Global Adaptive Generative Adjustment

TL;DR

The paper introduces the GAGA algorithm for signal recovery that automatically learns hyperparameters, guarantees model selection consistency, and outperforms existing penalized likelihood methods in simulations.

Contribution

It proposes a novel adaptive algorithm that automatically tunes hyperparameters and ensures consistent signal recovery, with a high-dimensional efficiency variant.

Findings

GAGA guarantees model selection and signal estimate consistency.

The algorithms outperform Adaptive LASSO, SCAD, and MCP in simulations.

The high-dimensional variant improves computational efficiency.

Abstract

Many traditional signal recovery approaches can behave well basing on the penalized likelihood. However, they have to meet with the difficulty in the selection of hyperparameters or tuning parameters in the penalties. In this article, we propose a global adaptive generative adjustment (GAGA) algorithm for signal recovery, in which multiple hyperpameters are automatically learned and alternatively updated with the signal. We further prove that the output of our algorithm directly guarantees the consistency of model selection and signal estimate. Moreover, we also propose a variant GAGA algorithm for improving the computational efficiency in the high-dimensional data analysis. Finally, in the simulated experiment, we consider the consistency of the outputs of our algorithms, and compare our algorithms to other penalized likelihood methods: the Adaptive LASSO, the SCAD and the MCP. The simulation results support the efficiency of our algorithms for signal recovery, and demonstrate that our algorithms outperform the other algorithms.