Collaborative Research: III: Medium: Conditional Transport: Theory, Methods, Computation, and Applications

测量概率分布之间的差异是统计学和机器学习（ML）中的一个基本问题。它在许多关键的机器学习和人工智能（AI）任务中起着至关重要的作用，例如构建深度生成模型来合成真实数据和训练深度强化学习代理。该项目的创新之处在于：1）建立条件传输（CT）作为概率分布之间的新统计距离，以解决现有方法的几个关键限制; 2）开发一种新的基于分布的学习框架，具有高效的近似计算算法; 3）应用CT更好地解决涉及大规模和高维数据和模型的现代ML/AI问题。该项目的影响是1）推进基于分布的ML/AI基础研究，2）为ML/AI在科学，工程和生物医学中的应用提供高效和强大的方法，特别是在逆材料设计和多组学数据分析中。调查人员将把拟议的研究与下一代劳动力发展的培训、教育和外联活动结合起来，开发新的ML/AI课程材料，以更好地为各级学生和研究人员做好准备，使他们具有多样化的教育背景，促进多样性、公平和包容性，重点是吸引来自代表性不足群体的人才。特别强调扩大跨学科计算的参与。该项目旨在建立CT及其支持的基于分布的学习框架，该框架具有范式转移的潜力，可以通过新的模型和推理算法进一步推进ML/AI研究。特别是，1）对CT的理论理解将为这种新的学习框架提供所需的模型表示能力以及学习稳定性的基础。2)最大似然估计、贝叶斯推理和熵正则化最优传输将基于CT进行重新讨论，从而利用现代深度网络模型和随机梯度下降工具实现高效的贝叶斯计算和优化。3)将开发新的和改进的ML/AI模型和推理算法，用于深度生成建模，对比表示学习和深度强化学习，以推进最新技术水平。4）逆向材料设计和多组学数据分析，这两个现实世界的应用需要可靠的不确定性量化，以进行后续的关键决策，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。

Measuring the difference between probability distributions is a fundamental problem in statistics and machine learning (ML). It plays essential roles in many critical ML and artificial intelligence (AI) tasks, such as building deep generative models to synthesize realistic data and training deep reinforcement learning agents. The project’s novelties are 1) establishing Conditional Transport (CT) as a new statistical distance between probability distributions to address several key limitations of existing methods, 2) developing a new distribution-based learning framework with efficient approximate computation algorithms, and 3) applying CT to better solve modern ML/AI problems involving large-scale and high-dimensional data and models. The project’s impacts are 1) advancing distribution-based ML/AI fundamental research, and 2) enabling efficient and robust methods for the ML/AI applications in science, engineering, and bio-medicine, in particular in inverse materials design and multi-omics data analysis. The investigators will integrate the proposed research with training, education, and outreach activities for next-generation workforce development, by developing new ML/AI course materials to better prepare students and researchers at all levels with a diversified educational background, promoting diversity, equity, and inclusion with the emphasis on attracting talents from under-represented groups, with a special emphasis on broadening participation in interdisciplinary computing. This project aims to establish CT and its enabled distribution-based learning framework, which has the paradigm-shift potential to further advance ML/AI research with new models and inference algorithms. In particular, 1) theoretical understanding of CT will provide the foundation of this new learning framework with desired model representation power as well as learning stability. 2) Maximum likelihood estimation, Bayesian inference, and entropy regularized optimal transport will be revisited based on CT, enabling efficient Bayesian computation and optimization taking advantage of modern deep network models and stochastic gradient descent tools. 3) New and improved ML/AI models and inference algorithms will be developed for deep generative modeling, contrastive representation learning, and deep reinforcement learning to advance the state of the art. 4) Inverse materials design and multi-omics data analysis, two real-world applications that require reliable uncertainty quantification for consequent critical decision making, will showcase the advantages of the CT-based methods.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.