Maximum Likelihood Logistic Regression Using Metaheuristics

Maximum likelihood-based logistic regression coefficients and fitness growth rates for several metaheuristic techniques were compared with results from Newton-Raphson iteration. Metaheuristics included genetic algorithms (GA), covariance matrix self-adaptation evolution strategies (CMSA-ES), particle swarm optimization (PSO), and ant colony optimization (ACO). Results indicate that fitness growth rates for GA were greatly inferior to fitness values for NR, CMSA-ES, PSO, and ACO. For the data sets considered, coefficients determined using CMSA-ES were identical to coefficients generated with NR, while coefficients from PSO- and ACO-based logistic regression were only slightly different. For the ionosphere data with a larger number of features, ACO likelihood fitness growth was slower when compared with CMSA-ES and PSO. Because this was an early investigation of metaheuristics in logistic regression, future studies employing similar metaheuristics should focus on investigation of global vs. local minima.