Abstract
The mean shift (MS) algorithm is a nonparametric method used to cluster sample points and find the local modes of kernel density estimates, using an idea based on iterative gradient ascent. In this paper we develop a mean-shift-inspired algorithm to estimate the maxima of regression functions and partition the sample points in the input space. We prove convergence of the sequences generated by the algorithm and derive the rates of convergence of the estimated local maxima for the underlying regression model. We also demonstrate the utility of the algorithm for data-enabled discovery through an application on biomolecular structure data.
Funding Statement
This work is partially supported by grants NSF DMS 1821154 and NSF FET 1900061. This material is additionally based upon work by AS supported by (while serving at) the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Acknowledgments
We are grateful to two anonymous referees for their helpful comments.
Citation
Wanli Qiao. Amarda Shehu. "Space partitioning and regression maxima seeking via a mean-shift-inspired algorithm." Electron. J. Statist. 16 (2) 5623 - 5658, 2022. https://doi.org/10.1214/22-EJS2073
