# Fast and Robust Least Squares Estimation in Corrupted Linear Models

arXiv: https://arxiv.org/abs/1406.3175 · HTML: https://mlsanity.com/paper/1406.3175/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2014.

## Built on by (most cited first, 8 of 8)

- [Inverse Reinforcement Learning from a Gradient-based Learner](https://mlsanity.com/paper/2007.07812/) (2020)
- [One Backward from Ten Forward, Subsampling for Large-Scale Deep Learning](https://mlsanity.com/paper/2104.13114/) (2021)
- [Algorithmic Decision-Making Safeguarded by Human Knowledge](https://mlsanity.com/paper/2211.11028/) (2022)
- [Long-term Data Sharing under Exclusivity Attacks](https://mlsanity.com/paper/2201.09137/) (2022)
- [Markov subsampling based Huber Criterion](https://mlsanity.com/paper/2112.06134/) (2021)
- [A Bayesian Robust Regression Method for Corrupted Data Reconstruction](https://mlsanity.com/paper/2212.12787/) (2022)
- [Provably Outlier-resistant Semi-parametric Regression for Transferable Calibration of Low-cost Air-quality Sensors](https://mlsanity.com/paper/2511.19810/) (2025)
- [Joint Model and Data Sparsification via the Marginal Likelihood](https://mlsanity.com/paper/2605.29908/) (2026)

## Abstract (arXiv)

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence that was developed for regression diagnostics can be used to detect such corrupted observations as shown in this paper. This property of influence -- for which we also develop a randomized approximation -- motivates our proposed subsampling algorithm for large scale corrupted linear regression which limits the influence of data points since highly influential points contribute most to the residual error. Under a general model of corrupted observations, we show theoretically and empirically on a variety of simulated and real datasets that our algorithm improves over the current state-of-the-art approximation schemes for ordinary least squares.