Matching Map Recovery with an Unknown Number of Outliers

@article{Minasyan2022MatchingMR,
  title={Matching Map Recovery with an Unknown Number of Outliers},
  author={Arshak Minasyan and Tigran Galstyan and S. A. Hunanyan and Arnak S. Dalalyan},
  journal={ArXiv},
  year={2022},
  volume={abs/2210.13354}
}
We consider the problem of finding the matching map between two sets of d -dimensional noisy feature-vectors. The distinctive feature of our setting is that we do not assume that all the vectors of the first set have their corresponding vector in the second set. If n and m are the sizes of these two sets, we assume that the matching map that should be recovered is defined on a subset of unknown cardinality k ∗ ≤ min( n, m ) . We show that, in the high-dimensional setting, if the signal-to-noise… 
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