Mathematics in Independent Component Analysis

52 Chapter 1. Statistical machine learning of biomedical data
Future work
In future work, the goal is to employ the above algorithms as preprocessing step in modeling of
biological processes, for example in quantitative systems biology. The idea is straight-forward,
see figure 1.28. Given multivariate data that encode for example biological parameters of multiple,
dependent experiments, we want to find regularized simple models that can explain the
data as well as predict future quantitative experiments. In a first step, denoising is to be performed,
especially removal of Gaussian subspaces that do not contain meaningful data apart
from their covariance structure. The signal subspace then is to be further processed using techniques
from dependent component analysis and independent subspace analysis. The resulting
subspaces themselves are analyzed with network analysis techniques, for example based on Gaussian
graphical models and corresponding high-dimensional regularizations (Dobra et al., 2004,
Schäfer and Strimmer, 2005). The derived structures are then expected to serve as models,
which may provide quantitative descriptions of the underlying processes. Finally, we hope to
drive further experiments by the model predictions.
This well-known coupling of experimentalists and theoreticians is characteristic of systems
biology in particular, and modern interdisciplinary research in general. With the past work,
we hope to have made some steps in this directions, and recent work in the field of microarray
analysis employing such techniques is already promising (Lutter et al., 2006, Schachtner et al.,
2007, Stadlthanner et al., 2006a). In theoretical terms, the long-term goal is to step from
multivariate analysis to network analysis, just as we have observed the field of signal processing
expanding from univariate to multivariate models in the past few decades.