Deriving an Optimal Noise Adding Mechanism for Privacy-Preserving Machine Learning

• Published in: Database and Expert Systems Applications Vol. 1062; pp. 108 - 118
• Main Authors: Kumar, Mohit, Rossbory, Michael, Moser, Bernhard A., Freudenthaler, Bernhard
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2019; Springer International Publishing
• Series: Communications in Computer and Information Science
• Subjects: Machine learning; Noise adding mechanism; Privacy
• ISBN: 9783030276836; 303027683X
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-030-27684-3_15

Differential privacy is a standard mathematical framework to quantify the degree to which individual privacy in a statistical dataset is preserved. We derive an optimal $$(\epsilon ,\delta )$$ –differentially private noise adding mechanism for real-valued data matrices meant for the training of models by machine learning algorithms. The aim is to protect a machine learning algorithm from an adversary who seeks to gain an information about the data from algorithm’s output by perturbing the value in a sample of the training data. The fundamental issue of trade-off between privacy and utility is addressed by presenting a novel approach consisting of three steps: (1) the sufficient conditions on the probability density function of noise for $$(\epsilon ,\delta )$$ –differential privacy of a machine learning algorithm are derived; (2) the noise distribution that, for a given level of entropy, minimizes the expected noise magnitude is derived; (3) using entropy level as the design parameter, the optimal entropy level and the corresponding probability density function of the noise are derived.