We introduce the concept of differential privacy, mathematical definition for privacy preserving data publishing and data mining. General definition in context of metric spaces and probability measure is given. Further, we present some theorems which help to alleviate the requirements of described definition. Laplace mechanism for numerical data and lower bounds on errors of response mechanisms are presented. We later turn focus to functional data. Using Gaussian processes and Reproducing Kernel Hilbert Spaces we present how differential privacy is used for privatization of density kernel estimator. Most of the described mechanisms are also implemented and results are presented at the end
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