Optimal Transport and Measure Optimization Foundation for Robust and Causal Machine Learning

• Applicant: Dr. Jia-Jie Zhu
• Subject Area: Mathematics ; Theoretical Computer Science
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 543963649

The project proposal focuses on the mathematical foundation for understanding and addressing distribution shift issues and in machine learning (ML), particularly for handling structured distribution shifts and causal inference with high-dimensional data. This involves dealing with discrepancies between training and test data distributions. The project aims to develop a rigorous theoretical framework for understanding and addressing structured distribution shifts using variational approaches to dynamical systems, gradient flows of probability measures, and optimal transport. Key objectives include: - Developing variational models for structured distribution shifts in high-dimensional data. This involves using gradient flow theory for measure optimization in new geometries suitable for structured distribution shifts. - Establishing a unified measure optimization framework for modeling and evaluating distribution shifts. This framework will advance knowledge in the domain of measure optimization and provide a more robust and trustworthy model for ML training, data generation, and prediction. We will then investigate structured distributionally robust learning algorithms. - Exploring state-of-the-art flow-based generative models for modeling structured distribution shift.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2298: Theoretical Foundations of Deep Learning