Statistics for a Computational Topologist

Lecture materials for Prof. Fasy's lectures at IMA's Tutorial on Multiparameter Persistence, Computation, and Applications

Homework

Create a list of topological descriptors, including:

• Name of descriptor.
• List of distances that can be used between descriptors.
• Short explanation (very short).
• Reference to where first used, or a good use of it.
• Pros: What is it good for?
• Cons: Where / when is it insufficient?

References

Day 1

• Bootstrap Paper I. Fasy, Lecci, Rinaldo, Wasserman, Balakrishnan, and Singh. Confidence Sets for Persistence Diagrams. The Annals of Statistics, 42(6):2301-2339, 2014.
• Bootstrap Paper II: Chazal, Fasy, Lecci, Rinaldo, Singh, and Wasserman. Robust
  On the Bootstrap for Persistence Diagrams and Landscapes. Modeling and Analysis of Information Systems, 2013. Also available at arXiv:1311.0376.
• Bootstrap Paper III. Chazal, Fasy, Lecci, Michel, Rinaldo, Wasserman. Topological Inference: Distance To a Measure and Kernel Distance. JMLR, 18(159):1−40, 2018.
• Wasserman. All of Statistics. Springer, 2004.
• Brainstorm Padlet

Day 2

• Functional Summaries of Persistence Diagrams
• Descriptors Padlet