  Hidden tree Markov models allow learning distributions for tree structured
data while being interpretable as nondeterministic automata. We provide a
concise summary of the main approaches in literature, focusing in particular on
the causality assumptions introduced by the choice of a specific tree visit
direction. We will then sketch a novel non-parametric generalization of the
bottom-up hidden tree Markov model with its interpretation as a
nondeterministic tree automaton with infinite states.
