Testing High-dimensional Multinomials with Applications to Text Analysis
T. Tony Cai, Zheng Tracy Ke, and Paxton Turner
Motivated by applications in text mining and discrete distribution inference, we investigate the testing for equality of probability mass functions of K groups of high-dimensional multinomial distributions. Special cases of this problem include global testing for topic models, two-sample testing in authorship attribution, and closeness testing for discrete distributions. A test statistic, which is shown to have an asymptotic standard normal distribution under the null, is proposed. This parameter-free null distribution holds true without requiring identical multinomial parameters within each group or equal group sizes. The optimal detection boundary for this testing problem is established, and the proposed test is shown to achieve this optimal detection boundary across the entire parameter space of interest. The proposed method is demonstrated in simulation studies and applied to analyze two real-world datasets to examine, respectively, variation among consumer reviews of Amazon movies and the diversity of statistical paper abstracts.