A comprehensive review of the use of Shapley value to assess node importance in the analysis of biological networks

Background: In 2017, Lundberg and Lee introduced SHAP, a breakthrough in Explainable AI, creatively applying the Shapley value to estimate the importance of input features in machine learning outputs. The Shapley value, from cooperative game theory, fairly distributes system gains among participants. Inspired by SHAP's success, this survey explores the application of Shapley value-based methods in biological network analysis. Method: We conducted a comprehensive literature search on the application of the Shapley value in biological network analysis from 2004 to 2024. From this, we focused on studies that applied the Shapley value in innovative and non-trivial ways, distinct from its typical usage. Result: The review identified six original studies that provide novel applications of the Shapley value in analyzing biological networks. These methods have also inspired further development and applications. For each, we discuss the foundational contributions, subsequent advancements, and applications. Discussion: Although the reviewed methods share the common objective of using the Shapley value to estimate an element's contribution within a system, each one takes a distinct approach to modeling the cooperative game. Some methods employ game settings that enable more efficient Shapley value calculations, albeit with a narrower scope, as they are tailored to specific problems. Other methods offer broader applicability but encounter the usual computational challenges associated with calculating the exact Shapley value due to its time complexity. Fortunately, these challenges can be mitigated through the use of approximation techniques. Despite the computational challenges, Shapley value-based methods demonstrate to be beneficial for the interpretation of biological networks.