Parameter Learning of Probabilistic Boolean Control Networks with Input-Output Data

Article Parameter Learning of Probabilistic Boolean Control Networks with Input-Output Data Hongwei Chen 1,*, Qi Chen 1, Bo Shen 1, and Yang Liu 2 1 College of Information Science and Technology, Donghua University, Shanghai 201620, China 2 School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China * Correspondence: hongwei@dhu.edu.cn Received: 23 September 2023 Accepted: 27 November 2023 Published: 26 March 2024 Abstract: This paper investigates the parameter learning problem for the probabilistic Boolean control networks (PBCNs) with input-output data. Firstly, an algebraic expression of the PBCNs is obtained by taking advantage of the semi-tensor product technique, and then, the parameter learning problem is transformed into an optimal problem to reveal the parameter matrices of a linear system in a computationally efficient way. Secondly, two recursive semi-tensor product based algorithms are designed to calculate the forward and backward probabilities. Thirdly, the expectation maximization algorithm is proposed as an elaborate technique to address the parameter learning problem. In addition, a useful index is introduced to describe the performance of the proposed parameter learning algorithm. Finally, two numerical examples are employed to demonstrate the reliability of the proposed parameter learning approach.