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Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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An R-Based Landscape Validation of a Competing Risk Model
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Published on: September 16, 2022

Criterion for evaluating the predictive ability of nonlinear regression models without cross-validation.

Hiromasa Kaneko1, Kimito Funatsu

  • 1Department of Chemical System Engineering, The University of Tokyo , 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Journal of Chemical Information and Modeling
|August 27, 2013
PubMed
Summary

New performance criteria for nonlinear regression models eliminate the need for cross-validation. These metrics effectively evaluate predictive ability, especially for big data applications.

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Area of Science:

  • Statistics
  • Computational Chemistry
  • Data Science

Background:

  • Cross-validation is a standard technique for evaluating predictive models.
  • However, cross-validation is computationally intensive and often infeasible for large datasets.
  • Updating regression models necessitates alternative methods for performance evaluation.

Purpose of the Study:

  • To propose novel predictive performance criteria for nonlinear regression models.
  • To offer an alternative to cross-validation, particularly for updated models and big data.
  • To enable robust evaluation of model predictive capabilities.

Main Methods:

  • Development of new performance criteria: determination coefficient and root-mean-square error.
  • Application of criteria to midpoints between k-nearest-neighbor data points.
  • Validation using numerical simulations and quantitative structure-activity relationship (QSAR) data.

Main Results:

  • The proposed criteria effectively quantify the predictive ability of nonlinear regression models.
  • These criteria are applicable even after models have been updated.
  • The method demonstrates efficacy in big data scenarios where cross-validation is impractical.

Conclusions:

  • The proposed performance criteria offer a viable alternative to cross-validation.
  • These metrics are particularly valuable for evaluating updated nonlinear regression models.
  • The approach facilitates accurate assessment of predictive performance in big data contexts.