Locally Adaptive and Differentiable Regression

• URL: http://arxiv.org/abs/2308.07418v2
• Date: Fri, 13 Oct 2023 02:27:42 GMT
• Title: Locally Adaptive and Differentiable Regression
• Authors: Mingxuan Han, Varun Shankar, Jeff M Phillips, Chenglong Ye
• Abstract summary: We propose a general framework to construct a global continuous and differentiable model based on a weighted average of locally learned models in corresponding local regions. We demonstrate that when we mix kernel ridge and regression terms in the local models, and stitch them together continuously, we achieve faster statistical convergence in theory and improved performance in various practical settings.
• Score: 10.194448186897906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern overparametrized, locally-adaptive models. We propose a general framework to construct a global continuous and differentiable model based on a weighted average of locally learned models in corresponding local regions. This model is competitive in dealing with data with different densities or scales of function values in different local regions. We demonstrate that when we mix kernel ridge and polynomial regression terms in the local models, and stitch them together continuously, we achieve faster statistical convergence in theory and improved performance in various practical settings.

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