Keywords: [ differential privacy ] [ generalization bounds ] [ margin theory ]
We present a series of new differentially private (DP) algorithms with dimension-independent margin guarantees. For the family of linear hypotheses, we give a pure DP learning algorithm that benefits from relative deviation margin guarantees, as well as an efficient DP learning algorithm with margin guarantees. We also present a new efficient DP learning algorithm with margin guarantees for kernel-based hypotheses with shift-invariant kernels, such as Gaussian kernels, and point out how our results can be extended to other kernels using oblivious sketching techniques. We further give a pure DP learning algorithm for a family of feed-forward neural networks for which we prove margin guarantees that are independent of the input dimension. Additionally, we describe a general label DP learning algorithm, which benefits from relative deviation margin bounds and is applicable to a broad family of hypothesis sets, including that of neural networks. Finally, we show how our DP learning algorithms can be augmented in a general way to include model selection, to select the best confidence margin parameter.