Observation-Level Watermarking and Detection for Tabular Data

As generative AI makes the creation of synthetic tabular data increasingly common, there is a growing need to verify data authenticity, protect intellectual property, and ensure traceability. Existing watermarking techniques for tabular data often struggle with discrete or mixed-type variables, require large sample sizes for detection, or operate only at the dataset level. This paper addresses these limitations by proposing a unified framework for embedding and detecting watermarks at the individual observation level.

The authors propose STAMP (Single-observation Tabular Attribution and Marking Procedure). The insertion process uses a distribution-invariant transformation that injects a secret key into the data while ensuring the watermarked output asymptotically follows the original distribution. To handle the challenge of unknown underlying distributions, the authors develop a refined empirical distribution function (EDF) with exponential tail extensions, which ensures invertibility and maintains statistical properties. The detection mechanism works by reversing this transformation and checking for the presence of the injected key, allowing for identification even when the sample size is as small as one observation.

STAMP provides a versatile solution that accommodates univariate and multivariate data, as well as continuous and discrete variables. Because the watermark is embedded at the observation level, the method is robust to subsetting—meaning the watermark remains detectable even if only a portion of the original dataset is available. Theoretical analysis confirms that the detection rate converges to one as the sample size increases, and empirical simulations demonstrate that the method maintains high data fidelity, making it suitable for downstream statistical or machine learning tasks.