A greedy regression algorithm with coarse weights offers novel advantages

Regularized regression analysis is a mature analytic approach to identify weighted sums of variables predicting outcomes. We present a novel Coarse Approximation Linear Function (CALF) to frugally select important predictors and build simple but powerful predictive models. CALF is a linear regressio...

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Bibliographic Details
Published in:Scientific reports Vol. 12; no. 1; pp. 5440 - 14
Main Authors: Jeffries, Clark D., Ford, John R., Tilson, Jeffrey L., Perkins, Diana O., Bost, Darius M., Filer, Dayne L., Wilhelmsen, Kirk C.
Format: Journal Article
Language:English
Published: London Nature Publishing Group UK 31.03.2022
Nature Publishing Group
Nature Portfolio
Subjects:
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Algorithms
Approximation
Area Under Curve
Humanities and Social Sciences
Humans
Linear Models
multidisciplinary
Prediction models
Regression analysis
ROC Curve
Science
Science (multidisciplinary)
ISSN:2045-2322, 2045-2322
Online Access:Get full text
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Summary:Regularized regression analysis is a mature analytic approach to identify weighted sums of variables predicting outcomes. We present a novel Coarse Approximation Linear Function (CALF) to frugally select important predictors and build simple but powerful predictive models. CALF is a linear regression strategy applied to normalized data that uses nonzero weights + 1 or − 1. Qualitative (linearly invariant) metrics to be optimized can be (for binary response) Welch (Student) t-test p-value or area under curve (AUC) of receiver operating characteristic, or (for real response) Pearson correlation. Predictor weighting is critically important when developing risk prediction models. While counterintuitive, it is a fact that qualitative metrics can favor CALF with ± 1 weights over algorithms producing real number weights. Moreover, while regression methods may be expected to change most or all weight values upon even small changes in input data (e.g., discarding a single subject of hundreds) CALF weights generally do not so change. Similarly, some regression methods applied to collinear or nearly collinear variables yield unpredictable magnitude or the direction (in p-space) of the weights as a vector. In contrast, with CALF if some predictors are linearly dependent or nearly so, CALF simply chooses at most one (the most informative, if any) and ignores the others, thus avoiding the inclusion of two or more collinear variables in the model.
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ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-022-09415-2