Nhan Lu-Chinh Phan

Mai Anh Vu, Thu Nguyen, Tu T. Do et al.

Missing data frequently occurs in datasets across various domains, such as medicine, sports, and finance. In many cases, to enable proper and reliable analyses of such data, the missing values are often imputed, and it is necessary that the method used has a low root mean square error (RMSE) between the imputed and the true values. In addition, for some critical applications, it is also often a requirement that the imputation method is scalable and the logic behind the imputation is explainable, which is especially difficult for complex methods that are, for example, based on deep learning. Based on these considerations, we propose a new algorithm named "conditional Distribution-based Imputation of Missing Values with Regularization" (DIMV). DIMV operates by determining the conditional distribution of a feature that has missing entries, using the information from the fully observed features as a basis. As will be illustrated via experiments in the paper, DIMV (i) gives a low RMSE for the imputed values compared to state-of-the-art methods; (ii) fast and scalable; (iii) is explainable as coefficients in a regression model, allowing reliable and trustable analysis, makes it a suitable choice for critical domains where understanding is important such as in medical fields, finance, etc; (iv) can provide an approximated confidence region for the missing values in a given sample; (v) suitable for both small and large scale data; (vi) in many scenarios, does not require a huge number of parameters as deep learning approaches; (vii) handle multicollinearity in imputation effectively; and (viii) is robust to the normally distributed assumption that its theoretical grounds rely on.

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.