Adaptive Sparse Estimation with Side Information

 

Trambak Banerjee, Gourab Mukherjee and Wenguang Sun

 

Summary. The article considers the problem of estimating a high-dimensional sparse parameter in the pres- ence of auxiliary data that encode side information on sparsity. We develop a general framework that involves first constructing an auxiliary sequence to capture the side information, and then incorporating the auxiliary sequence in inference to reduce the estimation risk. The proposed method, which carries out adaptive SURE-thresholding using side information (ASUS), is shown to have robust performance and enjoy optimality properties. We develop new theories to characterize regimes in which ASUS far outperforms competitive shrinkage estimators, and establish precise conditions under which ASUS is asymptotically optimal. Simulation studies are conducted to show that ASUS substantially improves the performance of existing methods in many settings. The methodology is applied for analysis of data from single cell virology studies and microarray time course experiments.

 

The paper and its supplementary material can be downloaded here.

 

The R package for implementing the proposed ASUS procedure is available at:

https://github.com/trambakbanerjee/asus#asus