We consider classification of graphs using graph kernels under differential privacy. We develop differentially private mechanisms for two well-known graph kernels, the random walk kernel and the graphlet kernel. We use the Laplace mechanism with restricted sensitivity to release private versions of the feature vector representations of these kernels. Further, we develop a new sampling algorithm for approximate computation of the graphlet kernel on large graphs with guarantees on sample complexity, and show that the method improves both privacy and computation speed. We also observe that the number of samples needed to obtain good accuracy in practice is much lower than the bound. Finally, we perform an extensive empirical evaluation examining the trade-off between privacy and accuracy and show that our private method is able to retain good accuracy in several classification tasks.
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