Predicting Bankruptcy Risk: A Gaussian Process Classifciation Model

Abstract: This thesis develops a Gaussian processes model for bankruptcy risk classification and prediction in a Bayesian framework. Gaussian processes and linear logistic models are discriminative methods used for classification and prediction purposes. The Gaussian processes model is a much more flexible model than the linear logistic model with smoothness encoded in the kernel with the potential to improve the modeling of the highly nonlinear relationships between accounting ratios and bankruptcy risk. We compare the linear logistic regression with the Gaussian process classification model in the context of bankruptcy prediction. The posterior distributions of the GPs are non-Gaussian, and we investigate the effectiveness of the Laplace approximation and the expectation propagation approximation across several different kernels for the Gaussian process. The approximate methods are compared to the gold standard of Markov Chain Monte Carlo (MCMC) sampling from the posterior. The dataset is an unbalanced panel consisting of 21846 yearly observations for about 2000 corporate firms in Sweden recorded between 1991−2008. We used 5000 observations to train the models and the rest for evaluating the predictions. We find that the choice of covariance kernel affects the GP model’s performance and we find support for the squared exponential covariance function (SEXP) as an optimal kernel. The empirical evidence suggests that a multivariate Gaussian processes classifier with squared exponential kernel can effectively improve bankruptcy risk prediction with high accuracy (90.19 percent) compared to the linear logistic model (83.25 percent).