AI RESEARCH
Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
arXiv CS.LG
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ArXi:2605.06959v1 Announce Type: cross This paper presents a parametric solution to piecewise linear regression through the Adaptive Block Gradient Descent (ABGD) algorithm. The heart of the method is the parametrization of piecewise linear functions as the difference of max-affine (DoMA) functions. A non-asymptotic local convergence analysis for ABGD is provided under sub-Gaussian covariate and noise distributions. To initialize ABGD, we adapt a prior algorithm originally developed for the simpler setting of max-affine functions.