Genetic Regulatory Networks: A Nonlinear Signal Processing Perspective - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 508

classification, some common tasks in signal processing include removal of
interference from signals, transforming signals into more suitable representa-
tions for various purposes, and analyzing and extracting some characteristics
from signals. 2
Of importance in nonlinear signal processing in particular is the optimal
design of nonlinear operators under various criteria and constraints. That is,
given a “true” signal and its noise-corrupted version, the goal is to find an
optimal estimator from some class of estimators (constraint), such that when
it is applied to the noisy signal, some error (criterion) between its output
and the true signal is minimized. Alternatively, if a representative signal is
not available for training, and one is armed with only the knowledge of the
noise characteristics and a class of operators, the goal is to select an optimal
estimator under a different criterion, such as minimizing the variance of the
noise at its output.
Although these approaches have much in common with machine learning
and statistical estimation theory, the nature of the constraints and criteria, and
consequently the ensuing theory and algorithms, are guided by application-
specific needs, such as detail and edge preservation, robustness to outliers,
and other statistical and structural constraints. At the same time, much of
the theory behind nonlinear signal processing, in particular nonlinear digital
filters, is tightly intertwined with dynamical systems theory, involving con-
structs such as finite and cellular automata. In this chapter, we consider these
topics in the context of computational genomics and, in particular, models of
genetic regulatory networks. We should point out that the role of nonlinear
signal processing extends well beyond models and inference of genetic net-
works, and can also be quite useful for the analysis of gene expression data
(e.g., Reference 3).

13.2 Genetic Regulatory Networks

In living organisms, genes code for proteins. These proteins are in turn used
to control the regulation of other genes. Such interactions, when considered
collectively, form complex gene regulatory networks. To gain an understand-
ing of the dynamical behavior and characteristics of such complex regulatory
systems, it is necessary to be able to observe them in a global, large-scale fash-
ion. The recent development of high-throughput technologies, such as cDNA
microarrays and oligonucleotide chips, 4 - 8 is empowering researchers in the
collection of broad-scope gene information. The diagnostic potential of gene
expression data has already been demonstrated. For example, cancer classifi-
cation using a variety of methods has been used to exploit the class-separating
power of expression data. 9 - 14 The next step is to dig deeper and understand
the underlying mechanisms and the functions of genes in health and disease.