Unifying multi-sample network inference from prior knowledge and omics data with CORNETO

Abstract

Understanding biological systems requires methods that extract interpretable insights from omics data. Networks offer a natural abstraction by representing molecules as vertices and their interactions as edges, providing a foundation for constructing context-specific models tailored to particular conditions—an essential step in many biological analyses. Most existing approaches fall into one of two categories: machine learning methods, which offer strong predictive power but lack interpretability and require large datasets, and knowledge-based methods, which are more interpretable but designed for analysing individual samples and difficult to generalize. Here we present CORNETO, a unified mathematical framework that generalizes a wide variety of methods that learn biological networks from omics data and prior knowledge. CORNETO reformulates these methods as mixed-integer optimization problems using network flows and structured sparsity, enabling joint inference across multiple samples. This improves the discovery of both shared and sample-specific molecular mechanisms while yielding sparser, more interpretable solutions. CORNETO supports a range of prior knowledge structures, including undirected, directed and signed (hyper)graphs. It extends a broad class of approaches, ranging from Steiner trees to flux balance analysis, within a unified optimization-based interface. We demonstrate CORNETO’s utility across diverse biological contexts, including signalling, metabolism and integration with biologically informed deep learning. We provide CORNETO as an open-source Python library for flexible network modelling.