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Bias/Variance Decompositions for Likelihood-Based Estimators

Heskes1

  • 1University of Nijmegen, Foundation for Neural Networks, Nijmegen, NL, Geert Grooteplein 21, 6525 EZ. tom@mbfys.kun.nl

Neural Computation
|August 11, 1998
PubMed
Summary

A novel decomposition method is introduced for error measures, extending beyond mean-squared error. This approach simplifies the analysis of various error metrics using probability models and Kullback-Leibler divergence.

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Area of Science:

  • Statistics
  • Information Theory
  • Machine Learning

Background:

  • The bias/variance decomposition is a fundamental concept for analyzing mean-squared error in statistical modeling.
  • Understanding error sources is crucial for improving model performance and reliability.

Purpose of the Study:

  • To derive a generalizable decomposition for various error measures.
  • To extend the principles of bias/variance analysis to a broader class of metrics.

Main Methods:

  • The study derives a decomposition applicable to error measures reducible from Kullback-Leibler divergence or log-likelihood.
  • It utilizes appropriate probability models to establish the decomposition.

Main Results:

  • A simple, general decomposition is presented for error measures derived from Kullback-Leibler divergence or log-likelihood.

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  • This decomposition offers a unified framework for analyzing different error metrics.

    • Conclusions:

    • The derived decomposition provides a more versatile tool for error analysis in statistical and machine learning models.
    • This work simplifies the understanding of error components for a wider range of error measures.