A Generalized Theory of Mixup for Structure-Preserving Synthetic Data

Mixup is a widely adopted data augmentation technique known for enhancing the generalization of machine learning models by interpolating between data points. Despite its success and popularity, limited attention has been given to understanding the statistical properties of the synthetic data it generates. In this paper, we delve into the theoretical underpinnings of mixup, specifically its effects on the statistical structure of synthesized data. We demonstrate that while mixup improves model performance, it can distort key statistical properties such as variance, potentially leading to unintended consequences in data synthesis. To address this, we propose a novel mixup method that incorporates a generalized and flexible weighting scheme, better preserving the original data's structure. Through theoretical developments, we provide conditions under which our proposed method maintains the (co)variance and distributional properties of the original dataset. Numerical experiments confirm that the new approach not only preserves the statistical characteristics of the original data but also sustains model performance across repeated synthesis, alleviating concerns of model collapse identified in previous research.

Confirmatory Aspect-based Opinion Mining Processes

A new opinion extraction method is proposed to summarize unstructured, user-generated content (i.e., online customer reviews) in the fixed topic domains. To differentiate the current approach from other opinion extraction approaches, which are often exposed to a sparsity problem and lack of sentiment scores, a confirmatory aspect-based opinion mining framework is introduced along with its practical algorithm called DiSSBUS. In this procedure, 1) each customer review is disintegrated into a set of clauses; 2) each clause is summarized to bi-terms-a topic word and an evaluation word-using a part-of-speech (POS) tagger; and 3) each bi-term is matched to a pre-specified topic relevant to a specific domain. The proposed processes have two primary advantages over existing methods: 1) they can decompose a single review into a set of bi-terms related to pre-specified topics in the domain of interest and, therefore, 2) allow identification of the reviewer's opinions on the topics via evaluation words within the set of bi-terms. The proposed aspect-based opinion mining is applied to customer reviews of restaurants in Hawaii obtained from TripAdvisor, and the empirical findings validate the effectiveness of the method. Keywords: Clause-based sentiment analysis, Customer review, Opinion mining, Topic modeling, User-generate-contents.