Efficient Shapley values computation for Boolean network models of gene regulation

TL;DR

This paper introduces an efficient, propagation-based method for computing Shapley values in Boolean gene regulatory networks, enabling accurate node importance assessment without exhaustive simulations.

Contribution

It presents a novel propagation approach that efficiently computes Shapley values, improving speed and accuracy for both acyclic and cyclic networks.

Findings

Accurately recovers node importance rankings in benchmark models.

Achieves substantial computational speed-ups.

Provides exact solutions for acyclic networks and good approximations for cyclic ones.

Abstract

Identifying dynamically influential nodes in biological networks is a central problem in systems biology, particularly for prioritizing intervention targets in gene regulatory networks. In this paper, we propose a Shapley-value-based framework for assessing the importance of nodes in a Boolean network with respect to a given target node. The framework comprises two complementary measures: the Knock-out and the Knock-in Shapley values. Moreover, we present a propagation-based method that enables their efficient computation. By exploiting the logical structure of the network, the method avoids exhaustive simulations. The approach is exact for acyclic networks and provides good approximations for cyclic networks. Evaluation on benchmark models from the Cell Collective database shows that the propagation method accurately recovers node importance rankings while achieving substantial speed-ups.