Bayesian Tensor Factorisation for Bottom-up Hidden Tree Markov Models
This work addresses a practical limitation in modeling tree-structured data, though it appears incremental as it builds on existing approximations.
The authors tackled the intractable state-transition matrix size in Bottom-Up Hidden Tree Markov Models for tree-structured data by proposing a Tucker tensor factorisation approximation, which outperformed existing approximations on two empirical tasks.
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.