SPSID: A Single-Parameter Shrinkage Inverse-Diffusion for Denoising Gene-Regulatory Networks

Abstract

Inferring gene regulatory networks (GRNs) from expression data is a fundamental problem in systems biology, but its accuracy is often undermined by structural noise arising from transitive correlations. These indirect interactions can obscure the true regulatory architecture, leading to a high rate of false positives. To address this, we introduce SPSID (Single-Parameter Shrinkage Inverse-Diffusion), a novel and robust network denoising framework. SPSID is a deterministic post-processing operator applied to an inferred GRN score matrix, rather than a generative diffusion model for gene expression. SPSID employs a principled spectral filter, built upon a shrinkage-regularized inverse-diffusion operator, to mathematically distinguish direct, one-step interactions from multi-step, indirect paths. This approach guarantees numerical stability and, through a fixed default parameter, effectively eliminates the need for data-dependent tuning. We conducted a comprehensive evaluation of SPSID on both extensive simulations and the gold-standard DREAM5 benchmark. The results demonstrate that SPSID outperforms state-of-the-art baseline methods in both AUROC and AUPR, exhibiting good stability across diverse network conditions. Furthermore, it functions as a post-processing tool, elevating the performance of multiple upstream GRN inference methods. By providing a computationally efficient and parameter-free solution to filter structural noise, SPSID offers a readily applicable tool for uncovering the underlying topology of complex biological networks with greater fidelity.