Collaborative Research: Mathematical Foundation of Learning with Information-Theoretic Criteria from Non-Gaussian Data

This project is focused on developing the mathematical foundations for information theory and specifically with information-theoretic criteria relevant for tackling heavily contaminated data. Such criteria are widely applied to machine learning tasks arising from real-world applications such as medical imaging, face recognition, and weather forecasting. Their theoretical understanding is lagging, and many fundamental problems remain open. The project will deepen the understanding of information-theoretic criteria, explore their cutting-edge applications, and help advance research in robust machine learning. This project is integrated with educational and outreach activities. This research involves three dedicated components towards information-theoretic criteria based learning; these are theoretical assessments, computational methodologies, and application explorations. Theoretical assessments aim at unveiling the mechanisms of learning in the presence of non-Gaussian noise. Computational methodologies integrate information-theoretic criteria and the involved non-convex optimization with modern machine learning techniques such as distributed learning and deep learning. The application component is dedicated to the exploration of new application domains such as biological spectral imaging. Theoretical and computational foundations of information-theoretic criteria based learning and new applications will enrich and broaden the current understanding of non-Gaussian data analysis. By introducing advanced learning techniques into this area, this project has the potential to realize more powerful and robust machine learning systems that are broadly applicable to a variety of modern applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.