Iteratively reweighted ℓ1-penalized robust regression

Abstract

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 moments, we show that iteratively reweighted 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. Numerical studies lend strong support to our methodology and theory.

Intermittent fasting modulates the intestinal microbiota and improves obesity and host energy metabolism

“…Associations between gut microorganisms and clinical parameters were analyzed by applying an ℓ1-penalized robust regression method 47 . The numeric results of the physical examination and blood biochemical parameters were used as the response variables, whereas the log 10 -transformed relative abundances of MAGs or KOs enriched either before or after the intervention served as the predictor variable matrix.…”

Intermittent fasting modulates the intestinal microbiota and improves obesity and host energy metabolism

“…Associations between gut microorganisms and clinical parameters were analyzed by applying an ℓ1penalized robust regression method. 40 The numeric results of the physical exam and blood biochemical parameters were used as the response variables, whereas the log10-transformed relative abundances of MAGs or KOs enriched either before or after the intervention served as the predictor variable matrix. The regression was performed in R (v4.1.2) using the ILAMM package (v1.0.0).…”

Graphit: Iterative Reweighted ℓ1Algorithm for Sparse Graph Inference in State-Space Models

“…Our study focuses on the class of non-convex sparsifying penalties that have been studied for instance in [37] (see also [38] in the context of robust estimation). We define γ exp(−λ|u|)…”