CAREER: A Statistical Inferential Framework for Online Learning Algorithms

科学和工程领域不断发展和改进的数据采集技术使从业者能够以廉价和在线的方式测量数千到数百万个观测单位。例子包括推荐系统、神经记录和流感预测，在这些系统中，决策会随着更多数据的到来而不断更新，因此，用捕获数据在线性质的模型来最好地代表问题。在统计学、计算机科学和优化的共同努力下，一个大型工具箱已经开发出来，可以一次基于一个数据点有效地对模型进行更新，而关于如何量化这些在线学习问题中预测的不确定性的探索则少得多。例如，我们可以在多大程度上信任在线学习算法的预测，以及通过使用更多数据更新模型，预测会有多大不同？研究者将开发一个涉及理论、算法和软件的新框架，以量化一大类在线学习算法的不确定性。通过本研究项目开发的方法将应用于在线学习中的大规模分类问题，目标是提高预测的可解释性。所有的方法都将在软件中实现，这些软件将广泛传播给从事在线学习任务的实践者。研究者将根据研究成果在本科和研究生阶段开发新的课程，以增加统计学、计算机科学和优化之间的互动，并将指导对这些领域感兴趣的学生。更具体地说，该项目将重点关注随机梯度下降及其许多变体的大规模数据集训练所产生的不确定性，这是一类非常流行的在线学习算法，它使用计算成本低但有噪声的梯度顺序更新模型参数。随机梯度下降算法的随机性是潜在的不可忽略的，甚至可能在最坏的情况下危及预测的解释。从完全推理的角度出发，本文提出了详细的研究议程，旨在通过三个基本主题(1)构建凸目标在线学习的置信区间，（2)深度神经网络的不确定性量化，以及(3)加速在线环境下的随机优化）深入了解随机梯度下降的不确定性量化。综上所述，拟议的研究项目将为使用流数据将统计推理思想整合到随机优化中奠定坚实的基础，并将研究成果反馈到分析在线数据集的实用方法的开发中。这项工作的完成将带来统计学、优化和机器学习等不同的视角，从而全面了解在线学习算法的推理特性，并提高随机梯度下降在广泛的科学和工程问题中应用的可信度。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。

The ever-evolving and improving data acquisition techniques in science and engineering allow practitioners to measure thousands to millions of observation units in a cheap and online fashion. Examples include recommender systems, neural recordings, and influenza prediction, where decision-making is constantly updated as more data arrives and thus the problems are best represented with models capturing the online nature of data. With collective efforts from statistics, computer science, and optimization, a large toolbox has been developed to efficiently make an update to the model based on one data point at a time, whereas much less is explored about how to quantify uncertainty of the predictions in these online learning problems. For example, to what extent can we trust the predictions of an online learning algorithm, and how different would the predictions be by updating the model with more data? The investigator will develop a new framework involving theory, algorithms, and software to quantify uncertainty for a large class of online learning algorithms. The methods developed through this research project will be applied to large-scale classification problems in online learning, with the goal of enhancing interpretability of the predictions. All methods will be implemented in software that will be broadly disseminated to practitioners who work on online learning tasks. The investigator will develop new courses at both undergraduate and graduate levels based on the research output to increase interaction across statistics, computer science, and optimization, and will mentor students with interests in these fields.More specifically, this project will focus on the uncertainty arising from training on large-scale datasets with stochastic gradient descent and many of its variants, a class of immensely popular online learning algorithms that sequentially update the model parameters using computationally cheap but noisy gradients. The algorithmic randomness of stochastic gradient descent is potentially non-negligible and could even jeopardize the interpretation of predictions at worst. Taking a fully inferential viewpoint, the proposed research has a detailed research agenda that aims to obtain an in-depth understanding of uncertainty quantification for stochastic gradient descent through three fundamental topics: (1) constructing confidence intervals for online learning with convex objectives, (2) quantifying uncertainty for deep neural networks, and (3) accelerating stochastic optimization in the online setting. Taken together, the proposed research projects will build a firm foundation for integrating statistical inferential ideas into stochastic optimization using streaming data, with research output feeding back into the development of practical methodology for analyzing online datasets. The completion of this work will bring in various perspectives from statistics, optimization, and machine learning, leading to a comprehensive understanding of inferential properties of online learning algorithms and improved trustworthiness of the application of stochastic gradient descent in a wide range of scientific and engineering problems.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.