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Multiobjective optimization for model selection in kernel methods in regression.

Di You, Carlos Fabian Benitez-Quiroz, Aleix M Martinez

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    |October 8, 2014
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    Summary
    This summary is machine-generated.

    This study introduces a new kernel smoothing criterion to balance model complexity and estimation error in regression. The method optimizes kernel parameters, reducing bias-variance tradeoff for improved function learning.

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    Area of Science:

    • Machine Learning
    • Statistical Modeling
    • Computer Vision

    Background:

    • Regression is crucial for learning functions from data.
    • Kernel methods enable nonlinear function estimation but face bias-variance tradeoffs and parameter selection challenges.

    Purpose of the Study:

    • To address the bias-variance tradeoff in kernel regression.
    • To develop a criterion for selecting optimal kernel parameters.
    • To improve the accuracy of learned functions while controlling model complexity.

    Main Methods:

    • Derivation of a novel smoothing kernel criterion measuring function roughness as model complexity.
    • Application of multiobjective optimization to derive a kernel parameter selection criterion.
    • Balancing model fit and complexity for optimal function estimation.

    Main Results:

    • The proposed approach effectively manages the bias-variance tradeoff.
    • Optimized kernel parameters lead to better function approximation.
    • Experimental evaluations show reduced estimation errors compared to existing methods.

    Conclusions:

    • The new kernel criterion and optimization approach offer a robust solution for kernel regression.
    • This method enhances model performance across various machine learning, pattern recognition, and computer vision tasks.
    • The findings contribute to more accurate and reliable function learning in complex datasets.