Statistical analysis for modeling dyadic interactions using machine learning methods
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Modeling dyadic interactions between entities is one of the fundamental problems in machine learning with many real-world applications, including recommender systems, data clustering, social network analysis and ranking. In this dissertation, we introduce several improved models for modeling dyadic interactions in machine learning by taking advantage of sophisticated information from different sources, such as prior structure, domain knowledge and side information. We start with exploiting different types of auxiliary information for several motivating applications, including signed link prediction, signed graph clustering, and dyadic rank aggregation. We then further move from an application-specific aspect to a general modeling aspect, where we aim to jointly exploit prior knowledge, problem structure and side information for learning low-rank modeling matrices from missing and corrupted observations. Such a modeling approach provides a general treatment to better model dyadic interactions in various machine learning applications. More importantly, we provide comprehensive theoretical analyses and performance guarantees to help us understand the utility of the additional information and quantify the merits of the proposed methods. These results therefore demonstrate the effectiveness of proposed approaches under both practical and theoretical aspects.