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A Tactile Automated Passive-Finger Stimulator (TAPS)

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Learning curves for Gaussian process regression: approximations and bounds.

Peter Sollich¹, Anason Halees

¹Department of Mathematics, King's College London, London WC2R 2LS, UK. peter.sollich@kcl.ac.uk

Neural Computation

|May 22, 2002

Summary

This summary is machine-generated.

This study introduces novel approximation schemes for calculating the generalization performance of Gaussian processes in regression. These new methods offer improved accuracy for learning curves across various input dimensions.

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Area of Science:

Machine Learning
Statistical Learning Theory
Gaussian Processes

Background:

Gaussian processes are powerful non-parametric models for regression tasks.
Calculating learning curves, which represent average generalization performance, is crucial for understanding model behavior.
Existing methods for approximating learning curves have limitations in accuracy and applicability.

Purpose of the Study:

To develop accurate approximation schemes for Gaussian process learning curves.
To analyze the conditions under which these approximations become exact.
To compare the performance of new approximations with existing bounds.

Main Methods:

Derivation of approximation schemes based on the eigenvalue decomposition of the covariance function.
Analysis of generalization error expressions.
Comparison with established bounds on learning curves.
Investigation of potential improvements to the derived approximations.

Main Results:

New approximation schemes for Gaussian process learning curves are derived.
These approximations are shown to be substantially more accurate than existing bounds.
The approximations are applicable to any input space dimension.
An exactly solvable learning scenario reveals fundamental limits on approximation quality.

Conclusions:

The proposed approximation schemes provide a significant improvement for estimating Gaussian process generalization performance.
The findings offer deeper insights into the relationship between covariance function properties and learning curve behavior.
Understanding the limits of approximations is essential for reliable model assessment.