Sign-aware Perturbations Regression
Zhongnian Li, Tao Zhang, Wei Shao, Songcan Chen, Daoqiang Zhang · Society for Industrial and Applied Mathematics eBooks · 2021
This paper presents the first study on Sign-aware Perturbations Regression (SaPR), where the observed response variables contain the aware sign (negative or positive) perturbations.In order to predict the non-perturbation response variables, we propose a novel parameter estimator SZOM (i.e.,Setting Zero Operator Method), which aims at taking full advantage of the aware perturbations information to correct the mistake values in the estimation process with computationally efficiency.In this paper, the two aspects of theoretical analysis are proposed to deeply understand our method.Firstly, we establish the perturbation parameter error upper bound and prove consistency guarantee in the linear regression scenario.Secondly, we introduce the generalization error bound for the proposed SZMO, which indicates that the error bound is related to the value and the number of negative and positive perturbations.The effectiveness of the proposed approach is well validated by the experimental results on both synthetic and real datasets.