A Discrete Perspective Towards the Construction of Sparse Probabilistic Boolean Networks

TL;DR

This paper introduces a new greedy algorithm for constructing sparse Probabilistic Boolean Networks, providing theoretical bounds and demonstrating superior performance over existing methods in both synthetic and real data.

Contribution

It presents the first study on lower bounds for sparse PBN construction and proposes a novel GER algorithm with proven efficiency and sparsity guarantees.

Findings

GER outperforms existing algorithms in numerical experiments

GER produces the sparsest decompositions on tested matrices

Theoretical upper bounds are established for all algorithms

Abstract

Boolean Network (BN) and its extension Probabilistic Boolean Network (PBN) are popular mathematical models for studying genetic regulatory networks. BNs and PBNs are also applied to model manufacturing systems, financial risk and healthcare service systems. In this paper, we propose a novel Greedy Entry Removal (GER) algorithm for constructing sparse PBNs. We derive theoretical upper bounds for both existing algorithms and the GER algorithm. Furthermore, we are the first to study the lower bound problem of the construction of sparse PBNs, and to derive a series of related theoretical results. In our numerical experiments based on both synthetic and practical data, GER gives the best performance among state-of-the-art sparse PBN construction algorithms and outputs sparsest possible decompositions on most of the transition probability matrices being tested.