Formality is one of the important characteristics of text documents. The automatic detection of the formality level of a text is potentially beneficial for various natural language processing tasks. Before, two large-scale datasets were introduced for multiple languages featuring formality annotation -- GYAFC and X-FORMAL. However, they were primarily used for the training of style transfer models. At the same time, the detection of text formality on its own may also be a useful application. This work proposes the first to our knowledge systematic study of formality detection methods based on statistical, neural-based, and Transformer-based machine learning methods and delivers the best-performing models for public usage. We conducted three types of experiments -- monolingual, multilingual, and cross-lingual. The study shows the overcome of Char BiLSTM model over Transformer-based ones for the monolingual and multilingual formality classification task, while Transformer-based classifiers are more stable to cross-lingual knowledge transfer.
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