{"title":"高度自适应套索估计器","authors":"David Benkeser, Mark van der Laan","doi":"10.1109/DSAA.2016.93","DOIUrl":null,"url":null,"abstract":"<p><p>Estimation of a regression functions is a common goal of statistical learning. We propose a novel nonparametric regression estimator that, in contrast to many existing methods, does not rely on local smoothness assumptions nor is it constructed using local smoothing techniques. Instead, our estimator respects global smoothness constraints by virtue of falling in a class of right-hand continuous functions with left-hand limits that have variation norm bounded by a constant. Using empirical process theory, we establish a fast minimal rate of convergence of our proposed estimator and illustrate how such an estimator can be constructed using standard software. In simulations, we show that the finite-sample performance of our estimator is competitive with other popular machine learning techniques across a variety of data generating mechanisms. We also illustrate competitive performance in real data examples using several publicly available data sets.</p>","PeriodicalId":92122,"journal":{"name":"Proceedings of the ... International Conference on Data Science and Advanced Analytics. IEEE International Conference on Data Science and Advanced Analytics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5662030/pdf/nihms870895.pdf","citationCount":"0","resultStr":"{\"title\":\"The Highly Adaptive Lasso Estimator.\",\"authors\":\"David Benkeser, Mark van der Laan\",\"doi\":\"10.1109/DSAA.2016.93\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Estimation of a regression functions is a common goal of statistical learning. We propose a novel nonparametric regression estimator that, in contrast to many existing methods, does not rely on local smoothness assumptions nor is it constructed using local smoothing techniques. Instead, our estimator respects global smoothness constraints by virtue of falling in a class of right-hand continuous functions with left-hand limits that have variation norm bounded by a constant. Using empirical process theory, we establish a fast minimal rate of convergence of our proposed estimator and illustrate how such an estimator can be constructed using standard software. In simulations, we show that the finite-sample performance of our estimator is competitive with other popular machine learning techniques across a variety of data generating mechanisms. We also illustrate competitive performance in real data examples using several publicly available data sets.</p>\",\"PeriodicalId\":92122,\"journal\":{\"name\":\"Proceedings of the ... International Conference on Data Science and Advanced Analytics. IEEE International Conference on Data Science and Advanced Analytics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5662030/pdf/nihms870895.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the ... International Conference on Data Science and Advanced Analytics. IEEE International Conference on Data Science and Advanced Analytics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DSAA.2016.93\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2016/12/26 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the ... International Conference on Data Science and Advanced Analytics. IEEE International Conference on Data Science and Advanced Analytics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DSAA.2016.93","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2016/12/26 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
Estimation of a regression functions is a common goal of statistical learning. We propose a novel nonparametric regression estimator that, in contrast to many existing methods, does not rely on local smoothness assumptions nor is it constructed using local smoothing techniques. Instead, our estimator respects global smoothness constraints by virtue of falling in a class of right-hand continuous functions with left-hand limits that have variation norm bounded by a constant. Using empirical process theory, we establish a fast minimal rate of convergence of our proposed estimator and illustrate how such an estimator can be constructed using standard software. In simulations, we show that the finite-sample performance of our estimator is competitive with other popular machine learning techniques across a variety of data generating mechanisms. We also illustrate competitive performance in real data examples using several publicly available data sets.