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

该项目的重点是发展信息理论的数学基础，特别是与处理严重污染数据相关的信息理论标准。这些标准被广泛应用于现实世界应用中的机器学习任务，如医学成像、人脸识别和天气预报。他们的理论认识是滞后的，许多根本性的问题仍然悬而未决。该项目将加深对信息理论标准的理解，探索其前沿应用，并帮助推进鲁棒机器学习的研究。本研究将结合教育与外展活动，包含三个面向资讯理论标准学习的部分，分别为理论评估、计算方法与应用探索。理论评估旨在揭示非高斯噪声存在下的学习机制。计算方法将信息理论标准和相关的非凸优化与现代机器学习技术（如分布式学习和深度学习）相结合。应用程序组件致力于探索新的应用领域，如生物光谱成像。基于信息论准则的学习和新应用的理论和计算基础将丰富和拓宽当前对非高斯数据分析的理解。通过将先进的学习技术引入这一领域，该项目有可能实现更强大和更强大的机器学习系统，广泛适用于各种现代应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.