A Hierarchical Variational Graph Fused Lasso for Recovering Relative Rates in Spatial Compositional Data

2025-09-24

AI Summary

To address spatial signal aliasing in imaging mass spectrometry (IMS) and imaging mass cytometry (IMC) caused by competitive sampling, this work proposes a scalable Bayesian deconvolution framework. Methodologically, it introduces a heavy-tailed graphical lasso prior to jointly model spatial sparsity and structural correlation of molecular abundances, and designs a novel hierarchical variational family for efficient posterior inference. Integrating variational graph fusion, automatic differentiation, and scalable optimization, the framework enables large-scale spatial omics analysis. Experiments demonstrate substantially improved posterior coverage reliability: the method accurately recovers tissue anatomical structures and eliminates artifacts in both simulated and real IMS data, while uncovering biologically active regions missed by conventional point estimators and mean-field approximations. This establishes a new paradigm for high-precision spatial molecular quantification.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Medical and Biological Imaging

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The analysis of spatial data from biological imaging technology, such as imaging mass spectrometry (IMS) or imaging mass cytometry (IMC), is challenging because of a competitive sampling process which convolves signals from molecules in a single pixel. To address this, we develop a scalable Bayesian framework that leverages natural sparsity in spatial signal patterns to recover relative rates for each molecule across the entire image. Our method relies on the use of a heavy-tailed variant of the graphical lasso prior and a novel hierarchical variational family, enabling efficient inference via automatic differentiation variational inference. Simulation results show that our approach outperforms state-of-the-practice point estimate methodologies in IMS, and has superior posterior coverage than mean-field variational inference techniques. Results on real IMS data demonstrate that our approach better recovers the true anatomical structure of known tissue, removes artifacts, and detects active regions missed by the standard analysis approach.

Problem

• Recovers relative molecular rates from competitive spatial sampling processes
• Addresses signal convolution challenges in biological imaging mass spectrometry
• Enables scalable Bayesian inference for spatial compositional data analysis

Innovation

• Hierarchical variational family for efficient Bayesian inference
• Heavy-tailed graphical lasso prior for spatial signal recovery
• Automatic differentiation variational inference for scalable computation