Weighted Missing Linear Discriminant Analysis: An Explainable Approach for Classification with Missing Data

As Artificial Intelligence (AI) models are gradually being adopted in real-life applications, the explainability of the model used is critical, especially in high-stakes areas such as medicine, finance, etc. Among the commonly used models, Linear Discriminant Analysis (LDA) is a widely used classification tool that is also explainable thanks to its ability to model class distributions and maximize class separation through linear feature combinations. Nevertheless, real-world data is frequently incomplete, presenting significant challenges for classification tasks and model explanations. In this paper, we propose a novel approach to LDA under missing data, termed Weighted missing Linear Discriminant Analysis (WLDA), to directly classify observations in data that contains missing values without imputation effectively by estimating the parameters directly on missing data and use a weight matrix for missing values to penalize missing entries during classification. Furthermore, we also analyze the theoretical properties and examine the explainability of the proposed technique in a comprehensive manner. Experimental results demonstrate that WLDA outperforms conventional methods by a significant margin, particularly in scenarios where missing values are present in both training and test sets.