Author(s)

Behrouz Madahian¹, Usef Faghihi²

¹Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA.
²Department of Computing and Technology, Cameron University, Lawton, OK, USA.

Nowadays a common problem when processing data sets with the large number of covariates compared to small sample sizes (fat data sets) is to estimate the parameters associated with each covariate. When the number of covariates far exceeds the number of samples, the parameter estimation becomes very difficult. Researchers in many fields such as text categorization deal with the burden of finding and estimating important covariates without overfitting the model. In this study, we developed a Sparse Probit Bayesian Model (SPBM) based on Gibbs sampling which utilizes double exponentials prior to induce shrinkage and reduce the number of covariates in the model. The method was evaluated using ten domains such as mathematics, the corpuses of which were downloaded from Wikipedia. From the downloaded corpuses, we created the TFIDF matrix corresponding to all domains and divided the whole data set randomly into training and testing groups of size 300. To make the model more robust we performed 50 re-samplings on selection of training and test groups. The model was implemented in R and the Gibbs sampler ran for 60 k iterations and the first 20 k was discarded as burn in. We performed classification on training and test groups by calculating P (y_i = 1) and according to [1] [2] the threshold of 0.5 was used as decision rule. Our model’s performance was compared to Support Vector Machines (SVM) using average sensitivity and specificity across 50 runs. The SPBM achieved high classification accuracy and outperformed SVM in almost all domains analyzed.

Bayesian LASSO, Shrinkage, Parameter Estimation, Generalized Linear Models, Machine Learning

Madahian, B. and Faghihi, U. (2014) A Fully Bayesian Sparse Probit Model for Text Categorization. Open Journal of Statistics, 4, 611-619. doi: 10.4236/ojs.2014.48057.