{"title":"使用流数据的高维广义线性模型在线推理。","authors":"Lan Luo, Ruijian Han, Yuanyuan Lin, Jian Huang","doi":"10.1214/23-ejs2182","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for realtime estimation and inference. We propose an online debiased lasso method that aligns with the data collection scheme of streaming data. Online debiased lasso differs from offline debiased lasso in two important aspects. First, it updates component-wise confidence intervals of regression coefficients with only summary statistics of the historical data. Second, online debiased lasso adds an additional term to correct approximation errors accumulated throughout the online updating procedure. We show that our proposed online debiased estimators in generalized linear models are asymptotically normal. This result provides a theoretical basis for carrying out real-time interim statistical inference with streaming data. Extensive numerical experiments are conducted to evaluate the performance of our proposed online debiased lasso method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. Furthermore, we illustrate the application of our method with a high-dimensional text dataset.</p>","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11346802/pdf/","citationCount":"0","resultStr":"{\"title\":\"Online inference in high-dimensional generalized linear models with streaming data.\",\"authors\":\"Lan Luo, Ruijian Han, Yuanyuan Lin, Jian Huang\",\"doi\":\"10.1214/23-ejs2182\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for realtime estimation and inference. We propose an online debiased lasso method that aligns with the data collection scheme of streaming data. Online debiased lasso differs from offline debiased lasso in two important aspects. First, it updates component-wise confidence intervals of regression coefficients with only summary statistics of the historical data. Second, online debiased lasso adds an additional term to correct approximation errors accumulated throughout the online updating procedure. We show that our proposed online debiased estimators in generalized linear models are asymptotically normal. This result provides a theoretical basis for carrying out real-time interim statistical inference with streaming data. Extensive numerical experiments are conducted to evaluate the performance of our proposed online debiased lasso method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. Furthermore, we illustrate the application of our method with a high-dimensional text dataset.</p>\",\"PeriodicalId\":49272,\"journal\":{\"name\":\"Electronic Journal of Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11346802/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/23-ejs2182\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/11/28 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/23-ejs2182","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/11/28 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Online inference in high-dimensional generalized linear models with streaming data.
In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for realtime estimation and inference. We propose an online debiased lasso method that aligns with the data collection scheme of streaming data. Online debiased lasso differs from offline debiased lasso in two important aspects. First, it updates component-wise confidence intervals of regression coefficients with only summary statistics of the historical data. Second, online debiased lasso adds an additional term to correct approximation errors accumulated throughout the online updating procedure. We show that our proposed online debiased estimators in generalized linear models are asymptotically normal. This result provides a theoretical basis for carrying out real-time interim statistical inference with streaming data. Extensive numerical experiments are conducted to evaluate the performance of our proposed online debiased lasso method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. Furthermore, we illustrate the application of our method with a high-dimensional text dataset.
期刊介绍:
The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.