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A greedy regression algorithm with coarse weights offers novel advantages.

Clark D Jeffries1, John R Ford2, Jeffrey L Tilson3

  • 1Renaissance Computing Institute, University of North Carolina, Chapel Hill, NC, USA. clark_jeffries@med.unc.edu.

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Summary

We introduce a novel Coarse Approximation Linear Function (CALF) for building simple yet powerful predictive models. CALF uses +1 or -1 weights to efficiently select key predictors, improving model stability and handling collinearity.

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • Regularized regression is a standard method for identifying predictors of outcomes.
  • Existing methods can be sensitive to data changes and struggle with collinear variables.

Purpose of the Study:

  • To present a novel Coarse Approximation Linear Function (CALF) for predictor selection and predictive modeling.
  • To develop a method that creates simple, powerful models with robust predictor weighting.

Main Methods:

  • CALF is a linear regression strategy applied to normalized data.
  • It utilizes non-zero weights of +1 or -1.
  • Optimization targets qualitative metrics like p-value, AUC, or Pearson correlation.

Main Results:

  • CALF effectively selects important predictors and builds simple, powerful models.
  • The method demonstrates stability, with weights largely unaffected by small data changes.
  • CALF robustly handles collinear or nearly collinear predictors by selecting at most one.

Conclusions:

  • CALF offers a frugal approach to predictor selection and predictive modeling.
  • Its use of fixed weights and handling of collinearity enhance model interpretability and stability.
  • CALF provides a valuable alternative for risk prediction modeling, especially when qualitative metrics are prioritized.