Private Aggregation of Trajectories

Ghazi, Badih; Kamal, Neel; Kumar, R. Prem; Manurangsi, Pasin; Zhang, Annika

doi:10.56553/popets-2022-0125

Cited by 7 publications

(15 citation statements)

References 49 publications

(76 reference statements)

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“…Our results differ from this line of work in that we require the output across two separate samples to be exactly the same with high probability, when the randomness is shared. Moreover, our work reaffirms (Ben-David et al, 2006) in that their notion of stability can be perfectly attained no matter the choice of k. Other notions of stability that are related to our work include differentially private clustering (Cohen et al, 2021;Ghazi et al, 2020), robust hierarchical clustering (Balcan et al, 2014), and robust online clustering (Lattanzi et al, 2021).…”

Section: Related Worksupporting

confidence: 75%

Almost Tight Approximation Algorithms for Explainable Clustering

Esfandiari

Mirrokni

Narayanan

2022

Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

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In this paper, we design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability in (Impagliazzo et al., 2022). A clustering algorithm is replicable if, with high probability, it outputs the exact same clusters after two executions with datasets drawn from the same distribution when its internal randomness is shared across the executions. We propose such algorithms for the statistical kmedians, statistical k-means, and statistical k-centers problems by utilizing approximation routines for their combinatorial counterparts in a black-box manner. In particular, we demonstrate a replicable O(1)-approximation algorithm for statistical Euclidean k-medians (k-means) with poly(d) sample complexity. We also describe a O(1)-approximation algorithm with an additional O(1)-additive error for statistical Euclidean k-centers, albeit with exp(d) sample complexity.

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Section: Related Worksupporting

confidence: 75%

Almost Tight Approximation Algorithms for Explainable Clustering

Esfandiari

Mirrokni

Narayanan

2022

Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

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“…Further, a range of works [Barak et al, 2007, Gupta et al, 2011, Cheraghchi et al, 2012 also study the query class of k-way conjunctions and provide fast algorithms when k is small. Further common problems in the privacy literature related to this paper include histogram release [Hay et al, 2009, Xiao et al, 2010, Acs et al, 2012, Qardaji et al, 2013, Xu et al, 2013, Meng et al, 2017, Nelson and Reuben, 2019, Abowd et al, 2019 and private clustering [Su et al, 2016, Balcan et al, 2017, Stemmer, 2020, Ghazi et al, 2020.…”

Section: Related Workmentioning

confidence: 99%

Sample-efficient private data release for Lipschitz functions under sparsity assumptions

Donhauser¹,

Lokna²,

Sanyal³

et al. 2023

Preprint

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Differential privacy is the de facto standard for protecting privacy in a variety of applications. One of the key challenges is private data release, which is particularly relevant in scenarios where limited information about the desired statistics is available beforehand. Recent work has presented a differentially private data release algorithm that achieves optimal rates of order n −1/d , with n being the size of the dataset and d being the dimension, for the worst-case error over all Lipschitz continuous statistics. This type of guarantee is desirable in many practical applications, as for instance it ensures that clusters present in the data are preserved. However, due to the "slow" rates, it is often infeasible in practice unless the dimension of the data is small. We demonstrate that these rates can be significantly improved to n −1/s when only guarantees over s-sparse Lipschitz continuous functions are required, or to n −1/(s+1) when the data lies on an unknown s-dimensional subspace, disregarding logarithmic factors. We therefore obtain practically meaningful rates for moderate constants s which motivates future work on computationally efficient approximate algorithms for this problem.

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“…Additional work has followed the publication of a preliminary version of this paper. The most relevant is the work of [GKKM22], in which it was shown that by evolving the discretization during the composition and making it progressively finer, one can further improve the running time of our accountant to polylog(k) from Õ( √ k) when composing the same mechanism k times. Further, the running time for composing k different mechanisms can be reduced to Õ(k) from Õ(k 1.5 ).…”

Section: Introductionmentioning

confidence: 99%

Numerical Composition of Differential Privacy

Gopi,

Lee,

Wutschitz

2024

JPC

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We give a fast algorithm to optimally compose privacy guarantees of differentially private (DP) algorithms to arbitrary accuracy. Our method is based on the notion of \emph{privacy loss random variables} to quantify the privacy loss of DP algorithms.The running time and memory needed for our algorithm to approximate the privacy curve of a DP algorithm composed with itself $k$ times is $\tilde{O}(\sqrt{k})$. This improves over the best prior method by Koskela et al. (2021) which requires $\tilde{\Omega}(k^{1.5})$ running time. We demonstrate the utility of our algorithm by accurately computing the privacy loss of DP-SGD algorithm of Abadi et al. (2016) and showing that our algorithm speeds up the privacy computations by a few orders of magnitude compared to prior work, while maintaining similar accuracy.

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Private Aggregation of Trajectories

Cited by 7 publications

References 49 publications

Almost Tight Approximation Algorithms for Explainable Clustering

Almost Tight Approximation Algorithms for Explainable Clustering

Sample-efficient private data release for Lipschitz functions under sparsity assumptions

Numerical Composition of Differential Privacy

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