With an abundance of data resulting from high-throughput technologies, like DNA microarrays,
a race has been on the last few years, to determine the structures and functions of genes and
their products, the proteins. Inference of gene interactions, lies in the core of these efforts.
In all this activity, three important research issues have emerged. First, in much of the current
literature on gene regulatory networks, dependencies among variables in our case genes - are
assumed to be linear in nature, when in fact, in real-life scenarios this is seldom the case.
This disagreement leads to systematic deviation and biased evaluation. Secondly, although
the problem of undersampling, features in every piece of work as one of the major causes for
poor results, in practice it is overlooked and rarely addressed explicitly. Finally, inference
of network structures, although based on rigid mathematical foundations and computational
optimizations, often displays poor fitness values and biologically unrealistic link structures, due
- to a large extend - to the discovery of pairwise only interactions.
In our search for robust, nonlinear measures of dependency, we advocate that mutual information
and related information theoretic functionals (conditional mutual information, total
correlation) are possibly the most suitable candidates to capture both linear and nonlinear
interactions between variables, and resolve higher order dependencies.
To address these issues, we researched and implemented under a common framework, a selection
nonparametric estimators of mutual information for continuous variables. The focus of their
assessment was, their robustness to the limited sample sizes and their expansibility to higher
dimensions - important for the detection of more complex interaction structures. Two different
assessment scenaria were performed, one with simulated data and one with bootstrapping the
estimators in state-of-the-art network inference algorithms and monitor their predictive power
and sensitivity. The tests revealed that, in small sample size regimes, there is a significant difference
in the performance of different estimators, and naive methods such as uniform binning,
gave consistently poor results compared with more sophisticated methods.
Finally, a custom, modular mechanism is proposed, for the inference of gene interactions,
targeting the identi cation of some of the most common substructures in genetic networks,
that we believe will help improve accuracy and predictability scores
