EPEM: Efficient Parameter Estimation for Multiple Class Monotone Missing Data

TL;DR

This paper introduces EPEM, a novel, exact, and efficient algorithm for maximum likelihood estimation in monotone missing data scenarios, significantly reducing computation time and improving accuracy over traditional imputation methods.

Contribution

The paper presents a new exact formula and algorithm for MLE in monotone missing data with equal covariance matrices, eliminating iterative imputation.

Findings

EPEM reduces error rates significantly.

EPEM requires less computation time.

The method is validated with empirical results.

Abstract

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.