Robust regression via error tolerance

Abstract Real-world datasets are often characterised by outliers; data items that do not follow the same structure as rest of data. These outliers might negatively influence modelling In analysis it is, therefore, important to consider methods robust outliers. this paper we develop a regression method finds largest subset can be approximated using sparse linear model given precision. We show yield best possible robustness However, problem is NP-hard and solve present an efficient approximation algorithm, termed SLISE. Our extends existing state-of-the-art methods, especially in terms speed on high-dimensional datasets. demonstrate our applying both synthetic real-world problems.