# Computationally Efficient Robust Estimation of Sparse Functionals

arXiv: https://arxiv.org/abs/1702.07709 · HTML: https://mlsanity.com/paper/1702.07709/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2017.

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

- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)

## Abstract (arXiv)

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse functionals, and provide a computationally and statistically efficient algorithm in the high-dimensional setting. Our theory identifies a unified set of deterministic conditions under which our algorithm guarantees accurate recovery. By further establishing that these deterministic conditions hold with high-probability for a wide range of statistical models, our theory applies to many problems of considerable interest including sparse mean and covariance estimation; sparse linear regression; and sparse generalized linear models.