Title: Global Adaptive Generative Adjustment Show Chinese title

Title: 全局自适应生成调整

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. Show Chinese abstract

Abstract: 许多传统的信号恢复方法可以根据惩罚似然很好地表现，然而它们必须面临超参数或惩罚项中的调节参数选择的困难。本文提出了一种全局自适应生成调整（GAGA）算法用于信号恢复，在该算法中多个超参数会自动学习并交替更新与信号一起更新。我们进一步证明了我们的算法的输出直接保证了模型选择和信号估计的一致性。此外，我们还提出了一个变体GAGA算法以提高高维数据分析中的计算效率。最后，在模拟实验中，我们考虑了我们算法输出的一致性，并将我们的算法与其他惩罚似然方法（自适应LASSO、SCAD和MCP）进行了比较。模拟结果支持了我们算法在信号恢复中的有效性，并表明我们的算法优于其他算法。