  A typical problem in causal modeling is the instability of model structure
learning, i.e., small changes in finite data can result in completely different
optimal models. The present work introduces a novel causal modeling algorithm
for longitudinal data, that is robust for finite samples based on recent
advances in stability selection using subsampling and selection algorithms. Our
approach uses exploratory search but allows incorporation of prior knowledge,
e.g., the absence of a particular causal relationship between two specific
variables. We represent causal relationships using structural equation models.
Models are scored along two objectives: the model fit and the model complexity.
Since both objectives are often conflicting we apply a multi-objective
evolutionary algorithm to search for Pareto optimal models. To handle the
instability of small finite data samples, we repeatedly subsample the data and
select those substructures (from the optimal models) that are both stable and
parsimonious. These substructures can be visualized through a causal graph. Our
more exploratory approach achieves at least comparable performance as, but
often a significant improvement over state-of-the-art alternative approaches on
a simulated data set with a known ground truth. We also present the results of
our method on three real-world longitudinal data sets on chronic fatigue
syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained
with our approach are generally in line with results from more
hypothesis-driven analyses in earlier studies and suggest some novel
relationships that deserve further research.
