# Multilevel Stochastic Optimization for Imputation in Massive Medical Data Records

arXiv: https://arxiv.org/abs/2110.09680 · HTML: https://mlsanity.com/paper/2110.09680/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 64 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 7 of 7)

- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Auto-Keras: An Efficient Neural Architecture Search System](https://mlsanity.com/paper/1806.10282/) (2018)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [MisGAN: Learning from Incomplete Data with Generative Adversarial Networks](https://mlsanity.com/paper/1902.09599/) (2019)
- [VIGAN: Missing View Imputation with Generative Adversarial Networks](https://mlsanity.com/paper/1708.06724/) (2017)
- [CollaGAN : Collaborative GAN for Missing Image Data Imputation](https://mlsanity.com/paper/1901.09764/) (2019)

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

- [Missing Data Imputation Based on Dynamically Adaptable Structural Equation Modeling with Self-Attention](https://mlsanity.com/paper/2308.12388/) (2023)
- [Precision Adaptive Imputation Network : An Unified Technique for Mixed Datasets](https://mlsanity.com/paper/2501.10667/) (2025)

## Abstract (arXiv)

It has long been a recognized problem that many datasets contain significant levels of missing numerical data. A potentially critical predicate for application of machine learning methods to datasets involves addressing this problem. However, this is a challenging task. In this paper, we apply a recently developed multi-level stochastic optimization approach to the problem of imputation in massive medical records. The approach is based on computational applied mathematics techniques and is highly accurate. In particular, for the Best Linear Unbiased Predictor (BLUP) this multi-level formulation is exact, and is significantly faster and more numerically stable. This permits practical application of Kriging methods to data imputation problems for massive datasets. We test this approach on data from the National Inpatient Sample (NIS) data records, Healthcare Cost and Utilization Project (HCUP), Agency for Healthcare Research and Quality. Numerical results show that the multi-level method significantly outperforms current approaches and is numerically robust. It has superior accuracy as compared with methods recommended in the recent report from HCUP. Benchmark tests show up to 75% reductions in error. Furthermore, the results are also superior to recent state of the art methods such as discriminative deep learning.