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A Framework for Private Matrix Analysis in Sliding Window Model

Upadhyay, Jalaj; Upadhyay, Sarvagya (January 2021, Proceedings of Machine Learning Research)

We perform a rigorous study of private matrix analysis when only the last 𝑊 updates to matrices are considered useful for analysis. We show the existing framework in the non-private setting is not robust to noise required for privacy. We then propose a framework robust to noise and use it to give first efficient 𝑜(𝑊) space differentially private algorithms for spectral approximation, principal component analysis (PCA), multi-response linear regression, sparse PCA, and non-negative PCA. Prior to our work, no such result was known for sparse and non-negative differentially private PCA even in the static data setting. We also give a lower bound to demonstrate the cost of privacy in the sliding window model.

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In this paper, we focus on answering queries, in a differentially private manner, on graph streams. We adopt the sliding window model of privacy, where we wish to perform analysis on the last W updates and ensure that privacy is preserved for the entire stream. We show that in this model, the price of ensuring differential privacy is minimal. Furthermore, since differential privacy is preserved under post-processing, our results can be used as a subroutine in many tasks, most notably solving cut functions and spectral clustering.