Abstract
As the importance of data privacy continues to grow, data masking has emerged as a crucial method. Notably, data masking techniques aim to protect individual privacy, while enabling data analysts to derive meaningful statistical results, such as the identification of directional or causal relationships between variables. Hence, this study demonstrates the advantages of a quantilebased discretization for protecting privacy and uncovering the relationships between variables in Gaussian directed acyclic graphical (DAG) models. Specifically, it introduces quantile-discretized Gaussian DAG models where each node variable is discretized based on the quantiles. Additionally, it proposes the bi-partition process, which aids in recovering the covariance matrix; hence, the models can be identifiable. Furthermore, a consistent algorithm is developed for learning the underlying structure using the quantile-based discretized data. Finally, through numerical experiments and the application of DAG learning algorithms to discretized MLB data, the proposed algorithm is demonstrated to significantly outperform the state-of-the-art DAG model learning algorithms.