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

度量概率分布之间的差异是统计学和机器学习中的一个基本问题。它在许多关键的ML和人工智能(AI)任务中扮演着重要的角色，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)将条件传输(CT)作为概率分布之间的一种新的统计距离，以解决现有方法的几个关键局限性；2)开发了一种新的基于分布的学习框架和高效的近似计算算法；3)应用条件传输更好地解决了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)推进基于分布式的ML/AI基础研究，以及2)为ML/AI在科学、工程和生物医学中的应用提供高效和健壮的方法，特别是在逆向材料设计和多组学数据分析方面。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，使具有多样化教育背景的各级学生和研究人员更好地做好准备，促进多样性、公平和包容性，重点是吸引代表性不足群体的人才，并特别强调扩大对跨学科计算的参与。本项目旨在建立CT及其使能的基于分布式的学习框架，该框架具有范式转换的潜力，以新的模型和推理算法进一步推动ML/AI研究。具体地说，1)对CT的理论理解将为这一新的学习框架提供基础，具有所需的模型表示能力和学习稳定性。2)基于CT的最大似然估计、贝叶斯推理和熵正则化最优传输将被重新讨论，从而能够利用现代深层网络模型和随机梯度下降工具进行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，用于深度产生式建模、对比表示学习和深度强化学习，以提高技术水平。4)逆向材料设计和多组学数据分析，这两个真实世界的应用程序需要可靠的不确定性量化来进行后续的关键决策，将展示基于CT的方法的优势。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.