Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm
This work provides a method for data-enabled discovery, such as in biomolecular structure analysis, but appears incremental as it extends mean shift concepts to regression.
The authors tackled the problem of estimating modes of regression functions and partitioning input space points by developing a mean-shift-inspired algorithm, proving its convergence and deriving non-asymptotic convergence rates for the estimated modes.
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 modes 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 non-asymptotic rates of convergence of the estimated local modes for the underlying regression model. We also demonstrate the utility of the algorithm for data-enabled discovery through an application on biomolecular structure data. An extension to subspace constrained mean shift (SCMS) algorithm used to extract ridges of regression functions is briefly discussed.