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的在线方式测量数千到数百万个观察单位。例如，推荐系统、神经记录和流感预测，随着更多数据的到来，决策不断更新，因此问题最好用捕捉数据在线性质的模型来表示。在统计学、计算机科学和优化的共同努力下，已经开发了一个大型工具箱，可以一次基于一个数据点有效地更新模型，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要少得多。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？研究人员将开发一个新的框架，涉及理论，算法和软件，以量化一大类在线学习算法的不确定性。通过该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，目的是提高预测的可解释性。 所有方法都将在软件中实施，并将广泛分发给从事在线学习任务的从业人员。研究者将根据研究成果开发本科和研究生阶段的新课程，以增加统计学，计算机科学和优化之间的互动，并指导对这些领域感兴趣的学生。更具体地说，该项目将专注于在大规模数据集上使用随机梯度下降及其许多变体进行训练所产生的不确定性，一类非常流行的在线学习算法，使用计算成本低但有噪声的梯度来顺序更新模型参数。随机梯度下降的算法随机性可能是不可忽略的，甚至可能在最坏的情况下危及预测的解释。从完全推理的角度来看，拟议的研究有一个详细的研究议程，旨在通过三个基本主题深入了解随机梯度下降的不确定性量化：（1）构建具有凸目标的在线学习的置信区间，（2）量化深度神经网络的不确定性，以及（3）加速在线设置中的随机优化。总的来说，拟议的研究项目将为使用流数据将统计推断思想融入随机优化奠定坚实的基础，研究成果将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来自统计，优化和机器学习的各种观点，导致对在线学习算法的推理特性的全面理解，并提高了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。

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.