# Deeply-Learned Generalized Linear Models with Missing Data

arXiv: https://arxiv.org/abs/2207.08911 · HTML: https://mlsanity.com/paper/2207.08911/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 18 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [Reinterpreting Importance-Weighted Autoencoders](https://mlsanity.com/paper/1704.02916/) (2017)
- [Identifiable Generative Models for Missing Not at Random Data Imputation](https://mlsanity.com/paper/2110.14708/) (2021)
- [Posterior Matching for Arbitrary Conditioning](https://mlsanity.com/paper/2201.12414/) (2022)

## Built on by (most cited first, 2 of 2)

- [Amortized Variational Inference for Logistic Regression with Missing Covariates](https://mlsanity.com/paper/2603.21244/) (2026)
- [LiD-GLM: Lipschitz-constrained Deep Generalized Linear Models](https://mlsanity.com/paper/2608.16340/) (2026)

## Abstract (arXiv)

Deep Learning (DL) methods have dramatically increased in popularity in recent years, with significant growth in their application to supervised learning problems in the biomedical sciences. However, the greater prevalence and complexity of missing data in modern biomedical 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, textitdlglm, 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 a 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.