# Robust Topological Inference in the Presence of Outliers

@article{Vishwanath2022RobustTI, title={Robust Topological Inference in the Presence of Outliers}, author={Siddharth Vishwanath and Bharath K. Sriperumbudur and Kenji Fukumizu and Satoshi Kuriki}, journal={ArXiv}, year={2022}, volume={abs/2206.01795} }

The distance function to a compact set plays a crucial role in the paradigm of topological data analysis. In particular,the sublevel sets of the distance function are used in the computation of persistent homology— a backbone of the topological data analysis pipeline. Despite its stability to perturbations in the Hausdorﬀ distance, persistent homology is highly sensitive to outliers. In this work, we develop a framework of statistical inference for persistent homology in the presence of…

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