Sufficient Tensor Screening with Spatially Adaptive Smoothing for Imaging Predictors

Thomas M. Menino Convention & Exhibition Center 

High-resolution imaging and other spatial biomedical measurements are naturally represented as tensors with ultrahigh-dimemsional correlated features, where sample sizes are modest and signals can be weak and spatially diffuse. We propose a fast, model-agnostic screening framework that ranks voxel- or region-level features by a kernel-based measure of outcome association, then improves stability and interpretability by smoothing the resulting importance map with anatomy-aware spatial regularization. The method is designed to preserve tensor structure by returning connected, axis-aligned subtensors. To address the common failure mode of purely marginal screening, we introduce a two-stage sufficient refinement. The first stage selects a small set of strong signals; the second stage evaluates remaining candidates conditionally on the first-stage set using low-rank summaries to keep computation scalable, with adaptive smoothing applied outside the initial selection. Simulation studies and brain imaging data show improved recovery of weak, spatially structured signals and more reproducible selected regions compared with marginal screening alone.

Imaging data

Sufficient dimension reduction

Tensor

Ultrahigh-dimensional screening 

Section on Statistics in Imaging