L-PASSO: Adaptive Log-penalized Variable Selector, with Sparse Selection and Robustness to the Pilot Estimator
Abstract
We study L-PASSO, a penalized least-squares regression method based on the logarithmic penalty λ∑jlog(1+|βj|/τ), and its two-stage adaptive form, in which the scales τj come from a pilot estimator. Although this concave penalty has been proposed previously, its variable-selection properties and sparsity relative to other popular penalties have not been fully characterized. We derive the exact orthogonal-design solution, and show that the single-stage estimator selects the true model under a weighted irrepresentable condition that holds for every design once τ is small. We further establish that, under matched tuning, the two-stage estimator possesses the oracle property and has half the asymptotic bias of the adaptive LASSO. Our main theoretical contribution concerns the robustness of the two-stage procedure to the pilot estimator. We show that two-stage L-PASSO remains selection consistent even when the weights associated with relevant variables are as small as exp{−o(1/ζn)}, whereas the adaptive LASSO fails to retain relevant variables whose pilot weights are sufficiently small relative to its tuning parameter ζn. We establish that both thresholds are sharp. In high-dimensional settings, we prove support recovery for a local minimizer without imposing any lower-bound condition on the weights of relevant variables, and provide conditions under which this local minimizer is also the unique global minimizer. We additionally establish the selection consistency of a BIC-based tuning-parameter selection procedure. Finally, simulations comparing L-PASSO with the LASSO, SCAD, MCP, SELO, uniLasso, and the adaptive LASSO show that L-PASSO most frequently recovers the true support. Two real-data examples further illustrate the method.
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BibTeX
@misc{ghosh2026lpasso,
title = {{L-PASSO: Adaptive Log-penalized Variable Selector, with Sparse Selection and Robustness to the Pilot Estimator}},
author = {Samiran Ghosh and Shuva Gupta and Shreyo Ghosh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38092},
eprint = {2610.38092},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38092},
}
RIS
TY - UNPB
TI - L-PASSO: Adaptive Log-penalized Variable Selector, with Sparse Selection and Robustness to the Pilot Estimator
AU - Samiran Ghosh
AU - Shuva Gupta
AU - Shreyo Ghosh
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38092
UR - https://arxiv.org/abs/2610.38092
AB - We study L-PASSO, a penalized least-squares regression method based on the logarithmic penalty λ∑_jlog(1+|β_j|/τ), and its two-stage adaptive form, in which the scales τ_j come from a pilot estimator. Although this concave penalty has been proposed previously, its variable-selection properties and sparsity relative to other popular penalties have not been fully characterized. We derive the exact orthogonal-design solution, and show that the single-stage estimator selects the true model under a weighted irrepresentable condition that holds for every design once τ is small. We further establish that, under matched tuning, the two-stage estimator possesses the oracle property and has half the asymptotic bias of the adaptive LASSO. Our main theoretical contribution concerns the robustness of the two-stage procedure to the pilot estimator. We show that two-stage L-PASSO remains selection consistent even when the weights associated with relevant variables are as small as exp{−o(1/ζ_n)}, whereas the adaptive LASSO fails to retain relevant variables whose pilot weights are sufficiently small relative to its tuning parameter ζ_n. We establish that both thresholds are sharp. In high-dimensional settings, we prove support recovery for a local minimizer without imposing any lower-bound condition on the weights of relevant variables, and provide conditions under which this local minimizer is also the unique global minimizer. We additionally establish the selection consistency of a BIC-based tuning-parameter selection procedure. Finally, simulations comparing L-PASSO with the LASSO, SCAD, MCP, SELO, uniLasso, and the adaptive LASSO show that L-PASSO most frequently recovers the true support. Two real-data examples further illustrate the method.
ER -