Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of work on SGD, much less is known about the statistical inferential properties of SGD-based predictions. Taking a fully inferential viewpoint, this paper introduces a novel procedure termed HiGrad to conduct statistical inference for online learning, without incurring additional computational cost compared with SGD. The HiGrad procedure begins by performing SGD updates for a while and then splits the single thread into several threads, and this procedure hierarchically operates in this fashion along each thread. With predictions provided by multiple threads in place, a $t$-based confidence interval is constructed by decorrelating predictions using covariance structures given by a Donsker-style extension of the Ruppert--Polyak averaging scheme, which is a technical contribution of independent interest. Under certain regularity conditions, the HiGrad confidence interval is shown to attain asymptotically exact coverage probability. Finally, the performance of HiGrad is evaluated through extensive simulation studies and a real data example. An R package \texttt{higrad} has been developed to implement the method.
Parameter-Free and Group Conditional Online Conformal Prediction
Data Science and AI Institute (DSAI), Johns Hopkins University（数据科学与人工智能研究院（DSAI），约翰霍普金斯大学）；Mathematical Institute for Data Science (MINDS), Johns Hopkins University（数据科学数学研究院（MINDS），约翰霍普金斯大学）；Department of Biomedical Engineering, Johns Hopkins University（生物医学工程系，约翰霍普金斯大学）；Department of Computer Science, Johns Hopkins University（计算机科学系，约翰霍普金斯大学）；Amazon Responsible AI（亚马逊负责任人工智能）
We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where performance guarantees may be desired not only over the full time horizon but also in all (sub-)intervals of time. We develop n…
Warrington College of Business, University of Florida（佛罗里达大学沃灵顿商学院）；Leonard N. Stern School of Business, New York University（纽约大学伦纳德·N·斯特恩商学院）；School of Management, Xi’an Jiaotong University（西安交通大学管理学院）；Shanghai University of Finance and Economics（上海财经大学）
Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision focuses on designing an online policy to maximize the revenue. However, the research on uncertainty quantification on the underlying true model function (e.g., demand function), a critical problem for practitioners, has not been well explored. In this paper, using the problem of demand function prediction in dynamic pricing as the motivating example, we study the…
To provide rigorous uncertainty quantification for online learning models, we develop a framework for constructing uncertainty sets that provably control risk -- such as coverage of confidence intervals, false negative rate, or F1 score -- in the online setting. This extends conformal prediction to apply to a larger class of online learning problems. Our method guarantees risk control at any user-specified level even when the underlying data distribution shifts drastically, even adversarially, over time in an unknown fashion. The technique we propose is highly flexible as it can be applied wit…
School of Statistics and Data Science, LPMC, KLMDASR and LEBPS, Nankai University（南开大学统计与数据科学学院）；Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）
Arizona State University（亚利桑那州立大学）；Georgia Institute of Technology（佐治亚理工学院）
In point-based sensing systems such as coordinate measuring machines (CMM) and laser ultrasonics where complete sensing is impractical due to the high sensing time and cost, adaptive sensing through a systematic exploration is vital for online inspection and anomaly quantification. Most of the existing sequential sampling methodologies focus on reducing the overall fitting error for the entire sampling space. However, in many anomaly quantification applications, the main goal is to estimate sparse anomalous regions in the pixel-level accurately. In this paper, we develop a novel framework name…
Error-quantified Conformal Inference for Time Series
School of Statistics and Data Science, LPMC, KLMDASR and LEBPS, Nankai University（统计与数据科学学院，LPMC，KLMDASR和LEBPS，南开大学）；Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院，清华大学）
IIT Kanpur（印度理工学院坎普尔分校）；University of Insubria（因苏布里亚大学）；Harvard University（哈佛大学）；QCRI-HBKU（卡塔尔计算研究学院-哈马德·本·哈利法大学）
The estimation of class prevalence, i.e., the fraction of a population that belongs to a certain class, is a very useful tool in data analytics and learning, and finds applications in many domains such as sentiment analysis, epidemiology, etc. For example, in sentiment analysis, the objective is often not to estimate whether a specific text conveys a positive or a negative sentiment, but rather estimate the overall distribution of positive and negative sentiments during an event window. A popular way of performing the above task, often dubbed quantification, is to use supervised learning to tr…
Statistical Inference for Linear Functionals of Online Least-squares SGD when $t \gtrsim d^{1+δ}$
Computer Science Department, Carnegie Mellon University（卡内基梅隆大学计算机科学系）；Department of Statistics, University of California, Davis（加州大学戴维斯分校统计系）；Department of Statistics, University of Chicago（芝加哥大学统计系）
High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization
Department of Statistics, University of California, Irvine（加州大学 Irvine 分校统计系）；Department of Mathematics, University of California, San Diego（加州大学圣地亚哥分校数学系）；Department of Statistics, University of Chicago（芝加哥大学统计系）
Academy of Statistics and Interdisciplinary Sciences, KLATASDS-MOE（统计与交叉科学研究院（KLATASDS-MOE））；East China Normal University（华东师范大学）；London School of Economics and Political Science（伦敦政治经济学院）；Bytedance（字节跳动）
Off-policy evaluation is critical in a number of applications where new policies need to be evaluated offline before online deployment. Most existing methods focus on the expected return, define the target parameter through averaging and provide a point estimator only. In this paper, we develop a novel procedure to produce reliable interval estimators for a target policy's return starting from any initial state. Our proposal accounts for the variability of the return around its expectation, focuses on the individual effect and offers valid uncertainty quantification. Our main idea lies in desi…
University of Technology Sydney（悉尼科技大学）；Southwest Jiaotong University（西南交通大学）；JD Digits（京东数科）
Weather forecasting is usually solved through numerical weather prediction (NWP), which can sometimes lead to unsatisfactory performance due to inappropriate setting of the initial states. In this paper, we design a data-driven method augmented by an effective information fusion mechanism to learn from historical data that incorporates prior knowledge from NWP. We cast the weather forecasting problem as an end-to-end deep learning problem and solve it by proposing a novel negative log-likelihood error (NLE) loss function. A notable advantage of our proposed method is that it simultaneously imp…
Algorithms with Calibrated Machine Learning Predictions
Department of Management Science \& Engineering, Stanford University, Stanford, CA, USA；Department of Computer Science, Stanford University, Stanford, CA, USA
Real-time Adaptation for Condition Monitoring Signal Prediction using Label-aware Neural Processes
Department of Systems & Information Engineering, University of Virginia（系统与信息工程系，弗吉尼亚大学）；Department of Industrial & Operations Engineering, University of Michigan（工业与运营工程系，密歇根大学）
