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Splitting Gaussian processes for computationally-efficient regression.

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  • 1Department of Industrial and Systems Engineering, University of Washington, Seattle, WA, United States of America.

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Summary

This study introduces a novel localized Gaussian process regression algorithm. It efficiently handles large datasets by partitioning input space, offering superior time and space complexity for scalable machine learning.

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Area of Science:

  • Machine Learning
  • Statistical Modeling

Background:

  • Gaussian processes (GPs) are powerful kernel methods for regression.
  • Standard GPs exhibit cubic time complexity, limiting scalability with large datasets.
  • Efficient updating of GP models is crucial for practical applications.

Purpose of the Study:

  • To develop a scalable Gaussian process regression algorithm.
  • To address the computational limitations of standard GP models.
  • To introduce a localized Gaussian process regression model with improved efficiency.

Main Methods:

  • Propose an algorithm for sequential input space partitioning.
  • Fit localized Gaussian processes to disjoint regions.
  • Achieve a model with tightly bounded update time complexity.

Main Results:

  • The algorithm demonstrates superior time and space complexity compared to existing methods.
  • The localized GP model achieves linear memory complexity.
  • Theoretical continuity properties of the model are established.

Conclusions:

  • The proposed localized Gaussian process regression model offers significant scalability improvements.
  • The algorithm enables efficient model updating with bounded time complexity.
  • The model's efficacy is validated on multi-dimensional regression tasks.