Abstract

Topological Data Analysis (TDA) provides a framework for extracting topological features from complex datasets, offering insights into their underlying structure. A prominent technique within TDA is persistent homology, which quantifies salient topological features across multiple scales. TDA offers valuable information, revealing scientific insights and extracting meaningful features for downstream learning tasks.
In this talk, I will present statistical inference methods for TDA, focusing on persistent homology. I will begin by introducing persistent homology, and discuss how randomness in data influences the resulting topological features. I will present methods to quantify this uncertainty through confidence sets, as well as how to identify statistically significant topological features.