Noise Statistics Oblivious GARD For Robust Regression With Sparse Outliers

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 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 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 a priori knowledge of noise statistics. Numerical simulations in real and synthetic data sets also point to the highly competitive performance of RRT-GARD. Index Terms: Robust regression, Sparse outliers, Greedy algorithm for robust regressionStep 1:-Identify the strongest residual in r k−1 GARD , i.e.,Step 2:-Update the matrixStep 3:-Estimate β and gout(S k GARD ) as [β Tĝ out(S k GARD ) T ] T = A k † y.Step 4:-Update the residual r k GARD = y − A k [β Tĝ out(S k GARD ) T ] T = (I n − P A k )y. k ← k + 1.Output:-Signal estimateβ. Outlier support estimate S k GARD .

Study on the Law of Harmful Gas Release from Limnoperna fortunei (Dunker 1857) during Maintenance Period of Water Tunnel Based on K-Means Outlier Treatment

“…Sci. 2021, 11, x FOR PEER REVIEW 3 of 20 regression is realized in sparse outlier [24]. It is also important to strengthen the identification of monitoring data and the processing of outliers to analyze the release characteristics of harmful gases from putrefied Limnoperna fortunei.…”

“…Aiming at the problem of large errors or outliers in data sets, Sreejith et al proposed a method that obtains the characteristic distribution model of the data through simulation experiment and then identifies whether the data point is an outlier or not according to the distance between the sampling value and the characteristic model value, for robust regression in the presence of sparse outliers. Finally, the recognition of outlier data is realized, and stable regression is realized in sparse outlier [24]. It is also important to strengthen the identification of monitoring data and the processing of outliers to analyze the release characteristics of harmful gases from putrefied Limnoperna fortunei.…”

Subspace clustering without knowing the number of clusters: A parameter free approach

“…Recently, parameter-free approaches have been developed in the areas of high dimensional outlier detection [31], sparse signal recovery [41] [42], robust regression [43] and these were shown to have results comparable with those which use the explicit knowledge about the parameters. Hence, we look for a parameter-free method for subspace clustering.…”

Highly Robust Complex Covariance Estimators With Applications to Sensor Array Processing

“…Additionally, the ability to handle large deviations from the true data is important for applications where outliers or impulsive noise may be present. Common sources of outliers include occlusions in image processing [6]; high-power equipment in wireless communications [7]; targets, clutter discretes, other radars, and jamming in adaptive radar [8]; measurement and instrument errors, cyber attacks, and communication interference in power systems [9]; and general sensor and human errors [10].…”