A Modified Entropy Approach for Construction of Probabilistic Boolean Networks

Boolean Network (BN) and its extension Probabilistic Boolean network (PBN) have received much attention in modeling genetic regulatory networks. In this paper, we consider the problem of constructing a PBN from a given positive stationary distribution. The problem can be divided into two subproblems: Construction of a PBN from a given sparse transition probability matrix and construction of a sparse transition matrix from a given stationary distribution. These are inverse problems of huge sizes and we proposed mathematical models based on entropy theory. To obtain a sparse solution, we consider a new objective function having an addition term of Lα -norm. Newton’s method in conjunction with CG method is then applied to solve the inverse problem. Numerical examples are given to demonstrate the effectiveness of our proposed method.