Sparse probabilistic Boolean network problems: A partial proximal-type operator splitting method

Abstract

The sparse probabilistic Boolean network (SPBN) model has been applied in various fields of industrial engineering and management. The goal of this model is to find a sparse probability distribution based on a given transition-probability matrix and a set of Boolean networks (BNs). In this paper, a partial proximal-type operator splitting method is proposed to solve a separable minimization problem arising from the study of the SPBN model. All the subproblem-solvers of the proposed method do not involve matrix multiplication, and consequently the proposed method can be used to deal with large-scale problems. The global convergence to a critical point of the proposed method is proved under some mild conditions. Numerical experiments on some real probabilistic Boolean network problems show that the proposed method is effective and efficient compared with some existing methods.

New Inexact Parallel Splitting Algorithm for a Class of Separable Convex Programming

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A geometric proximal gradient method for sparse least squares regression with probabilistic simplex constraint

“…We see from Table 5.2 that the proposed algorithm provides a high-precision solution. We now focus on the following two numerical examples on the inverse problem of reconstructing a probabilistic Boolean network (PBN) from a prescribed transition probability matrix [9,10,14,26].…”

“…In [26], Wen et al presented a projection-based gradient descent method for solving problem (1.1). In [14], Deng et al provided a partial proximal-type operator splitting method for solving the 1/2 regularization version of problem (1.1):…”

A Modified Orthogonal Matching Pursuit for Construction of Sparse Probabilistic Boolean Networks

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“…Example 4.5 We consider a network in [11] with three genes (n = 3), where the prescribed transition probability matrix of the PBN is given by…”