  A conditional independence graph is a concise representation of pairwise
conditional independence among many variables. Graphical Random Forests (GRaFo)
are a novel method for estimating pairwise conditional independence
relationships among mixed-type, i.e. continuous and discrete, variables. The
number of edges is a tuning parameter in any graphical model estimator and
there is no obvious number that constitutes a good choice. Stability Selection
helps choosing this parameter with respect to a bound on the expected number of
false positives (error control).
  The performance of GRaFo is evaluated and compared with various other methods
for p = 50, 100, and 200 possibly mixed-type variables while sample size is n =
100 (n = 500 for maximum likelihood). Furthermore, GRaFo is applied to data
from the Swiss Health Survey in order to evaluate how well it can reproduce the
interconnection of functional health components, personal, and environmental
factors, as hypothesized by the World Health Organization's International
Classification of Functioning, Disability and Health (ICF). Finally, GRaFo is
used to identify risk factors which may be associated with adverse
neurodevelopment of children who suffer from trisomy 21 and experienced
open-heart surgery.
  GRaFo performs well with mixed data and thanks to Stability Selection it
provides an error control mechanism for false positive selection.
