Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces

@article{Blumberg2014RobustSH,
  title={Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces},
  author={A. Blumberg and I. Gal and Michael A. Mandell and Matthew Pancia},
  journal={Foundations of Computational Mathematics},
  year={2014},
  volume={14},
  pages={745-789}
}
  • A. Blumberg, I. Gal, +1 author Matthew Pancia
  • Published 2014
  • Mathematics, Computer Science
  • Foundations of Computational Mathematics
  • We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis. 
    47 Citations
    Tropical Sufficient Statistics for Persistent Homology
    • 12
    • PDF
    Confidence sets for persistence diagrams
    • 169
    • PDF
    Persistent Homology and Applied Homotopy Theory
    • 6
    • PDF
    Statistical topological data analysis using persistence landscapes
    • Peter Bubenik
    • Mathematics, Computer Science
    • J. Mach. Learn. Res.
    • 2015
    • 388
    • PDF
    A topological study of functional data and Fréchet functions of metric measure spaces
    • 3
    • PDF
    Topological spaces of persistence modules and their properties
    • 20
    • PDF
    Multiple testing with persistent homology
    • 2
    • PDF
    Medians of populations of persistence diagrams
    • 2

    References

    SHOWING 1-10 OF 61 REFERENCES
    Persistent homology for random fields and complexes
    • 81
    • Highly Influential
    • PDF
    Statistical topological data analysis using persistence landscapes
    • Peter Bubenik
    • Mathematics, Computer Science
    • J. Mach. Learn. Res.
    • 2015
    • 388
    • PDF
    Statistical topology via Morse theory, persistence and nonparametric estimation
    • 41
    • PDF
    Persistent Homology — a Survey
    • 592
    • PDF
    Statistical topology using persistence landscapes
    • 34
    • PDF
    Probability measures on the space of persistence diagrams
    • 159
    • Highly Influential
    • PDF
    Gromov‐Hausdorff Stable Signatures for Shapes using Persistence
    • 186
    • PDF
    Stability of persistence diagrams
    • 816
    • PDF
    Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)
    • 142
    • Highly Influential
    • PDF
    Persistence stability for geometric complexes
    • 155
    • PDF