Bayesian Optimization for Parameter of Discrete Weibull Regression
Adesina, Olumide Sunday *
Department of Mathematical Sciences, Redeemer’s University, Ede, Osun State, Nigeria.
Onanaye, Adeniyi Samson
Department of Mathematical Sciences, Redeemer’s University, Ede, Osun State, Nigeria.
Okewole, Dorcas Modupe
Department of Mathematical Sciences, Redeemer’s University, Ede, Osun State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study aim at optimizing the parameter θ of Discrete Weibull (DW) regression obtained by maximizing the likelihood function. Also to examine the strength of three acquisition functions used in solving auxiliary optimization problem. The choice of Discrete Weibull regression model among other models for fitting count data is due to its robustness in fitting count data. Count data of hypertensive patients visits to the doctor was obtained at Medicare Clinics Ota, Nigeria, and was used for the analysis. First, parameter θ and β were obtained using Metropolis Hasting Monte Carlo Markov Chain (MCMC) algorithm. Then Bayesian optimization was used to optimize the parameter the likelihood function of DW regression, given β to examine what θ would be, and making the likelihood function of DW the objective function. Upper confidence bound (UCB), Expectation of Improvement (EI), and probability of Improvement (PI) were used as acquisition functions. Results showed that fitting Bayesian DW regression to the data, there is significant relationship between the response variable, β and the covariate. On implementing Bayesian optimization to obtain parameter new parameter θ of discrete Weibull regression using the known β, the results showed promising applicability of the technique to the model, and found that EI fits the data better relative to PI and UCB in terms of accuracy and speed.
Keywords: Machine learning, Bayesian optimization, Gaussian process, acquisition function, discrete weibull regression, medicine, count data.