  There is an abundance of complex dynamic systems that are critical to our
daily lives and our society but that are hardly understood, and even with
today's possibilities to sense and collect large amounts of experimental data,
they are so complex and continuously evolving that it is unlikely that their
dynamics will ever be understood in full detail. Nevertheless, through
computational tools we can try to make the best possible use of the current
technologies and available data. We believe that the most useful models will
have to take into account the imbalance between system complexity and available
data in the context of limited knowledge or multiple hypotheses. The complex
system of biological cells is a prime example of such a system that is studied
in systems biology and has motivated the methods presented in this paper. They
were developed as part of the DARPA Rapid Threat Assessment (RTA) program,
which is concerned with understanding of the mechanism of action (MoA) of
toxins or drugs affecting human cells. Using a combination of Gaussian
processes and abstract network modeling, we present three fundamentally
different machine-learning-based approaches to learn causal relations and
synthesize causal networks from high-dimensional time series data. While other
types of data are available and have been analyzed and integrated in our RTA
work, we focus on transcriptomics (that is gene expression) data obtained from
high-throughput microarray experiments in this paper to illustrate capabilities
and limitations of our algorithms. Our algorithms make different but overall
relatively few biological assumptions, so that they are applicable to other
types of biological data and potentially even to other complex systems that
exhibit high dimensionality but are not of biological nature.
