Optimizing logistic regression coefficients for discrimination and calibration using estimation of distribution algorithms |
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Authors: | V Robles C Bielza P Larrañaga S González L Ohno-Machado |
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Institution: | (1) Departamento de Arquitectura y Tecnologia de Sistemas Informáticos, Universidad Politecnica de Madrid, Madrid, Spain;(2) Departamento de Inteligencia Artificial, Universidad Politecnica de Madrid, Madrid, Spain;(3) Division of Health Science and Technology, Harvard University and MIT, Boston, USA |
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Abstract: | Logistic regression is a simple and efficient supervised learning algorithm for estimating the probability of an outcome or
class variable. In spite of its simplicity, logistic regression has shown very good performance in a range of fields. It is
widely accepted in a range of fields because its results are easy to interpret. Fitting the logistic regression model usually
involves using the principle of maximum likelihood. The Newton–Raphson algorithm is the most common numerical approach for
obtaining the coefficients maximizing the likelihood of the data.
This work presents a novel approach for fitting the logistic regression model based on estimation of distribution algorithms
(EDAs), a tool for evolutionary computation. EDAs are suitable not only for maximizing the likelihood, but also for maximizing
the area under the receiver operating characteristic curve (AUC).
Thus, we tackle the logistic regression problem from a double perspective: likelihood-based to calibrate the model and AUC-based
to discriminate between the different classes. Under these two objectives of calibration and discrimination, the Pareto front
can be obtained in our EDA framework. These fronts are compared with those yielded by a multiobjective EDA recently introduced
in the literature.
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Keywords: | Logistic regression Evolutionary algorithms Estimation of distribution algorithms Calibration and discrimination |
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