Elements of information theory
Elements of information theory
Iterative solution methods
Coefficient of determination in nonlinear signal processing
Signal Processing - Special section on signal processing technologies for short burst wireless communications
Could correlation-based methods be used to derive genetic association networks?
Information Sciences—Applications: An International Journal
Evolutionary modeling and inference of gene network
Information Sciences—Informatics and Computer Science: An International Journal - Bioinformatics-selected papers from 4th CBGI & 6th JCIS Proceedings
CMSB '03 Proceedings of the First International Workshop on Computational Methods in Systems Biology
On Learning Gene Regulatory Networks Under the Boolean Network Model
Machine Learning
External Control in Markovian Genetic Regulatory Networks
Machine Learning
Genomic Signal Processing (Princeton Series in Applied Mathematics)
Genomic Signal Processing (Princeton Series in Applied Mathematics)
Simulation study in Probabilistic Boolean Network models for genetic regulatory networks
International Journal of Data Mining and Bioinformatics
A Multiple Regression Approach for Building Genetic Networks
BMEI '08 Proceedings of the 2008 International Conference on BioMedical Engineering and Informatics - Volume 01
Inference of gene regulatory networks based on a universal minimum description length
EURASIP Journal on Bioinformatics and Systems Biology
Replacement strategies to preserve useful diversity in steady-state genetic algorithms
Information Sciences: an International Journal
Information Sciences: an International Journal
A chance to learn: On matching probabilities to optimize utilities
Information Sciences: an International Journal
Particle swarm optimization with preference order ranking for multi-objective optimization
Information Sciences: an International Journal
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Modeling gene regulation is an important problem in genomic research. Boolean networks (BN) and its generalization probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem which is ill-posed and challenging. Because there may be many networks or no network having the given properties and the size of the inverse problem is huge. In this paper, we consider the problem of constructing PBNs from a given stationary distribution and a set of given Boolean Networks (BNs). We first formulate the inverse problem as a constrained least squares problem. We then propose a heuristic method based on Conjugate Gradient (CG) algorithm, an iterative method, to solve the resulting least squares problem. We also introduce an estimation method for the parameters of the PBNs. Numerical examples are then given to demonstrate the effectiveness of the proposed methods.