Uyen Dang

Tuan L. Vo, Quan Huu Do, Uyen Dang et al.

The covariance matrix is a foundation in numerous statistical and machine-learning applications such as Principle Component Analysis, Correlation Heatmap, etc. However, missing values within datasets present a formidable obstacle to accurately estimating this matrix. While imputation methods offer one avenue for addressing this challenge, they often entail a trade-off between computational efficiency and estimation accuracy. Consequently, attention has shifted towards direct parameter estimation, given its precision and reduced computational burden. In this paper, we propose Direct Parameter Estimation for Randomly Missing Data with Categorical Features (DPERC), an efficient approach for direct parameter estimation tailored to mixed data that contains missing values within continuous features. Our method is motivated by leveraging information from categorical features, which can significantly enhance covariance matrix estimation for continuous features. Our approach effectively harnesses the information embedded within mixed data structures. Through comprehensive evaluations of diverse datasets, we demonstrate the competitive performance of DPERC compared to various contemporary techniques. In addition, we also show by experiments that DPERC is a valuable tool for visualizing the correlation heatmap.

Nhan Phan, Thu Nguyen, Uyen Dang et al.

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of eXplainable Artificial Intelligence (XAI) methods for the decision of the model. In this work, we analyze the potential issues with this approach and propose Principal Components-based Initialization (PCsInit), a strategy to incorporate PCA into the first layer of a neural network via initialization of the first layer in the network with the principal components, and its two variants PCsInit-Act and PCsInit-Sub. We will show that explanations using these strategies are more simple, direct and straightforward than using PCA prior to training a neural network on the principal components. We also show that the proposed techniques possess desirable theoretical properties. Moreover, as will be illustrated in the experiments, such training strategies can also allow further improvement of training via backpropagation compared to training neural networks on principal components.

Tuan L. Vo, Uyen Dang, Thu Nguyen

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.