主题报告专场（二）| 首届机器学习与统计会议

摘要：This paper is devoted to studying the semi-supervised sparse statistical inference in a distributed setup. An efficient multi-round distributed debiased estimator, which integrates both labeled and unlabeled data, is developed. We will show that the additional unlabeled data helps to improve the statistical rate of each round of iteration. Our approach offers tailored debiasing methods for $M$-estimation and generalized linear model according to the specific form of the loss function. Our method also applies to a non-smooth loss like absolute deviation loss. Furthermore, our algorithm is computationally efficient since it requires only one estimation of a high-dimensional inverse covariance matrix.  We demonstrate the effectiveness of our method by presenting simulation studies and real data applications that highlight the benefits of incorporating unlabeled data.

简介：毛晓军，上海交通大学长聘教轨副教授。他的研究领域包括分布式统计推断，推荐系统和高维数据分析。主要研究成果已经发表于JASA, JMLR, IEEE TSP, ICML, WWW,《管理世界》等顶级期刊及会议上。入选2023年度上海市青年科技启明星计划，2019年度上海市青年科技英才扬帆计划。目前是国际重要学术期刊Journal of Multivariate Analysis的Early Career Advisory Board成员。

摘要：We study the change point detection problem for high-dimensional linear regression models. In this work, we propose a novel tail-adaptive approach for simultaneous change point testing and estimation. The method is built on a new loss function which is a weighted combination between the composite quantile and least squared losses, allowing us to borrow information of the possible change points from both the conditional mean and quantiles. For the change point testing, based on the adjusted L2-norm aggregation of a weighted score CUSUM process, we pro-pose a family of individual testing statistics with different weights to account for the unknown tail structures. Through a combination of the individual tests, a tail-adaptive test is further constructed that is powerful for sparse alternatives of regression coefficients’ changes under various tail structures. For the change point estimation, a family of argmax-based individual estimators is proposed once a change point is detected. In theory, for both individual and tail-adaptive tests, bootstrap procedures are proposed to approximate their limiting null distributions. Under some mild conditions, we justify the validity of the new tests in terms of size and power under the high-dimensional setup. The corresponding change point estimators are shown to be rate optimal up to a logarithm factor.

简介：刚博文 2014年本科毕业于麦吉尔大学，2020年博士毕业于南加州大学，现为复旦大学统计与数据科学系助理教授。研究方向为多重假设检验，高维统计推断。论文发表于JASA，Statistica Sinica 等期刊上。

摘要：We consider a high-dimensional dynamic pricing problem under non-stationarity, where a firm sells products to T sequentially arriving consumers that behave according to an unknown demand model with potential changes at unknown times. The demand model is assumed to be a high-dimensional generalized linear model (GLM), allowing for a feature vector in R^d that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential change-points. To tackle such a problem, we first design a novel penalized likelihood based online change-point detection algorithm for high-dimensional GLMs, which is the first algorithm in the change-point literature that achieves optimal minimax localization error rate for high-dimensional GLMs. A change-point detection assisted dynamic pricing (CPDP) policy is further proposed and achieves a near-optimal regret of order O(slog(Td)\sqrt{MT}), where s is the sparsity level and M is the number of change-points. This regret is accompanied with a minimax lower bound, demonstrating the optimality of CPDP (up to logarithmic factors). In particular, the optimality with respect to M is seen for the first time in the dynamic pricing literature, and is achieved via a novel accelerated exploration mechanism. Extensive simulation experiments and a real data application on online lending illustrate the efficiency of the proposed policy and the importance and practical value of handling non-stationarity in dynamic pricing.

简介：蒋斐宇是复旦大学管理学院统计与数据科学系青年副研究员，他的主要研究方向为时间序列分析、变点分析、金融计量等，研究成果发表于JRSSB，JOE，Sinica等期刊，并受到上海市扬帆计划和国家自然科学基金青年科学基金的资助。他获得2023 IMS New Researcher Travel Award和ICSA China Junior Researcher Award。