Fig. 2
From: RegCloser: a robust regression approach to closing genome gaps
IRLS algorithm for computing the robust M-estimate. a The Huber loss function used in the M-estimation. Since it is convex, any local optimum is global. b The Huber \(\psi\)-function, namely, the derivative of the Huber loss function. It shows the influence of any outlier is bounded. c The Huber weight function. Beyond a threshold, the weight of an observation drops gradually as the error goes to large. d Pseudocode of the iteratively reweighted least squares (IRLS) algorithm. The inputs comprise the design matrix \({\varvec{X}}\), response vector \({\varvec{Y}}\) of the linear regression model, the tuning constant \(c\), the convergence threshold \(\alpha\), and the iteration limit \(N\). The output is the robust M-estimate of the model parameters, which minimizes the Huber loss function