Optimizing multivariate adaptive regression splines (MARS) with coordinate descent to accurately select the best model for house price prediction

Multivariate Adaptive Regression Splines (MARS) have proved to be a powerful tool for modeling non-parametric regression analysis problems and for selecting the model in multi-dimensional data. A major challenge lies in model over-fitting and under-fitting on multi-dimensional data. Applying optimization methods to design and select the model can reduce the over-fitting and under-fitting in MARS modeling. Particularly, information-based model selection criteria have shown to be effective for modeling in MARS. This study proposes a model selection method in MARS using coordinate descent (CD-MARS) that can accurately select the best model. We have integrated coordinate descent (CD) features in the information-based model selection and evaluation criteria formulation. In this formulation, the CD was used as a penalty term to the negative log-likelihood in information-based model selection and evaluation criteria. To test the model, the study generated a dataset for testing the model and then the study applied house prices dataset that is publicly available online to evaluate the model’s success. The dataset have the variables that do and do not add to the dependent variable. We measure the performance of the proposed model using mean squared error (MSE), the Coefficient of Determination (Rsquared) and Mean absolute error. The results show that, the model’s mean squared error (MSE) was small compared to that of MARS. Additionally, the CD-MARS model scored the Rsquared of 0.931 (93.1%) whereas the traditional MARS score was 0.8952 (89.52%). Thus, the proposed model improves the traditional MARS by 3.58%. This indicates that the proposed model fits well the data compared to the traditional MARS and can produce good generalizability in MARS modeling.