Abstract: Controlling the False Discovery Rate (FDR) in a variable selection procedure is critical for reproducible discoveries, which receives an extensive study in sparse linear models. However, it remains largely open in the scenarios where the sparsity constraint is not directly imposed on the parameters, but on a linear transformation of the parameters to be estimated. Examples include total variations, wavelet transforms, fused LASSO, and trend filtering, etc. In this paper, we propose a data adaptive FDR control in this transformational sparsity setting, the Split Knockoff method. The proposed scheme exploits both variable and data splitting. The linear transformation constraint is relaxed to its Euclidean proximity in a lifted parameter space, yielding an orthogonal design for improved power and orthogonal Split Knockoff copies. To overcome the challenge that exchangeability fails due to the heterogeneous noise brought by the transformation, new inverse supermartingale structures are developed for provable the FDR control with directional effects. Simulation experiments show that the proposed methodology achieves desired (directional) FDR and power. An application to Alzheimer's Disease study is provided that atrophy brain regions and their abnormal connections can be discovered based on a structural Magnetic Resonance Imaging dataset (ADNI). This is a joint work with CAO, Yang and SUN, Xinwei.

Bio:YAO, Yuan is currently Professor of Mathematics in the Hong Kong University of Science and Technology. Dr. Yao received his PhD in Mathematics from UC Berkeley with Prof. Steve Smale and worked in Stanford University and Peking University before joining HKUST in 2016. His main research interests lie in mathematics of data science and machine learning, with applications in computational biology and information technology.