Adaptive Huber Regression

Active Regression with Adaptive Huber Loss

This paper addresses the scalar regression problem presenting a solution for optimizing the Huber loss in a general semi-supervised setting, which combines multi-view learning and manifold regularization. To this aim, we propose a principled algorithm to 1) avoid computationally expensive iterative solutions while 2) adapting the Huber loss threshold in a data-driven fashion and 3) actively bal...

Sparse Quantile Huber Regression for Efficient and Robust Estimation

We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In addition, the sparsity consideration in quantile regression enables the exploration of the entire conditional distribution of the response variable given the ...

Martina Huber KTH report

Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator

In regression we can delete outliers based upon a preliminary estimator and reestimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the p...

Adaptive functional linear regression

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [2010] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows to cover the prediction problem with respect to the mean squared predictio...