Energetic Variational Inference: Foundations, Algorithms, and Applications

能量变分推理：基础、算法和应用

• 批准号: 2153029
• 负责人: Lulu Kang
• 金额: $ 30万
• 依托单位: Illinois Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2153029&HistoricalAwards=false
• 关键词: Energetic; Variational; Inference; Foundations; Algorithms; Energetic; Variational; Inference; Foundations; Algorithms

Variational Inference is a powerful tool used to boost efficiency and flexibility in machine learning and artificial intelligence algorithms, particularly those based on large amounts of data. In this project, the investigators plan to create a unified and systematic framework for variational inference methods, making two key contributions. First, the investigators will establish the theoretical foundations for the proposed framework, which will support and justify using existing and new variational inference algorithms in machine learning applications. Second, the investigators will provide a systemic procedure to create new variational inference algorithms and apply them to emerging machine learning problems. In addition to these new scientific developments, the investigators will create new courses and workshops on machine learning, recruit both undergraduate and graduate students for summer, project-based research programs, and provide mentorship to local high school students through hands-on machine learning training programs. Collaborations are planned with industrial data science partners to apply these new algorithms in practice and to train the workforce with the start-of-the-art machine learning tools.The proposed "Energetic Variational Inference" framework is based on an energetic variational approach, which has been successfully used to study complicated non-equilibrium systems in physics and biology. The investigators will provide a blueprint for generating new algorithms by introducing various options for the four essential components of the proposed framework: the divergence functional, the dissipation functional, the representation of the probability density, and the temporal discretization. The investigators will study convergence in the continuous formulation as well as estimate the error bounds after temporal discretization of the underlying continuous dynamic system. More importantly, these theoretical results can be applied or extended to other flow-based variational inference approaches. These methods will be applied to problems in supervised learning, density estimation, and generative learning. Additional novel applications in machine learning, statistics, and statistical physics will also be developed. The algorithms will be packaged into open-source software for public use.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.

变分推断是一种强大的工具，用于提高机器学习和人工智能算法的效率和灵活性，尤其是基于大量数据的工具。在这个项目中，调查人员计划为各种推理方法创建一个统一的系统框架，从而做出了两个关键的贡献。首先，调查人员将建立针对拟议框架的理论基础，该框架将使用机器学习应用程序中现有和新的变异推理算法来支持和证明合理性。其次，研究人员将提供一个系统的程序，以创建新的变分推理算法并将其应用于新兴的机器学习问题。除了这些新的科学发展外，研究人员还将创建有关机器学习的新课程和讲习班，招募夏季的本科生和研究生，基于项目的研究计划，并通过动手的机器学习培训计划向当地高中生提供指导。计划与工业数据科学合作伙伴进行合作，以在实践中应用这些新算法，并使用最初的机器学习工具来训练劳动力。拟议的“能量变异推理”框架是基于一种能量的变异方法，该方法已成功地用于研究物理学中的非平衡系统。 研究人员将通过为提出的框架的四个基本组成部分引入各种选项来提供用于生成新算法的蓝图：差异功能，耗散功能，概率密度的表示和时间离散化。研究人员将研究连续公式中的收敛，并估计基础连续动态系统时间离散后的误差界限。更重要的是，这些理论结果可以应用或扩展到其他基于流动的变异推理方法。这些方法将应用于监督学习，密度估计和生成学习中的问题。还将开发机器学习，统计和统计物理学中的其他新颖应用。该算法将被包装到开源软件中，以供公众使用。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。