ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.
arXiv preprint arXiv:2207.09660 , year=
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Sp-GD recovers sparse max-affine parameters to epsilon accuracy with O(s log(d/s)) samples in the noise-free case under sub-Gaussian assumptions, supported by sparse-PCA initialization and an RMD transformation for generalized polynomials.
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Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.