Group Regularization for Zero-Inflated Count Regression Models

• Activity Number: 129 - High-Dimensional Data and Inference
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Shrabanti Chowdhury* and Saptarshi Chatterjee and Himel Mallick and Prithish Banerjee and Broti Garai
• Companies: Icahn School of Medicine at Mount Sinai and Northern Illinois University and Merck & Co., Inc. and JP Morgan Chase & Co and NBCUniversal
• Keywords: Zero-inflated Outcome; Group regularization; Bi-level variable selection; Least square approximation; German healthcare; Insurance ratemaking

Abstract

In many biomedical applications, covariates are naturally grouped, with variables in the same group being systematically related or statistically correlated. Under such settings, variable selection must be conducted at both group and individual variable levels. Motivated by the widespread availability of zero-inflated count outcomes and grouped covariates in many practical applications, we consider group regularization for zero-inflated regression models. Using a least squares approximation of the mixture likelihood and a variety of group-wise penalties on the coefficients, we propose a unified algorithm (Google: Group Regularization for Zero-inflated Count Regression Models) to efficiently compute the entire regularization path of the estimators. We investigate the finite sample performance of these methods through extensive simulation experiments and the analysis of a German Healthcare demand data set and an auto insurance claim data set from SAS Enterprise Miner database. Finally, we derive theoretical properties of these methods under reasonable assumptions, which further provide deeper insight into the asymptotic behavior of these approaches.