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Sufficient dimension reduction via squared-loss mutual information estimation.

Taiji Suzuki1, Masashi Sugiyama

  • 1Department of Mathematical Informatics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan. t-suzuki@mist.i.u-tokyo.ac.jp

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This study introduces a new sufficient dimension reduction technique using squared-loss mutual information. The method effectively identifies essential input features for supervised learning without assuming data distribution structures.

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Area of Science:

  • Machine Learning
  • Statistics
  • Data Science

Background:

  • Sufficient dimension reduction aims to find a low-dimensional subspace capturing all information about output values from input features.
  • Existing methods often require assumptions about data distributions.

Purpose of the Study:

  • Propose a novel sufficient dimension reduction method using squared-loss mutual information.
  • Develop a flexible approach that does not require prespecified structures on underlying distributions.

Main Methods:

  • Utilized a squared-loss variant of mutual information as a dependency measure.
  • Applied a density-ratio estimator for approximating squared-loss mutual information, formulated as a minimum contrast estimator.
  • Developed a natural gradient algorithm on the Grassmann manifold for efficient sufficient subspace search.

Main Results:

  • The proposed method demonstrated favorable comparisons with existing dimension reduction approaches in numerical experiments.
  • Asymptotic bias and convergence rates for parametric and nonparametric models were elucidated.
  • The method's effectiveness was validated on artificial and benchmark datasets.

Conclusions:

  • The novel method offers a robust and efficient approach to sufficient dimension reduction in supervised learning.
  • The technique's flexibility and performance make it a valuable contribution to the field.