CAREER: Stein Variational Gradient Descent: A New Foundation for Inference

近年来，机器学习（ML）和人工智能（AI）取得了令人瞩目的进展。智能计算机程序现在可以比人类更好地对图像进行分类，击败世界围棋冠军，并在从医疗保健到教育等领域提出智能建议。在底层，许多这些技术都是通过使用高度灵活和结构化的概率模型来表达和推理复杂现象的想法而成为可能的。与此同时，现代机器学习系统所需的概率模型越来越复杂，有效计算概率的能力成为现代学习系统的主要瓶颈之一。该项目的目标是为高度复杂的概率模型开发一种新的有效和近似计算概率的理论和算法框架。该项目为本科生提供了研究机会，并开发了面向高中生和本科生的拓展活动的教育模块。马尔可夫链蒙特卡罗算法（MCMC）和变分推理算法（VI）是目前文献中主要的两种近似推理算法。然而，它们都有自己的关键弱点。MCMC精度高，但收敛速度慢；VI通常更快，但会引入确定性错误，并且缺乏理论保证。该项目旨在引入一种新的Stein变分范式，用于近似推理，该范式集成了MCMC和VI的优点，使算法像MCMC一样灵活和准确，像VI一样快速。关键思想是直接优化基于非参数粒子的表示，以适应具有快速确定性梯度更新的难处理分布，这是通过整合和推广Stein方法中的关键数学工具实现的。最佳输运和相互作用粒子系统。从这个框架衍生出来的一个基本算法，称为Stein变分梯度下降（SVGD），已经被发现是一个强大的工具，在一系列应用中。该项目通过(1)系统地研究基础理论问题，(2)开发更有效和实用的算法和软件，以及(3)展示其在各种跨学科应用中的能力，包括强化学习和分子动力学，将这一初步成功扩展到更高的水平。该奖项反映了美国国家科学基金会的法定使命，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。

In recent years, machine learning (ML) and artificial intelligence (AI) have achieved remarkable progress. Smart computer programs can now categorize images better than humans, beat the world champion at Go, and make intelligent recommendations in areas from health care to education. Under the hood, many of these technologies are made possible by the idea of using highly flexible and structured probabilistic models to express and reason with complex phenomena. Meanwhile, probabilistic models required for modern machine learning systems are becoming increasingly complex, and the ability to compute probabilities efficiently becomes one of the main bottlenecks of modern learning systems. The goal of this project is to develop a new theoretical and algorithmic framework of efficient and approximate computation of probabilities for highly complex probabilistic models. This project provides research opportunities for undergraduates and it also develops educational modules for outreach activities to high school students and undergraduates.Markov chain Monte Carlo (MCMC) and variational inference (VI) have been the two major types of approximate inference algorithms that dominate the literature. However, both of them have their own critical weaknesses. MCMC is accurate but suffers from slow convergence; VI is typically faster but introduces deterministic errors and lacks theoretical guarantees. This project aims to introduce a new Stein variational paradigm for approximate inference that integrates the advantages of MCMC and VI, enabling algorithms that are as flexible and accurate as MCMC and as fast as VI. The key idea is to directly optimize a non-parametric particle-based representation to fit intractable distributions with fast deterministic gradient-based updates, which is made possible by integrating and generalizing key mathematical tools from Stein's method, optimal transport and interacting particle systems. A basic algorithm derived from this framework, called Stein variational gradient descent (SVGD), has already been found to be a powerful tool in a range of applications. This project extends this initial success to a higher level, by (1) systematically investigating basic theoretical problems, (2) developing more efficient and practical algorithms and software, and (3) demonstrating its power in various interdisciplinary applications, including reinforcement learning and molecule dynamics.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.