We
address the system identification problem of genetic networks
using noisy and correlated time series data of gene expression level
measurements. Least-squares (LS) is a commonly used method for the
parameter estimation in the network reconstruction problems. The LS
algorithm implicitly assumes that the measurement noise is confined
only to the dependent variables. However, a discrete time model for
the genetic network systems will lead to serially correlated noise
terms that appear in both the dependent and independent variables.
A constrained total least-squares algorithm (CTLS) used in signal
and image processing applications showed significant improvements
in such an estimation problem over the LS and total least-squares
(TLS) methods. In this paper, we propose an extended CTLS algorithm
that estimates parameters for all the dependent variables simultaneously,
instead of estimating them separately for each dependent variable,
as in the original CTLS algorithm. In addition, the CTLS algorithm
is further generalized to assign weights to the error terms according
to the variances or covariances of the measurement noise. We demonstrate
its improved performance over the original CTLS method, as well as
the commonly used LS and TLS methods on a widely adopted artificial
genetic network example, under a variety of noise conditions.
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