Analysis and tuning of hierarchical topic models based on Renyi entropy approach

Hierarchical topic modeling is a potentially powerful instrument for determining topical structures of text collections that additionally allows constructing a hierarchy representing the levels of topic abstractness. However, parameter optimization in hierarchical models, which includes finding an appropriate number of topics at each level of hierarchy, remains a challenging task. In this paper, we propose an approach based on Renyi entropy as a partial solution to the above problem. First, we introduce a Renyi entropy-based metric of quality for hierarchical models. Second, we propose a practical approach to obtaining the "correct" number of topics in hierarchical topic models and show how model hyperparameters should be tuned for that purpose. We test this approach on the datasets with the known number of topics, as determined by the human mark-up, three of these datasets being in the English language and one in Russian. In the numerical experiments, we consider three different hierarchical models: hierarchical latent Dirichlet allocation model (hLDA), hierarchical Pachinko allocation model (hPAM), and hierarchical additive regularization of topic models (hARTM). We demonstrate that the hLDA model possesses a significant level of instability and, moreover, the derived numbers of topics are far from the true numbers for the labeled datasets. For the hPAM model, the Renyi entropy approach allows determining only one level of the data structure. For hARTM model, the proposed approach allows us to estimate the number of topics for two levels of hierarchy.