Mortality Rate Forcasting Using Compositionally-Warped Gaussian Processes Equipped with Grid Search
The standard Gaussian Process (GP) is often commended for its capability of depicting the model's uncertainty and imposing prior knowledge on the dataset with judiciously chosen kernels. Despite its flexibilities, the standard GP is hamstrung by its inability to accurately model non-Gaussian data. To overcome this deficiency, we tweak the standard GP by a novel warping technique called the Compositionally-Warped Gaussian Process (CWGP) to fit non-Gaussian data. On the contrary, we can also perform an inverse warping onto non-Gaussian data and transform it back into a GP. This is made efficiently owing to the fact that the CWGP is solely comprised of combinations of explicitly differentiable and invertible functions. We further adopt the idea of Grid Search to find the best combination among the architecture of the CWGP, the mean function, and the kernel based on a given metric, in our case, the Root Mean Squared Error (RMSE). We then unveil the potential of the CWGP by incorporating it along with Grid Search to aid GP in forecasting the mortality rate of the Japanese population using real-world data. Our results conclude that it not only out-performs the standard GP but is also superior than the conventional Lee-Carter Model.