Noise Statistics Oblivious GARD For Robust Regression With Sparse Outliers

TL;DR

This paper introduces RRT-GARD, a noise statistics oblivious algorithm for robust regression with sparse outliers, performing comparably to existing methods that require prior noise knowledge.

Contribution

The paper proposes RRT-GARD, a novel robust regression algorithm that does not require prior noise or outlier statistics, unlike existing methods.

Findings

RRT-GARD performs nearly as well as GARD with known noise statistics.

RRT-GARD is effective in real and synthetic data sets.

The algorithm is robust to sparse outliers without prior noise information.

Abstract

Linear regression models contaminated by Gaussian noise (inlier) and possibly unbounded sparse outliers are common in many signal processing applications. Sparse recovery inspired robust regression (SRIRR) techniques are shown to deliver high quality estimation performance in such regression models. Unfortunately, most SRIRR techniques assume \textit{a priori} knowledge of noise statistics like inlier noise variance or outlier statistics like number of outliers. Both inlier and outlier noise statistics are rarely known \textit{a priori} and this limits the efficient operation of many SRIRR algorithms. This article proposes a novel noise statistics oblivious algorithm called residual ratio thresholding GARD (RRT-GARD) for robust regression in the presence of sparse outliers. RRT-GARD is developed by modifying the recently proposed noise statistics dependent greedy algorithm for robust de-noising (GARD). Both finite sample and asymptotic analytical results indicate that RRT-GARD performs nearly similar to GARD with \textit{a priori} knowledge of noise statistics. Numerical simulations in real and synthetic data sets also point to the highly competitive performance of RRT-GARD.