Polynomial-time SDP and ellipsoid-based approximation of Kolmogorov widths yields efficient robust detection boundaries matching upper bounds up to polylog factors for structured constrained signals.
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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.
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Efficient Robust Constrained Signal Detection via Kolmogorov Width Approximations
Polynomial-time SDP and ellipsoid-based approximation of Kolmogorov widths yields efficient robust detection boundaries matching upper bounds up to polylog factors for structured constrained signals.
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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.