Adaptive Convex Clustering of Generalized Linear Models With Application in Purchase Likelihood Prediction

In the pricing of customized products, it is challenging to accurately predict the purchase likelihood of potential clients for each personalized request. The heterogeneity of customers and their responses to the personalized products leads to very different purchase behavior. Thus, it is often not appropriate to use a single model to analyze all the pricing data. There is a great need to construct distinctive models for different data segments. In this work, we propose an adaptive convex clustering method to perform data segmentation and model fitting simultaneously for generalized linear models. The proposed method segments data points using the fused penalty to account for the similarity in model structures. It ensures that the data points sharing the same model structure are grouped into the same segment. Accordingly, we develop an efficient algorithm for parameter estimation and study its consistency properties in estimation and clustering. The performance of our approach is evaluated by both numerical examples and case studies of real business data.