Probabilistic robust regression with adaptive weights-a case study on face recognition  

作　　者：Jin Li Quan Chen Jingwen Leng Weinan Zhang Minyi Guo 

机构地区：[1]Department of Computer Science,Shanghai Jiao Tong University,Shanghai,200240,China

出　　处：《Frontiers of Computer Science》2020年第5期123-134,共12页中国计算机科学前沿（英文版）

基　　金：We thank our anonymous reviewers for their feedback and suggestions.This work was partially sponsored by the National Basic Research 973 Program of China(2015CB352403);the National Natural Science Foundation of China(NSFC)(Grant Nos.61702328,61602301,61632017).

摘　　要：Robust regression plays an important role in many machine learning problems.A primal approach relies on the use of Huber loss and an iteratively reweightedℓ2 method.However,because the Huber loss is not smooth and its corresponding distribution cannot be represented as a Gaussian scale mixture,such an approach is extremely difficult to handle using a probabilistic framework.To address those limitations,this paper proposes two novel losses and the corresponding probability functions.One is called Soft Huber,which is well suited for modeling non-Gaussian noise.Another is Nonconvex Huber,which can help produce much sparser results when imposed as a prior on regression vector.They can represent anyℓq loss(1/2≤q<2)with tuning parameters,which makes the regression model more robust.We also show that both distributions have an elegant form,which is a Gaussian scale mixture with a generalized inverse Gaussian mixing density.This enables us to devise an expectation maximization(EM)algorithm for solving the regression model.We can obtain an adaptive weight through EM,which is very useful to remove noise data or irrelevant features in regression problems.We apply our model to the face recognition problem and show that it not only reduces the impact of noise pixels but also removes more irrelevant face images.Our experiments demonstrate the promising results on two datasets.

关 键 词：robust regression nonconvex loss face recognition 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]