A new alternating direction method of multipliers for sparse Probabilistic Boolean Networks

Probabilistic Boolean network (PBN) is widely used in modeling genetic regulatory networks, which main task is to construct a sparse probabilistic Boolean networks (PBNs) based on a given transition-probability matrix and a set of Boolean networks (BNs). In this paper, a new alternating direction method of multipliers is proposed for achieving this purpose. At each iteration of the proposed method, three subproblems need to be solved and a multiplier updating with closed form needs to be performed. The former two subproblems are solved in a parallel fashion, while the last subproblem is handled in an alternative fashion with the former two. The proposed method can be interpreted as a classical alternating direction method of multipliers with an operator splitting. All subproblem solvers do not involve matrix computation, and consequently, the proposed method can be directly used to solve very large scale problem. Some numerical experiments demonstrate that efficiency and validity of the proposed method with comparison to some existing methods.