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

Hierarchical topic modeling is a potentially powerful instrument for determining the topical structure of text collections that allows constructing a topical hierarchy representing levels of topical abstraction. However, tuning of parameters of hierarchical models, including the number of topics on each hierarchical level, remains a challenging task and an open issue. In this paper, we propose a Renyi entropy-based approach for a partial solution to the above problem. First, we propose a Renyi entropy-based metric of quality for hierarchical models. Second, we propose a practical concept of hierarchical topic model tuning tested on datasets with human mark-up. In the numerical experiments, we consider three different hierarchical models, namely, hierarchical latent Dirichlet allocation (hLDA) model, hierarchical Pachinko allocation model (hPAM), and hierarchical additive regularization of topic models (hARTM). We demonstrate that hLDA model possesses a significant level of instability and, moreover, the derived numbers of topics are far away from the true numbers for labeled datasets. For hPAM model, the Renyi entropy approach allows us to determine only one level of the data structure. For hARTM model, the proposed approach allows us to estimate the number of topics for two hierarchical levels.