Evolutionary algorithms applied to likelihood function maximization during poisson, logistic, and Cox proportional hazards regression analysis

Abstract

Metaheuristics based on genetic algorithms (GA), covariance matrix self-adaptation evolution strategies (CMSA-ES), particle swarm optimization (PSO), and ant colony optimization (ACO) were used for minimizing deviance for Poisson regression and maximizing the log-likelihood function for logistic regression and Cox proportional hazards regression. We observed that, in terms of regression coefficients, CMSA-ES and PSO metaheuristics were able to obtain solutions that were in better agreement with Newton-Raphson (NR) when compared with GA and ACO. The rate of convergence to the NR solution was also faster for CMSA-ES and PSO when compared with ACO and GA. Overall, CMSA-ES was the best-performing method used. Key factors which strongly influence performance are multicollinearity, shape of the log-likelihood gradient, and positive definiteness of the Hessian matrix.