Novel Prediction Techniques Based on Clusterwise Linear Regression
This work addresses a specific bottleneck in applying CLR for predictive modeling, offering incremental improvements for regression tasks in domains like health insurance.
The paper tackles the problem of using Clusterwise Linear Regression (CLR) for prediction on unseen test points by proposing two novel approaches: predictive CLR, which uses a classification model to predict cluster labels, and constrained CLR, which applies user-specified constraints for label assignment. The results show that both methods significantly improve over existing CLR-based regression, with predictive CLR outperforming linear regression and random forest and matching support vector regression on UCI datasets, while constrained CLR achieves the best performance on a health insurance dataset with only about 20 times increased computational time over linear regression.
In this paper we explore different regression models based on Clusterwise Linear Regression (CLR). CLR aims to find the partition of the data into $k$ clusters, such that linear regressions fitted to each of the clusters minimize overall mean squared error on the whole data. The main obstacle preventing to use found regression models for prediction on the unseen test points is the absence of a reasonable way to obtain CLR cluster labels when the values of target variable are unknown. In this paper we propose two novel approaches on how to solve this problem. The first approach, predictive CLR builds a separate classification model to predict test CLR labels. The second approach, constrained CLR utilizes a set of user-specified constraints that enforce certain points to go to the same clusters. Assuming the constraint values are known for the test points, they can be directly used to assign CLR labels. We evaluate these two approaches on three UCI ML datasets as well as on a large corpus of health insurance claims. We show that both of the proposed algorithms significantly improve over the known CLR-based regression methods. Moreover, predictive CLR consistently outperforms linear regression and random forest, and shows comparable performance to support vector regression on UCI ML datasets. The constrained CLR approach achieves the best performance on the health insurance dataset, while enjoying only $\approx 20$ times increased computational time over linear regression.