# Directly Handling Missing Data in Linear Discriminant Analysis for Enhancing Classification Accuracy and Interpretability

arXiv: https://arxiv.org/abs/2407.00710 · HTML: https://mlsanity.com/paper/2407.00710/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 30 Jun 2024.

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

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Towards Explainable Artificial Intelligence](https://mlsanity.com/paper/1909.12072/) (2019)
- [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)
- [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)
- [Shapley-based Explainable AI for Clustering Applications in Fault Diagnosis and Prognosis](https://mlsanity.com/paper/2303.14581/) (2023)
- [Correlation visualization under missing values: a comparison between imputation and direct parameter estimation methods](https://mlsanity.com/paper/2305.06044/) (2023)
- [Explainable Data Imputation using Constraints](https://mlsanity.com/paper/2205.04731/) (2022)
- [PWSHAP: A Path-Wise Explanation Model for Targeted Variables](https://mlsanity.com/paper/2306.14672/) (2023)
- [BSED: Baseline Shapley-Based Explainable Detector](https://mlsanity.com/paper/2308.07490/) (2023)
- [Conditional expectation with regularization for missing data imputation](https://mlsanity.com/paper/2302.00911/) (2023)

## Abstract (arXiv)

As the adoption of Artificial Intelligence (AI) models expands into critical real-world applications, ensuring the explainability of these models becomes paramount, particularly in sensitive fields such as medicine and finance. Linear Discriminant Analysis (LDA) remains a popular choice for classification due to its interpretable nature, derived from its capacity to model class distributions and enhance class separation through linear combinations of features. However, real-world datasets often suffer from incomplete data, posing substantial challenges for both classification accuracy and model interpretability. In this paper, we introduce a novel and robust classification method, termed Weighted missing Linear Discriminant Analysis (WLDA), which extends LDA to handle datasets with missing values without the need for imputation. Our approach innovatively incorporates a weight matrix that penalizes missing entries, thereby refining parameter estimation directly on incomplete data. This methodology not only preserves the interpretability of LDA but also significantly enhances classification performance in scenarios plagued by missing data. We conduct an in-depth theoretical analysis to establish the properties of WLDA and thoroughly evaluate its explainability. Experimental results across various datasets demonstrate that WLDA consistently outperforms traditional methods, especially in challenging environments where missing values are prevalent in both training and test datasets. This advancement provides a critical tool for improving classification accuracy and maintaining model transparency in the face of incomplete data.