Piecewise Linear Regression under Noise Level Variation via Convex Optimization

Piecewise linear regression is a fundamental challenge in science and engineering. For typical applications where noise level varies in observations, the problem becomes much more challenging. In this paper, we propose a convex optimization based piecewise linear regression method which incorporates variation of the noise level. More precisely, we newly design a convex data-fidelity function as a weighted sum of approximation errors to mitigate effect of the noise level variation. The weights are automatically adjusted to the varying noise level within the framework of convex optimization. Numerical examples show performance improvements by the proposed method.