Replicable Clustering
- URL: http://arxiv.org/abs/2302.10359v3
- Date: Fri, 27 Oct 2023 00:14:27 GMT
- Title: Replicable Clustering
- Authors: Hossein Esfandiari, Amin Karbasi, Vahab Mirrokni, Grigoris Velegkas,
Felix Zhou
- Abstract summary: We propose algorithms for the statistical $k$-medians, statistical $k$-means, and statistical $k$-centers problems by utilizing approximation routines for their counterparts in a black-box manner.
We also provide experiments on synthetic distributions in 2D using the $k$-means++ implementation from sklearn as a black-box that validate our theoretical results.
- Score: 57.19013971737493
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We design replicable algorithms in the context of statistical clustering
under the recently introduced notion of replicability from Impagliazzo et al.
[2022]. According to this definition, a clustering algorithm is replicable if,
with high probability, its output induces the exact same partition of the
sample space after two executions on different inputs drawn from the same
distribution, when its internal randomness is shared across the executions. We
propose such algorithms for the statistical $k$-medians, 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 $\operatorname{poly}(d)$ sample
complexity. We also describe an $O(1)$-approximation algorithm with an
additional $O(1)$-additive error for statistical Euclidean $k$-centers, albeit
with $\exp(d)$ sample complexity. In addition, we provide experiments on
synthetic distributions in 2D using the $k$-means++ implementation from sklearn
as a black-box that validate our theoretical results.
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