# Bayesian Tensor Factorisation for Bottom-up Hidden Tree Markov Models

## TL;DR

This paper introduces a tensor factorisation-based approximation for Bottom-Up Hidden Tree Markov Models, enabling practical use and improved performance on tree-structured data tasks.

## Contribution

It proposes a novel Tucker tensor factorisation approach to approximate the intractable state-transition matrix in Hidden Tree Markov Models, with a new probabilistic model and learning algorithm.

## Key findings

- The new model outperforms existing approximations on two tasks.
- Empirical results demonstrate improved accuracy and efficiency.
- The approach enables practical application of complex tree models.

## Abstract

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.