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Topological density estimation

We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We show that TDE has performance and runtime advantages over competing methods of kernel density estimation for highly multimodal probability density functions. We also show that TDE yields useful auxiliary information, that it can determine its own suitability for use, and we explain its performance.