# Compound Density Networks for Risk Prediction using Electronic Health Records

arXiv: https://arxiv.org/abs/2208.01320 · HTML: https://mlsanity.com/paper/2208.01320/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 2 Aug 2022.

## Builds on (most cited first, 15 of 15)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Analyzing the Role of Model Uncertainty for Electronic Health Records](https://mlsanity.com/paper/1906.03842/) (2019)
- [Robust, Accurate Stochastic Optimization for Variational Inference](https://mlsanity.com/paper/2009.00666/) (2020)
- [Variational Bayesian Monte Carlo](https://mlsanity.com/paper/1810.05558/) (2018)
- [Imputation of Clinical Covariates in Time Series](https://mlsanity.com/paper/1812.00418/) (2018)
- [UNITE: Uncertainty-based Health Risk Prediction Leveraging Multi-sourced Data](https://mlsanity.com/paper/2010.11389/) (2020)
- [Constructing Deep Neural Networks by Bayesian Network Structure Learning](https://mlsanity.com/paper/1806.09141/) (2018)

## Built on by (most cited first, 3 of 3)

- [Handling missing values in healthcare data: A systematic review of deep learning-based imputation techniques](https://mlsanity.com/paper/2210.08258/) (2022)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Hypergraph Convolutional Networks for Fine-grained ICU Patient Similarity Analysis and Risk Prediction](https://mlsanity.com/paper/2308.12575/) (2023)

## Abstract (arXiv)

Electronic Health Records (EHRs) exhibit a high amount of missing data due to variations of patient conditions and treatment needs. Imputation of missing values has been considered an effective approach to deal with this challenge. Existing work separates imputation method and prediction model as two independent parts of an EHR-based machine learning system. We propose an integrated end-to-end approach by utilizing a Compound Density Network (CDNet) that allows the imputation method and prediction model to be tuned together within a single framework. CDNet consists of a Gated recurrent unit (GRU), a Mixture Density Network (MDN), and a Regularized Attention Network (RAN). The GRU is used as a latent variable model to model EHR data. The MDN is designed to sample latent variables generated by GRU. The RAN serves as a regularizer for less reliable imputed values. The architecture of CDNet enables GRU and MDN to iteratively leverage the output of each other to impute missing values, leading to a more accurate and robust prediction. We validate CDNet on the mortality prediction task on the MIMIC-III dataset. Our model outperforms state-of-the-art models by significant margins. We also empirically show that regularizing imputed values is a key factor for superior prediction performance. Analysis of prediction uncertainty shows that our model can capture both aleatoric and epistemic uncertainties, which offers model users a better understanding of the model results.