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Differential privacy is the standard privacy definition for performinganalyses over sensitive data. Yet, its privacy budget bounds the number oftasks an analyst can perform with reasonable accuracy, which makes itchallenging to deploy in practice. This can be alleviated by private sketching,where the dataset is compressed into a single noisy sketch vector which can beshared with the analysts and used to perform arbitrarily many analyses.However, the algorithms to perform specific tasks from sketches must bedeveloped on a case-by-case basis, which is a major impediment to their use. Inthis paper, we introduce the generic moment-to-moment (M$^2$M) method toperform a wide range of data exploration tasks from a single private sketch.Among other things, this method can be used to estimate empirical moments ofattributes, the covariance matrix, counting queries (including histograms), andregression models. Our method treats the sketching mechanism as a black-boxoperation, and can thus be applied to a wide variety of sketches from theliterature, widening their ranges of applications without further engineeringor privacy loss, and removing some of the technical barriers to the wideradoption of sketches for data exploration under differential privacy. Wevalidate our method with data exploration tasks on artificial and real-worlddata, and show that it can be used to reliably estimate statistics and trainclassification models from private sketches.

M$^2$M: A general method to perform various data analysis tasks from a differentially private sketch