Piecewise Linear Regression via a Difference of Convex Functions

Jul 12, 2020

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We present a new piecewise linear regression methodology that utilises fitting a difference of convex functions (DC functions) to the data. These are functions f that may be represented as the difference ϕ_1 - ϕ_2 for a choice of convex functions ϕ_1, ϕ_2. The method proceeds by estimating piecewise-liner convex functions, in a manner similar to max-affine regression, whose difference approximates the data. The choice of the function is regularised by a new seminorm over the class of DC functions that controls the ℓ_∞ Lipschitz constant of the estimate. The resulting methodology can be efficiently implemented via Quadratic programming even in high dimensions, and is shown to have close to minimax statistical risk. We empirically validate the method, showing it to be practically implementable, and to outperform existing regression methods in accuracy on real-world datasets.

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About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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