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，在围棋比赛中击败世界冠军，并在从医疗保健到教育等领域提出智能建议。在引擎盖下，这些技术中的许多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实现的。与此同时，现代机器学习系统所需的概率模型变得越来越复杂，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个新的理论和算法框架，用于有效和近似计算概率。该项目为本科生提供研究机会，并开发教育模块，为高中生和本科生的外展活动。马尔可夫链蒙特卡罗（MCMC）和变分推理（VI）一直是两种主要类型的近似推理算法，占主导地位的文献。然而，两者都有自己的致命弱点。MCMC是准确的，但收敛速度慢; VI通常更快，但引入了确定性错误，缺乏理论保证。 该项目旨在引入一种新的Stein变分范式进行近似推理，该范式集成了MCMC和VI的优点，使算法与MCMC一样灵活和准确，与VI一样快速。其关键思想是直接优化非参数的基于粒子的表示，以适应棘手的分布与快速确定性的基于梯度的更新，这是通过整合和推广关键的数学工具，从斯坦的方法，最佳运输和相互作用的粒子系统。一个基本的算法来自这个框架，称为斯坦变分梯度下降（SVGD），已经被发现是一个强大的工具，在一系列的应用。该项目将这一最初的成功扩展到更高的水平，通过（1）系统地研究基本理论问题，（2）开发更有效和实用的算法和软件，以及（3）在各种跨学科应用中展示其力量，包括强化学习和分子动力学。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。

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.