Robust regression using sparse learning for high dimensional parameter estimation problems

Algorithms such as Least Median of Squares (LMedS) and Random Sample Consensus (RANSAC) have been very successful for low-dimensional robust regression problems. However, the combinatorial nature of these algorithms makes them practically unusable for high-dimensional applications. In this paper, we introduce algorithms that have cubic time complexity in the dimension of the problem, which make them computationally efficient for highdimensional problems. We formulate the robust regression problem by projecting the dependent variable onto the null space of the independent variables which receives significant contributions only from the outliers. We then identify the outliers using sparse representation/learning based algorithms. Under certain conditions, that follow from the theory of sparse representation, these polynomial algorithms can accurately solve the robust regression problem which is, in general, a combinatorial problem. We present experimental results that demonstrate the ...

• Type: Conference
• Year: 2010
• Where: ICASSP
• Authors: Kaushik Mitra, Ashok Veeraraghavan, Rama Chellappa
• Keywords: Algorithms, ICASSP 2010, Low-dimensional Robust Regression, Robust Regression Problem, Signal Processing