On the Limit Imbalanced Logistic Regression by Binary Predictors

In this work, we introduce a modified (rescaled) likelihood for imbalanced logistic regression. This new approach makes easier the use of exponential priors and the computation of lasso regularization path. Precisely, we study a limiting behavior for which class imbalance is artificially increased b...

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Bibliographic Details
Published inarXiv.org
Main Author Runge, Vincent
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.04.2018
Subjects
Algorithms
Computer simulation
Inversions
Maximum likelihood estimates
Pharmacology
Regression analysis
Regularization
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Summary:In this work, we introduce a modified (rescaled) likelihood for imbalanced logistic regression. This new approach makes easier the use of exponential priors and the computation of lasso regularization path. Precisely, we study a limiting behavior for which class imbalance is artificially increased by replication of the majority class observations. If some strong overlap conditions are satisfied, the maximum likelihood estimate converges towards a finite value close to the initial one (intercept excluded) as shown by simulations with binary predictors. This solution corresponds to the extremum of a concave function that we refer to as "rescaled" likelihood. In this context, the use of exponential priors has a clear interpretation as a shift on the predictor means for the minority class. Thanks to the simple binary structure, some random designs give analytic path estimators for the lasso regularization problem. An effective approximate path algorithm by piecewise logarithmic functions based on matrix inversions is also presented. This work was motivated by its potential application to spontaneous reports databases in a pharmacovigilance context.
ISSN:2331-8422