Tight Lower Bounds for Homology Inference

@article{Balakrishnan2013TightLB,
  title={Tight Lower Bounds for Homology Inference},
  author={Sivaraman Balakrishnan and Alessandro Rinaldo and Aarti Singh and Larry A. Wasserman},
  journal={CoRR},
  year={2013},
  volume={abs/1307.7666}
}
The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and sometimes the dimension of the manifold. In earlier work [1], we have considered the statistical problem of estimating the homology of a manifold from noiseless samples and from noisy samples under several different noise models. We derived upper and lower… CONTINUE READING
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