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Predictive approaches for choosing hyperparameters in gaussian processes.

S Sundararajan1, S S Keerthi

  • 1Department of Computer Science and Automation, India Institute of Science, Bangalore-560012, India.

Neural Computation
|May 22, 2001
PubMed
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This study introduces predictive methods for Gaussian process hyperparameter tuning, outperforming traditional techniques. These new approaches, based on predictive sample reuse (PSR) and cross-validation (CV), offer competitive performance in regression modeling.

Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Computational Statistics

Background:

  • Gaussian processes are versatile regression models defined by parameterized mean and covariance functions.
  • Hyperparameter selection in Gaussian processes typically relies on maximum likelihood or maximum a posteriori estimation.
  • Existing methods for hyperparameter tuning may not always yield optimal predictive performance.

Purpose of the Study:

  • To propose and investigate novel predictive approaches for Gaussian process hyperparameter selection.
  • To compare the performance of these new predictive methods against standard techniques.
  • To explore the relationship between predictive methods and generalized cross-validation (GCV).

Main Methods:

  • Utilizing Geisser's predictive sample reuse (PSR) methodology.

Related Experiment Videos

  • Applying Stone's cross-validation (CV) methodology.
  • Deriving and analyzing Geisser's surrogate predictive probability (GPP) and Geisser's predictive mean square error (GPE).

    • Main Results:

    • The proposed predictive approaches, including GPP and GPE, demonstrate strong competitiveness with existing hyperparameter selection methods.
    • A comparative study was conducted, evaluating performance across various problems.
    • The generalized cross-validation (GCV) was approximated and its connection to GPP and GPE was established.

    Conclusions:

    • Predictive approaches offer a viable and effective alternative for hyperparameter tuning in Gaussian processes.
    • These methods show promise for improving the performance of Gaussian process regression models.
    • The findings suggest that predictive criteria can be as effective, if not more so, than likelihood-based methods.