<ul><li>Persistent homology is a key tool in topological data analysis, but it is highly sensitive to outliers.</li><li>In response, researchers have developed a framework of statistical inference for persistent homology in the presence of outliers.</li><li>They propose a 	extit{median-of-means} variant of the distance function and establish its statistical properties.</li><li>Simulations and applications demonstrate the advantages of the proposed methodology.</li></ul>

Adversarially Robust Topological Inference

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