Topological consistency via kernel estimation

Understand

We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions.

• Our method is based on kernel estimation.
• We apply this procedure to two problems: (1) inferring the homology structure of manifolds from noisy observations, (2) inferring the persistent homology (a multi-scale extension of homology) of either density or regression functions.
• We prove consistency for both of these problems.