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2019

Iteratively Reweighted $\ell_1$-Penalized Robust Regression

Pan, Xiaoou, Sun, Qiang, Zhou, Wen-Xin

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This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization.

When the additive errors in linear models have only bounded second moment, we show that iteratively reweighted $\ell_1$-penalized adaptive Huber regression estimator satisfies exponential deviation bounds and oracle properties, including the oracle convergence rate and variable selection consistency, under a weak beta-min condition.
Computationally, we need as many as $O(\log s + \log\log d)$ iterations to reach such an oracle estimator, where $s$ and $d$ denote the sparsity and ambient dimension, respectively.
Extension to a general class of robust loss functions is also considered.

Iteratively Reweighted $\ell_1$-Penalized Robust Regression · Around

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Chinot, G
Original
1905
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1964
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