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

Bayesian Tensor Factorisation for Bottom-up Hidden Tree Markov Models