# EPEM: Efficient Parameter Estimation for Multiple Class Monotone Missing Data

arXiv: https://arxiv.org/abs/2009.11360 · HTML: https://mlsanity.com/paper/2009.11360/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [Missing Value Estimation using Clustering and Deep Learning within Multiple Imputation Framework](https://mlsanity.com/paper/2202.13734/) (2022)
- [Correlation visualization under missing values: a comparison between imputation and direct parameter estimation methods](https://mlsanity.com/paper/2305.06044/) (2023)
- [Explainability of Machine Learning Models under Missing Data](https://mlsanity.com/paper/2407.00411/) (2024)
- [Principal Component Analysis based frameworks for efficient missing data imputation algorithms](https://mlsanity.com/paper/2205.15150/) (2022)
- [Conditional expectation with regularization for missing data imputation](https://mlsanity.com/paper/2302.00911/) (2023)
- [Blockwise Principal Component Analysis for monotone missing data imputation and dimensionality reduction](https://mlsanity.com/paper/2305.06042/) (2023)
- [DPER: Efficient Parameter Estimation for Randomly Missing Data](https://mlsanity.com/paper/2106.05190/) (2021)
- [Directly Handling Missing Data in Linear Discriminant Analysis for Enhancing Classification Accuracy and Interpretability](https://mlsanity.com/paper/2407.00710/) (2024)
- [DPERC: Direct Parameter Estimation for Mixed Data](https://mlsanity.com/paper/2501.10540/) (2025)

## Abstract (arXiv)

The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations through the data before yielding convergence. Moreover, those approaches may introduce extra noises and biases to the subsequent modeling. In this work, we derive exact formulas and propose a novel algorithm to compute the maximum likelihood estimators (MLEs) of a multiple class, monotone missing dataset when all the covariance matrices of all categories are assumed to be equal, namely EPEM. We then illustrate an application of our proposed methods in Linear Discriminant Analysis (LDA). As the computation is exact, our EPEM algorithm does not require multiple iterations through the data as other imputation approaches, thus promising to handle much less time-consuming than other methods. This effectiveness was validated by empirical results when EPEM reduced the error rates significantly and required a short computation time compared to several imputation-based approaches. We also release all codes and data of our experiments in one GitHub repository to contribute to the research community related to this problem.