Bounding the Excess Risk for Linear Models Trained on Marginal-Preserving, Differentially-Private, Synthetic Data

The growing use of machine learning (ML) has raised concerns that an ML model may reveal private information about an individual who has contributed to the training dataset. To prevent leakage of sensitive data, we consider using differentially-private (DP), synthetic training data instead of real training data to train an ML model. A key desirable property of synthetic data is its ability to preserve the low-order marginals of the original distribution. Our main contribution comprises novel upper and lower bounds on the excess empirical risk of linear models trained on such synthetic data, for continuous and Lipschitz loss functions. We perform extensive experimentation alongside our theoretical results.

MetaDIP: Accelerating Deep Image Prior with Meta Learning

Deep image prior (DIP) is a recently proposed technique for solving imaging inverse problems by fitting the reconstructed images to the output of an untrained convolutional neural network. Unlike pretrained feedforward neural networks, the same DIP can generalize to arbitrary inverse problems, from denoising to phase retrieval, while offering competitive performance at each task. The central disadvantage of DIP is that, while feedforward neural networks can reconstruct an image in a single pass, DIP must gradually update its weights over hundreds to thousands of iterations, at a significant computational cost. In this work we use meta-learning to massively accelerate DIP-based reconstructions. By learning a proper initialization for the DIP weights, we demonstrate a 10x improvement in runtimes across a range of inverse imaging tasks. Moreover, we demonstrate that a network trained to quickly reconstruct faces also generalizes to reconstructing natural image patches.