Moritz Hanke | Searcharxiv

arXiv2024

An Alternating Direction Method of Multipliers Algorithm for the Weighted Fused LASSO Signal Approximator

We present an Alternating Direction Method of Multipliers (ADMM) algorithm designed to solve the Weighted Generalized Fused LASSO Signal Approximator (wFLSA). First, we show that wFLSAs can always be reformulated as a Generalized LASSO problem. With the availability of algorithms tailored to the Generalized LASSO, the issue appears to be, in principle, resolved. However, the computational complexity of these algorithms is high, with a time complexity of $O(p^4)$ for a single iteration, where $p$ represents the number of coefficients. To overcome this limitation, we propose an ADMM algorithm specifically tailored for wFLSA-equivalent problems, significantly reducing the complexity to $O(p^2)$. Our algorithm is publicly accessible through the R package wflsa.

stat.ME↗

arXiv2023

Variable selection in linear regression models: choosing the best subset is not always the best choice

Variable selection in linear regression settings is a much discussed problem. Best subset selection (BSS) is often considered the intuitive 'gold standard', with its use being restricted only by its NP-hard nature. Alternatives such as the least absolute shrinkage and selection operator (Lasso) or the elastic net (Enet) have become methods of choice in high-dimensional settings. A recent proposal represents BSS as a mixed integer optimization problem so that much larger problems have become feasible in reasonable computation time. We present an extensive neutral comparison assessing the variable selection performance, in linear regressions, of BSS compared to forward stepwise selection (FSS), Lasso and Enet. The simulation study considers a wide range of settings that are challenging with regard to dimensionality (with respect to the number of observations and variables), signal-to-noise ratios and correlations between predictors. As main measure of performance, we used the best possible F1-score for each method to ensure a fair comparison irrespective of any criterion for choosing the tuning parameters, and results were confirmed by alternative performance measures. Somewhat surprisingly, it was only in settings where the signal-to-noise ratio was high and the variables were (nearly) uncorrelated that BSS reliably outperformed the other methods, even in low-dimensional settings. Further, the FSS's performance was nearly identical to BSS. Our results shed new light on the usual presumption of BSS being, in principle, the best choice for variable selection. Especially for correlated variables, alternatives like Enet are faster and appear to perform better in practical settings.

stat.ME↗