Online Sufficient Dimension Reduction Through Sliced Inverse Regression

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.

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Work Title Online Sufficient Dimension Reduction Through Sliced Inverse Regression
Access
Open Access
Creators
  1. Zhanrui Cai
  2. Runze Li
  3. Liping Zhu
Keyword
  1. Dimension reduction
  2. Online learning
  3. Perturbation
  4. Singular value decomposition
  5. Sliced inverse regression
  6. Gradient descent
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Journal of Machine Learning Research
Publication Date 2020
Related URLs
Deposited July 19, 2022

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Version 1
published

  • Created
  • Added 18-567.pdf
  • Added Creator Zhanrui Cai
  • Added Creator Runze Li
  • Added Creator Liping Zhu
  • Published
  • Updated Keyword, Related URLs, Publication Date Show Changes
    Keyword
    • Dimension reduction, Online learning, Perturbation, Singular value decomposition, Sliced inverse regression, Gradient descent
    Related URLs
    • https://www.jmlr.org/papers/v21/18-567.html
    Publication Date
    • 2020-01-01
    • 2020
  • Updated