  Bottom-Up Hidden Tree Markov Model is a highly expressive model for
tree-structured data. Unfortunately, it cannot be used in practice due to the
intractable size of its state-transition matrix. We propose a new approximation
which lies on the Tucker factorisation of tensors. The probabilistic
interpretation of such approximation allows us to define a new probabilistic
model for tree-structured data. Hence, we define the new approximated model and
we derive its learning algorithm. Then, we empirically assess the effective
power of the new model evaluating it on two different tasks. In both cases, our
model outperforms the other approximated model known in the literature.
