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In this paper we revisit the classical problem of classification, but imposeprivacy constraints. Under such constraints, the raw data$(X_1,Y_1),\ldots,(X_n,Y_n)$ cannot be directly observed, and all classifiersare functions of the randomised outcome of a suitable local differentialprivacy mechanism. The statistician is free to choose the form of this privacymechanism, and here we add Laplace distributed noise to a discretisation of thelocation of each feature vector $X_i$ and to its label $Y_i$. Theclassification rule is the privatized version of the well-studied partitioningclassification rule. In addition to the standard Lipschitz and marginconditions, a novel characteristic is introduced, by which the exact rate ofconvergence of the classification error probability is calculated, both fornon-private and private data.

On rate-optimal classification from non-private and from private data