Large-scale modern data often involves estimation and testing for high-dimensional unknown parameters. It is desirable to identify the sparse signals, ``the needles in the haystack'', with accuracy and false discovery control. However, the unprecedented complexity and heterogeneity in modern data structure require new machine learning tools to effectively exploit commonalities and to robustly adjust for both sparsity and heterogeneity. In addition, estimates for high-dimensional parameters often lack uncertainty quantification. In this paper, we propose a novel Spike-and-Nonparametric mixture prior (SNP) -- a spike to promote the sparsity and a nonparametric structure to capture signals. In contrast to the state-of-the-art methods, the proposed methods solve the estimation and testing problem at once with several merits: 1) an accurate sparsity estimation; 2) point estimates with shrinkage/soft-thresholding property; 3) credible intervals for uncertainty quantification; 4) an optimal multiple testing procedure that controls false discovery rate. Our method exhibits promising empirical performance on both simulated data and a gene expression case study.

翻译：大型现代数据往往涉及对高维未知参数的估计和测试。 有必要确定稀有信号, 即“ 干草堆中的针头 ”, 准确性和虚假的发现控制。 然而,现代数据结构的空前复杂性和异质性需要新的机器学习工具,以有效地利用共性,并强有力地适应宽度和异质性。 此外, 对高维参数的估计往往缺乏不确定性的量化。 在本文中,我们建议先用一个新的 Spik-and-nectric 混合物(SNP) -- -- 一种刺激孔隙性和非参数结构来捕捉信号的激增。 与最先进的方法不同,拟议方法可以同时用几种优点解决估计和测试问题:(1) 准确的宽度估计;(2) 使用缩放/软性财产的点估计;(3) 可靠的不确定性量化间隔;(4) 一种控制虚假发现率的最佳多重测试程序。 我们的方法显示,在模拟数据和基因表达案例研究方面,有希望有经验性。