Is Anonymization Through Discretization Reliable? Modeling Latent Probability Distributions for Ordinal Data as a Solution to the Small Sample Size Problem

Stefan Michael Stroka () and Christian Heumann
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Stefan Michael Stroka: Department of Statistics, Ludwig-Maximilians-University Munich, 80539 Munich, Germany
Christian Heumann: Department of Statistics, Ludwig-Maximilians-University Munich, 80539 Munich, Germany

Stats, 2024, vol. 7, issue 4, 1-20

Abstract: The growing interest in data privacy and anonymization presents challenges, as traditional methods such as ordinal discretization often result in information loss by coarsening metric data. Current research suggests that modeling the latent distributions of ordinal classes can reduce the effectiveness of anonymization and increase traceability. In fact, combining probability distributions with a small training sample can effectively infer true metric values from discrete information, depending on the model and data complexity. Our method uses metric values and ordinal classes to model latent normal distributions for each discrete class. This approach, applied with both linear and Bayesian linear regression, aims to enhance supervised learning models. Evaluated with synthetic datasets and real-world datasets from UCI and Kaggle, our method shows improved mean point estimation and narrower prediction intervals compared to the baseline. With 5–10% training data randomly split from each dataset population, it achieves an average 10% reduction in MSE and a ~5–10% increase in R ² on out-of-sample test data overall.

Keywords: re-identification; modeling latent class distribution; ordinal class; Bayesian inference; uncertainty quantification; supervised learning regression enhancement (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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