper/1702.08169/) (2017)
- [Communication-efficient distributed eigenspace estimation](https://mlsanity.com/paper/2009.02436/) (2020)

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

- [Provable Model-Parallel Distributed Principal Component Analysis with Parallel Deflation](https://mlsanity.com/paper/2502.17615/) (2025)

## Abstract (arXiv)

We develop an eigenspace estimation algorithm for distributed environments with arbitrary node failures, where a subset of computing nodes can return structurally valid but otherwise arbitrarily chosen responses. Notably, this setting encompasses several important scenarios that arise in distributed computing and data-collection environments such as silent/soft errors, outliers or corrupted data at certain nodes, and adversarial responses. Our estimator builds upon and matches the performance of a recently proposed non-robust estimator up to an additive tildeO(σ √α) error, where σ2 is the variance of the existing estimator and α is the fraction of corrupted nodes.