Structural systems identification of genetic regulatory networks

Abstract

The Matlab code is available upon request and the SOS data can be downloaded from http://www.weizmann.ac.il/mcb/UriAlon/Papers/SOSData/, courtesy of Uri Alon. Zak's data is available from his website, http://www.che.udel.edu/systems/people/zak.

Codimensional matrix pairing perspective of BYY harmony learning: hierarchy of bilinear systems, joint decomposition of data-covariance, and applications of network biology

“…In recent years, SSM has been adopted for time course gene expressions. Most of existing studies [136][137][138][139][140][141][142][143][144][145] treat data x j,t from j = 1, 2, · · · , n as multiple observation series from one same underlying SSM. In Ref.…”

“…(88). Later on, most of efforts [138][139][140][141][142][143][144][145][146] turned back to a standard SSM because it has been shown that the additional term Cx t−1 basically has no help and may even cause instability [143]. Likely, such an input driven term has not been included in a standard SSM during the past extensive studies [68] just because of an awareness of its useless.…”

“…In addition to the usual assumption on e t and ε t , extra constraints are imposed also on either or both of A and B. Mostly, A is imposed to be an identity matrix I [144] or its permutation [138,141] or a diagonal matrix [143]. These over-simplified SSM studies actually work as a filter to removing noises in gene expression data.…”

“…Sanguinetti et al [138] adopted the sparsity constraint on A in a same way as made in NCA [76], which can be regarded as an extension of NCA into SSM. Similarly but with more assumptions, constrained SSMs are suggested in [140] and [144], also based on a known network structure. If a pair of genes is represented by two states that is known to have no interaction, the corresponding entry in the matrix B are all set to be zero.…”

“…4 for modeling TRN with the help of the BYY harmony learning, with the following advantages and improvements: 1) As addressed above, imposing that A = I [145] or its permutation [138,141] or that A is diagonal [144] actually makes the role of SSM degenerated to a filter for observation noises. This limitation can be removed by considering the TFA by Eq.…”