@Article{EAJAM-2-1,
author = {Xi Chen, Hao Jiang and Wai-Ki Ching},
title = {On Construction of Sparse Probabilistic Boolean Networks},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {2},
number = {1},
pages = {1--18},
abstract = {<p style="text-align: justify;">In this paper we envisage building Probabilistic Boolean Networks (PBNs)
from a prescribed stationary distribution. This is an inverse problem of huge size that
can be subdivided into two parts — viz. (i) construction of a transition probability
matrix from a given stationary distribution (Problem ST), and (ii) construction of a
PBN from a given transition probability matrix (Problem TP). A generalized entropy
approach has been proposed for Problem ST and a maximum entropy rate approach for
Problem TP respectively. Here we propose to improve both methods, by considering a
new objective function based on the entropy rate with an additional term of $L_α$-norm
that can help in getting a sparse solution. A sparse solution is useful in identifying the
major component Boolean networks (BNs) from the constructed PBN. These major BNs
can simplify the identification of the network structure and the design of control policy,
and neglecting non-major BNs does not change the dynamics of the constructed PBN
to a large extent. Numerical experiments indicate that our new objective function is
effective in finding a better sparse solution.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.030511.060911a},
url = {http://global-sci.org/intro/article_detail/eajam/10863.html}
}