Deeply Learned Generalized Linear Models with Missing Data

Abstract

Deep Learning (DL) methods have dramatically increased in popularity in recent years, with significant growth in their application to various supervised learning problems. However, the greater prevalence and complexity of missing data in such datasets present significant challenges for DL methods. Here, we provide a formal treatment of missing data in the context of deeply learned generalized linear models, a supervised DL architecture for regression and classification problems. We propose a new architecture, dlglm, that is one of the first to be able to flexibly account for both ignorable and non-ignorable patterns of missingness in input features and response at training time. We demonstrate through statistical simulation that our method outperforms existing approaches for supervised learning tasks in the presence of missing not at random (MNAR) missingness. We conclude with a case study of the Bank Marketing dataset from the UCI Machine Learning Repository, in which we predict whether clients subscribed to a product based on phone survey data. Supplementary materials for this article are available online.

KEYWORDS:

• Deeply learned glm
• Missing data
• MNAR
• Supervised learning

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors gratefully acknowledge NIH grants U01-CA274298, P50-CA257911, P50-CA058223, T32-CA106209, 1R01AA02687901A1, and 1OT2OD032581-02-321, and NSF grants IIS2133595 and DMS2324394 for funding this research.