文献详情
Online Sufficient Dimension Reduction Through Sliced Inverse Regression
文献类型：期刊
通讯作者：Cai, ZR (reprint author), Penn State Univ, Dept Stat, University Pk, PA 16802 USA.
期刊名称：JOURNAL OF MACHINE LEARNING RESEARCH
年：2020
卷：21
ISSN：1532-4435
关键词：Dimension reduction; online learning; perturbation; singular value decomposition; sliced inverse regression; gradient descent
所属部门：统计与大数据研究院
摘要：Sliced inverse regression is an effective paradigm that achieves the goal of dimension reduction through replacing high dimensional covariates with a small number of linear combinations. It does not impose parametric assumptions on the dependence structure. More importantly, such a reduction of dimension is sufficient in that it does not cause loss of information. In this paper, we adapt the stationary sliced inverse regression to cope with the rapidly changing environments. We propose to implem ...More
Sliced inverse regression is an effective paradigm that achieves the goal of dimension reduction through replacing high dimensional covariates with a small number of linear combinations. It does not impose parametric assumptions on the dependence structure. More importantly, such a reduction of dimension is sufficient in that it does not cause loss of information. In this paper, we adapt the stationary sliced inverse regression to cope with the rapidly changing environments. We propose to implement sliced inverse regression in an online fashion. This online learner consists of two steps. In the first step we construct an online estimate for the kernel matrix; in the second step we propose two online algorithms, one is motivated by the perturbation method and the other is originated from the gradient descent optimization, to perform online singular value decomposition. The theoretical properties of this online learner are established. We demonstrate the numerical performance of this online learner through simulations and real world applications. All numerical studies confirm that this online learner performs as well as the batch learner. ...Hide

百度学术：Online Sufficient Dimension Reduction Through Sliced Inverse Regression
语言：外文
基金：NSFNational Science Foundation (NSF) [DMS 1820702]; Beijing Natural Science FoundationBeijing Natural Science Foundation [Z190002]; National Natural Science Foundation of ChinaNational Natural Science Foundation of China [11731011, 11931014, 11690015]
作者其他论文



MODEL-FREE FEATURE SCREENING FOR ULTRAHIGH DIMENSIONAL DATATHROUGH A MODIFIED BLUM-KIEFER-ROSENBLATT CORRELATION.Zhou, Yeqing, Zhu, Liping,.STATISTICA SINICA. 2018, 28(3), 1351-1370.
A ROBUST AND EFFICIENT APPROACH TO CAUSAL INFERENCE BASED ON SPARSE SUFFICIENT DIMENSION REDUCTION.Ma, Shujie, Zhu, Liping, Zhang, Zhiwei, et al. .ANNALS OF STATISTICS. 2019, 47(3), 1505-1535.
SEMIPARAMETRIC ESTIMATION AND INFERENCE OF VARIANCE FUNCTION WITH LARGE DIMENSIONAL COVARIATES.Ma, Yanyuan, Zhu, Liping,.STATISTICA SINICA. 2019, 29(2), 567-588.
NONLINEAR INTERACTION DETECTION THROUGH MODEL-BASED SUFFICIENT DIMENSION REDUCTION.Fan, Guoliang, Zhu, Liping, Ma, Shujie,.STATISTICA SINICA. 2019, 29(2), 917-937.
A ROBUST AND EFFICIENT APPROACH TO CAUSAL INFERENCE BASED ON SPARSE SUFFICIENT DIMENSION REDUCTION.Ma, Shujie, Zhu, Liping, Zhang, Zhiwei, et al. .ANNALS OF STATISTICS. 2019, 47(3), 1505-1535.