Differentially Private Clustering in Data Streams
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arXiv
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| Format: | Preprint |
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2023
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| author | Epasto, Alessandro Mukherjee, Tamalika Zhong, Peilin |
| author_facet | Epasto, Alessandro Mukherjee, Tamalika Zhong, Peilin |
| contents | Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central concern in many real-world applications, non-private clustering algorithms may not be as applicable in many scenarios.
In this work, we provide the first differentially private algorithms for $k$-means and $k$-median clustering of $d$-dimensional Euclidean data points over a stream with length at most $T$ using space that is sublinear (in $T$) in the continual release setting where the algorithm is required to output a clustering at every timestep.
We achieve (1) an $O(1)$-multiplicative approximation with $\tilde{O}(k^{1.5} \cdot poly(d,\log(T)))$ space and $poly(k,d,\log(T))$ additive error, or (2) a $(1+γ)$-multiplicative approximation with $\tilde{O}_γ(poly(k,2^{O_γ(d)},\log(T)))$ space for any $γ>0$, and the additive error is $poly(k,2^{O_γ(d)},\log(T))$. Our main technical contribution is a differentially private clustering framework for data streams which only requires an offline DP coreset or clustering algorithm as a blackbox. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07449 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Differentially Private Clustering in Data Streams Epasto, Alessandro Mukherjee, Tamalika Zhong, Peilin Data Structures and Algorithms Cryptography and Security Machine Learning Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central concern in many real-world applications, non-private clustering algorithms may not be as applicable in many scenarios. In this work, we provide the first differentially private algorithms for $k$-means and $k$-median clustering of $d$-dimensional Euclidean data points over a stream with length at most $T$ using space that is sublinear (in $T$) in the continual release setting where the algorithm is required to output a clustering at every timestep. We achieve (1) an $O(1)$-multiplicative approximation with $\tilde{O}(k^{1.5} \cdot poly(d,\log(T)))$ space and $poly(k,d,\log(T))$ additive error, or (2) a $(1+γ)$-multiplicative approximation with $\tilde{O}_γ(poly(k,2^{O_γ(d)},\log(T)))$ space for any $γ>0$, and the additive error is $poly(k,2^{O_γ(d)},\log(T))$. Our main technical contribution is a differentially private clustering framework for data streams which only requires an offline DP coreset or clustering algorithm as a blackbox. |
| title | Differentially Private Clustering in Data Streams |
| topic | Data Structures and Algorithms Cryptography and Security Machine Learning |
| url | https://arxiv.org/abs/2307.07449 |