Bayesian Optimization for Parameter of Discrete Weibull Regression
Loading...
Date
2020-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of Advances in Mathematics and Computer Science
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.
Description
Keywords
Machine learning, Bayesian optimization, Gaussian process, Acquisition function, Discrete weibull regression, Medicine, Count data