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Storage-efficient privacy-preserving learning is crucial due to increasingamounts of sensitive user data required for modern learning tasks. We propose aframework for reducing the storage cost of user data while at the same timeproviding privacy guarantees, without essential loss in the utility of the datafor learning. Our method comprises noise injection followed by lossycompression. We show that, when appropriately matching the lossy compression tothe distribution of the added noise, the compressed examples converge, indistribution, to that of the noise-free training data as the sample size of thetraining data (or the dimension of the training data) increases. In this sense,the utility of the data for learning is essentially maintained, while reducingstorage and privacy leakage by quantifiable amounts. We present experimentalresults on the CelebA dataset for gender classification and find that oursuggested pipeline delivers in practice on the promise of the theory: theindividuals in the images are unrecognizable (or less recognizable, dependingon the noise level), overall storage of the data is substantially reduced, withno essential loss (and in some cases a slight boost) to the classificationaccuracy. As an added bonus, our experiments suggest that our method yields asubstantial boost to robustness in the face of adversarial test data.

Lossy Compression of Noisy Data for Private and Data-Efficient Learning