Alternating minimization with spectral-plus-random-search initialization converges geometrically and attains near-minimax optimal estimation rates for max-affine regression when k is fixed and the design is random.
Sliced inverse regression for dimension reduction
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Max-Affine Regression: Provable, Tractable, and Near-Optimal Statistical Estimation
Alternating minimization with spectral-plus-random-search initialization converges geometrically and attains near-minimax optimal estimation rates for max-affine regression when k is fixed and the design is random.