Geodesic
On the Bootstrap for Persistence Diagrams and Landscapes
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 6, pp. 111-120.

Voir la notice de l'article provenant de la source Math-Net.Ru

Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular, we derive confidence sets for persistence diagrams and confidence bands for persistence landscapes. The article is published in the author's wording.
Keywords: persistent homology, bootstrap, topological data analysis. 
@article{MAIS_2013_20_6_a8,
     author = {F. Chazal and B. T. Fasy and F. Lecci and A. Rinaldo and A. Singh and L. Wasserman},
     title = {On the {Bootstrap} for {Persistence} {Diagrams} and {Landscapes}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {111--120},
     publisher = {mathdoc},
     volume = {20},
     number = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2013_20_6_a8/}
}
TY  - JOUR
AU  - F. Chazal
AU  - B. T. Fasy
AU  - F. Lecci
AU  - A. Rinaldo
AU  - A. Singh
AU  - L. Wasserman
TI  - On the Bootstrap for Persistence Diagrams and Landscapes
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2013
SP  - 111
EP  - 120
VL  - 20
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2013_20_6_a8/
LA  - en
ID  - MAIS_2013_20_6_a8
ER  - 
%0 Journal Article
%A F. Chazal
%A B. T. Fasy
%A F. Lecci
%A A. Rinaldo
%A A. Singh
%A L. Wasserman
%T On the Bootstrap for Persistence Diagrams and Landscapes
%J Modelirovanie i analiz informacionnyh sistem
%D 2013
%P 111-120
%V 20
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2013_20_6_a8/
%G en
%F MAIS_2013_20_6_a8
F. Chazal; B. T. Fasy; F. Lecci; A. Rinaldo; A. Singh; L. Wasserman. On the Bootstrap for Persistence Diagrams and Landscapes. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 6, pp. 111-120. http://geodesic.mathdoc.fr/item/MAIS_2013_20_6_a8/

[1] Sivaraman Balakrishnan, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, Larry Wasserman, Statistical inference for persistent homology, 2013, arXiv: 1303.7117

[2] Peter Bubenik, Statistical topology using persistence landscapes, 2012, arXiv: 1207.6437

[3] Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot, The structure and stability of persistence modules, July 2012, arXiv: 1207.3674

[4] David Cohen-Steiner, Herbert Edelsbrunner, John Harer, “Stability of persistence diagrams”, Discrete Comput. Geom., 37:1 (2007), 103–120 | DOI | MR | Zbl

[5] Anthony Christopher Davison, D. V. Hinkley, Bootstrap Methods and Their Application, v. 1, Cambridge UP, 1997 | MR

[6] Persi Diaconis, Susan Holmes, Mehrdad Shahshahani, Sampling from a manifold, 2012, arXiv: 1206.6913

[7] Herbert Edelsbrunner, John Harer, Computational Topology. An Introduction, Amer. Math. Soc., Providence, RI, 2010 | MR

[8] Bradley Efron, “Bootstrap methods: Another look at the jackknife”, Ann. Statist., 1979, 1–26 | MR

[9] Bradley Efron, Robert Tibshirani, John D. Storey, Virginia Tusher, “Empirical {B}ayes analysis of a microarray experiment”, J. Amer. Statist. Assoc., 96:456 (2001), 1151–1160 | DOI | MR | Zbl

[10] Evarist Giné, Armelle Guillou, “Rates of strong uniform consistency for multivariate kernel density estimators”, Annales de l'Institut Henri Poincare (B) Probability and Statistics, 38 (2002), 907–921 | DOI | MR | Zbl

[11] Evarist Giné, Joel Zinn, “Bootstrapping general empirical measures”, The Annals of Probability, 1990, 851–869 | MR | Zbl

[12] Michael R. Kosorok, Introduction to Empirical Processes and Semiparametric Inference, Springer, 2008 | MR

[13] Aad Van der Vaart, Asymptotic statistics, v. 3, Cambridge university press, 2000 | MR

[14] Aad Van der Vaart, Jon Wellner, Weak Convergence and Empirical Processes: With Applications to Statistics, Springer, 1996 | MR | Zbl