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A Novel Evaluation Metric for Synthetic Data Generation

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Part of the Lecture Notes in Computer Science book series (LNISA,volume 12490)


Differentially private algorithmic synthetic data generation (SDG) solutions take input datasets \(D_p\) consisting of sensitive, private data and generate synthetic data \(D_s\) with similar qualities. The importance of such solutions is increasing both because more and more people realize how much data is collected about them and used in machine learning contexts, as well as a consequence of newly introduced data privacy regulations, e.g. the EU’s General Data Protection Regulation (GDPR). We aim to develop a novel and composite SDG evaluation metric which takes into account macro-statistical dataset similarities and data utility in machine learning tasks against privacy boundaries of the synthetic data. We formalize the mathematical foundations for quantitatively measuring both the statistical similarities and the data utility of synthetic data. We use two well-known datasets containing (potentially) personally identifiable information as inputs (\(D_p\)) and existing SDG algorithms PrivBayes and DPGroupFields to generate synthetic data (\(D_s\)) based on them. We then test our evaluation metric for different values of privacy budget \(\epsilon \). Based on our experiments we conclude that the proposed composite evaluation metric is appropriate for quantitatively measuring the quality of synthetic data generated by different SDG solutions and possesses an expected sensitivity to various privacy budget values.


  • Synthetic data generation
  • Differential privacy
  • Evaluation metrics

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  1. 1.

    Since this paper is focusing on evaluation, most popular SDG approaches are just listed here since their detailed description is out of the scope of this paper.

  2. 2.

    The important role of \(\epsilon \) in DP justifies its presence as subscript of G in our evaluation metric definition since we evaluate G at varying of \(\epsilon \).


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This research was co-funded by EIT Digital Industrial Doctorate and Ericsson Hungary. Project no. ED_18-1-2019-0030 (Application domain specific highly reliable IT solutions subprogramme) has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the Thematic Excellence Programme funding scheme. We are thankful to Gian Marco Canneori for the fruitful discussions leading to the final mathematical foundations presented in this paper.

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Galloni, A., Lendák, I., Horváth, T. (2020). A Novel Evaluation Metric for Synthetic Data Generation. In: Analide, C., Novais, P., Camacho, D., Yin, H. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2020. IDEAL 2020. Lecture Notes in Computer Science(), vol 12490. Springer, Cham.

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