Deep robust regression

In this paper, we consider the use of deep neural networks in the context of robust regression. We address the standard linear model with observations that are corrupted by outliers. We build upon Huber's robust regression and the classical least trimmed squares estimator, and propose a deep neural network that generalizes both and provides high accuracy with low computational complexity. The network is trained for arbitrary linear models using a single training phase. Numerical experiments with synthetic data demonstrate that the network can handle on a large range of Signal-to-Noise Ratio (SNR) and is robust to different types of outliers.