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Data distillation aims to generate a small data set that closely mimics theperformance of a given learning algorithm on the original data set. Thedistilled dataset is hence useful to simplify the training process thanks toits small data size. However, distilled data samples are not necessarilyprivacy-preserving, even if they are generally humanly indiscernible. Toaddress this limitation, we introduce differentially private kernel inducingpoints (DP-KIP) for privacy-preserving data distillation. Unlike our originalintention to simply apply DP-SGD to the framework of KIP, we find that KIPusing infinitely-wide convolutional neural tangent kernels (conv-NTKs) performsbetter compared to KIP using fully-connected NTKs. However, KIP with conv-NTKs,due to its convolutional and pooling operations, introduces an unbearablecomputational complexity, requiring hundreds of V100 GPUs in parallel to train,which is impractical and more importantly, such computational resources areinaccessible to many. To overcome this issue, we propose an alternative thatdoes not require pre-training (to avoid a privacy loss) and can well capturecomplex information on images, as those features from conv-NKTs do, while thecomputational cost is manageable by a single V100 GPU. To this end, we proposeDP-KIP-ScatterNet, which uses the wavelet features from Scattering networks(ScatterNet) instead of those from conv-NTKs, to perform DP-KIP at a reasonablecomputational cost. We implement DP-KIP-ScatterNet in -- computationallyefficient -- JAX and test on several popular image datasets to show itsefficacy and its superior performance compared to state-of-the art methods inimage data distillation with differential privacy guarantees.

Differentially Private Kernel Inducing Points using features from ScatterNets (DP-KIP-ScatterNet) for Privacy Preserving Data Distillation