Cyclic graphs with noisy-max structures and its modeling on signaling pathways

It is common that a real world system with causal or inter-dependent relationships has cyclic or feed-back properties, especially in biological systems. The signaling pathway in a cell is such a typical system. As a fundamental part, it regulates essential functions including growth, protein synthesis, and apoptosis. With randomized experiments of intervening some parts and observing on other parts, pathways are supposed to be revealed by gene expression data. This paper presents a probabilistic framework that allows cyclic relationships. The interactions of the signaling molecules can be represented in it. With interventional data, inference and learning can be driven in this framework. Both analysis and experiments show its effectiveness.