First poly(n,d,1/ε)-time algorithm for ε-approximate maximum-likelihood log-concave distribution estimation on n points in R^d.
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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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A Polynomial Time Algorithm for Log-Concave Maximum Likelihood via Locally Exponential Families
First poly(n,d,1/ε)-time algorithm for ε-approximate maximum-likelihood log-concave distribution estimation on n points in R^d.
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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.