Latent Dirichlet Allocation is a popular machine-learning technique that identifies latent structures in a corpus of documents. This paper addresses the ongoing concern that formal procedures for determining the optimal LDA configuration do not exist by introducing a set of parametric tests that rely on the assumed multinomial distribution specification underlying the original LDA model. Our methodology defines a set of rigorous statistical procedures that identify and evaluate the optimal topic model. The U.S. Presidential Inaugural Address Corpus is used as a case study to show the numerical results. We find that 92 topics best describe the corpus. We further validate the method through a simulation study confirming the superiority of our approach compared to other standard heuristic metrics like the perplexity index.

There have been a number of major evaluations of the performance of retrieval systems against large full text and surrogate (bibliographic) databases. These evaluations have concentrated on the experimental determination of the Precision Ratio, the fraction of retrieved items that are relevant to an information request, and the Recall Ratio, the fraction of the total number of relevant items that were actually retrieved. While these measures have met with general acceptance, they have also generated much controversy. The purpose of this article is to review the results of several of the largest evaluations and to propose a simple model for the performance of such systems that may help explain the relationship between these measures and user behavior.