Global Adaptive Generative Adjustment
This work addresses a key bottleneck in signal recovery for researchers and practitioners by automating hyperparameter tuning, though it is incremental as it builds on existing penalized likelihood methods.
The authors tackled the problem of hyperparameter selection in penalized likelihood methods for signal recovery by proposing the GAGA algorithm, which automatically learns multiple hyperparameters and achieves consistency in model selection and signal estimation, outperforming Adaptive LASSO, SCAD, and MCP in simulations.
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.