Orthogonal Inductive Matrix Completion.

Area of Science:

• Machine Learning
• Data Science
• Linear Algebra

Background:

• Matrix completion is crucial for recommender systems and data recovery.
• Existing methods often lack interpretability or struggle to integrate diverse side information effectively.
• Incorporating prior knowledge can significantly improve matrix completion performance.

Purpose of the Study:

• To introduce Orthogonal Inductive Matrix Completion (OMIC), a novel and interpretable matrix completion framework.
• To enable the injection of prior knowledge about singular vectors into the completion process.
• To provide theoretical guarantees on generalization capabilities and analyze empirical performance.

Main Methods:

• Developed OMIC, utilizing a sum of orthonormal side information terms and nuclear-norm regularization.
• Designed a provably converging algorithm for simultaneous optimization of all model components.
• Investigated generalization in distribution-free and uniform marginal settings, analyzing learning guarantees based on injected knowledge quality.

Main Results:

• OMIC demonstrated superior adaptability to varying user bias relevance on synthetic datasets compared to other methods.
• The framework successfully integrated user/item biases and community information additively.
• On real-life recommendation datasets, OMIC surpassed state-of-the-art performance while offering enhanced interpretability.

Conclusions:

• OMIC provides a powerful and interpretable approach to matrix completion by effectively leveraging side information.
• The method's theoretical guarantees and empirical success highlight its potential for various data recovery tasks.
• OMIC represents a significant advancement in incorporating prior knowledge for improved and understandable matrix completion.