Consistent Bayesian Local Spatial Feature Selection with Application to Spatial Multimodal Omics

2026-05-28

AI Summary

This study addresses the challenge of local spatial feature selection in high-dimensional spatial multi-omics regression by proposing a Bayesian joint modeling framework. The approach employs a stochastic regional partitioning prior to adaptively identify contiguous spatial clusters with flexible shapes and incorporates a local feature selection prior within each cluster, thereby simultaneously performing region delineation and selection of relevant variables—including basis functions. The work establishes, for the first time, theoretical guarantees on posterior consistency and contraction rates for this joint model. To facilitate inference, it introduces a coupled hyperparameter prior structure and an efficient informed reversible jump Markov chain Monte Carlo algorithm. Empirical evaluations demonstrate superior performance over existing methods on simulated data and successfully uncover biologically meaningful spatially heterogeneous patterns in breast cancer spatial multi-omics datasets.

Abstract

Motivated by a high-dimensional regression problem in spatial multimodal omics (SMO), we propose a Bayesian framework for local spatial feature selection, where a random domain partition prior is introduced to divide the spatial domain into several contiguous clusters with flexible shapes and an unknown number of clusters, conditional on which a local feature selection prior is imposed within each cluster. The notion of "feature" is general and may include both covariates and functional bases, allowing the framework to perform both local variable selection and local basis selection, the latter being essential for adaptively approximating spatially varying functions with localized characteristics. We derive coupled hyperparameter conditions linking domain partition and local feature selection priors, under which the consistency theory and posterior contraction rates of both the domain partition and feature selection are established. We develop an efficient informed reversible jump Markov chain Monte Carlo algorithm to address the computational challenges encountered in joint posterior sampling of domain partitions and selected features. Simulation studies demonstrate the effectiveness of the proposed model and algorithm, highlighting its advantages over existing methods. The application of our model to an SMO dataset reveals biologically meaningful spatial patterns within breast cancer tissue.

Problem

• spatial multimodal omics
• local feature selection
• domain partition
• spatially varying functions
• high-dimensional regression

Innovation

• Bayesian spatial feature selection
• random domain partition
• local basis selection
• posterior consistency
• informed reversible jump MCMC