We develop in this paper a theoretical framework for the topological study of time series
data. Broadly speaking, we describe geometrical and topological properties of sliding …

Confidence sets for persistence diagrams Page 1 The Annals of Statistics 2014, Vol. 42, No.
6, 2301–2339 DOI: 10.1214/14-AOS1252 © Institute of Mathematical Statistics, 2014 …

Persistent homology is a multiscale method for analyzing the shape of sets and functions
from point cloud data arising from an unknown distribution supported on those sets. When …

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 …

In order to use persistence diagrams as a true statistical tool, it would be very useful to have
a good notion of mean and variance for a set of diagrams. In 23, Mileyko and his …

This dissertation extends the theory of persistent homology to time varying systems. Most of
the previous work has been dedicated to using this powerful tool in topological data analysis …

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a
widely used method in TDA that summarizes homological features of data at multiple scales …

The persistence diagram is the fundamental object in topological data analysis. It inherits the
stochastic variability of the data we use as input. As such we need to understand how to …

In order to use persistence diagrams as a true statistical tool, it would be very useful to have
a good notion of mean and variance for a set of diagrams. In [20], Mileyko and his …

Until very recently, topological data analysis and topological inference methods mostly
relied on deterministic approaches. The major part of this habilitation thesis presents a …