AI-Augmented Statistical Network Estimation with Proxy Gene Embeddings

2026-07-06

AI Summary

This study addresses the challenge of accurately recovering genome-wide latent structures from gene interaction networks observed only on a restricted set of genes. To this end, the authors propose PLANE, a novel method that integrates proxy gene embeddings generated by external foundation models with statistical network modeling. PLANE jointly models the target network by aligning both sources in a shared latent space and incorporating a data-adaptive weighting mechanism. The approach employs gradient descent with block-wise Gram normalization, latent variable modeling, and a weighted reconstruction loss, supported by a theoretical framework establishing deterministic contraction bounds for alignment error. Experiments demonstrate that PLANE significantly improves network reconstruction accuracy, recovery of latent structures, and imputation performance for unobserved genes on both synthetic and single-cell perturbation datasets.

Abstract

Gene--gene networks are often observed only on a restricted target set, while modern biomedical foundation models provide proxy gene embeddings over substantially larger gene universes. To leverage externally learned representations to improve latent-structure recovery in partially observed target networks, we propose \emph{Proxy-Latent Assisted Network Estimation} (PLANE), an adaptively weighted joint network--embedding latent variable model. PLANE combines the two sources of information through the common latent positions of the target network and proxy embeddings. Under mild rank conditions, the target network enables the identification of latent positions and loading of all nodes up to an orthogonal rotation. We show that zero-order optimality analyses sharply control the weighted reconstruction loss, but are insufficient to identify the optimal weighting. To understand the network and embedding information trade-off for latent-factor recovery, we analyze blockwise Gram-normalized gradient descent and prove deterministic contraction of aligned, curvature-weighted errors up to an explicit statistical tolerance. We then specialize the weighted statistical error bound to derive the target-block error bound, yielding an optimal, data-adaptive choice of the network embedding weights. Simulations and single-cell perturbation analyses show that informative proxy embeddings improve latent recovery, network reconstruction, and imputation beyond the observed target network.

Problem

• gene--gene networks
• proxy gene embeddings
• latent structure recovery
• network estimation
• foundation models

Innovation

• PLANE
• proxy gene embeddings
• latent variable model
• adaptive weighting
• network estimation