  We propose a non-parametric regression methodology, Random Forests on
Distance Matrices (RFDM), for detecting genetic variants associated to
quantitative phenotypes representing the human brain's structure or function,
and obtained using neuroimaging techniques. RFDM, which is an extension of
decision forests, requires a distance matrix as response that encodes all
pair-wise phenotypic distances in the random sample. We discuss ways to learn
such distances directly from the data using manifold learning techniques, and
how to define such distances when the phenotypes are non-vectorial objects such
as brain connectivity networks. We also describe an extension of RFDM to detect
espistatic effects while keeping the computational complexity low. Extensive
simulation results and an application to an imaging genetics study of
Alzheimer's Disease are presented and discussed.
