# Conditional expectation with regularization for missing data imputation

arXiv: https://arxiv.org/abs/2302.00911 · HTML: https://mlsanity.com/paper/2302.00911/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [VAEs in the Presence of Missing Data](https://mlsanity.com/paper/2006.05301/) (2020)
- [MIDA: Multiple Imputation using Denoising Autoencoders](https://mlsanity.com/paper/1705.02737/) (2017)
- [Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning](https://mlsanity.com/paper/1912.06989/) (2019)
- [Multiple imputation for continuous variables using a Bayesian principal component analysis](https://mlsanity.com/paper/1401.5747/) (2014)
- [Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models with Local Dependence](https://mlsanity.com/paper/1410.0438/) (2014)
- [EPEM: Efficient Parameter Estimation for Multiple Class Monotone Missing Data](https://mlsanity.com/paper/2009.11360/) (2020)
- [Robust training of recurrent neural networks to handle missing data for disease progression modeling](https://mlsanity.com/paper/1808.05500/) (2018)
- [Explainable Data Imputation using Constraints](https://mlsanity.com/paper/2205.04731/) (2022)

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

- [A parameter-free clustering algorithm for missing datasets](https://mlsanity.com/paper/2404.05363/) (2024)
- [Directly Handling Missing Data in Linear Discriminant Analysis for Enhancing Classification Accuracy and Interpretability](https://mlsanity.com/paper/2407.00710/) (2024)

## Abstract (arXiv)

Missing data frequently occurs in datasets across various domains, such as medicine, sports, and finance. In many cases, to enable proper and reliable analyses of such data, the missing values are often imputed, and it is necessary that the method used has a low root mean square error (RMSE) between the imputed and the true values. In addition, for some critical applications, it is also often a requirement that the imputation method is scalable and the logic behind the imputation is explainable, which is especially difficult for complex methods that are, for example, based on deep learning. Based on these considerations, we propose a new algorithm named "conditional Distribution-based Imputation of Missing Values with Regularization" (DIMV). DIMV operates by determining the conditional distribution of a feature that has missing entries, using the information from the fully observed features as a basis. As will be illustrated via experiments in the paper, DIMV (i) gives a low RMSE for the imputed values compared to state-of-the-art methods; (ii) fast and scalable; (iii) is explainable as coefficients in a regression model, allowing reliable and trustable analysis, makes it a suitable choice for critical domains where understanding is important such as in medical fields, finance, etc; (iv) can provide an approximated confidence region for the missing values in a given sample; (v) suitable for both small and large scale data; (vi) in many scenarios, does not require a huge number of parameters as deep learning approaches; (vii) handle multicollinearity in imputation effectively; and (viii) is robust to the normally distributed assumption that its theoretical grounds rely on.