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We consider the problem of computing the maximum likelihood multivariate log-concave distribution for a set of points.
The log-concave maximum likelihood estimator is optimal in high dimensions
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Limit distribution theory for maximum likelihood estimation of a log-concave density
F. Balabdaoui, K. Rufibach, and J. A. Wellner · 2009
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Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency
L. Dumbgen and K. Rufibach · 2009
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On the rate of convergence of the maximum likelihood estimator of a k k -monotone density
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Estimation of a discrete monotone density
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Global rates of convergence of the mles of log-concave and s s -concave densities
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Estimation of a k k -monotone density: characterizations, consistency and minimax lower bounds
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Maximum likelihood estimation of a multi-dimensional log-concave density
M. Cule, R. Samworth, and M. Stewart · 2010
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R. Koenker and I. Mizera · 2010
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logcondens: Computations related to univariate log-concave density estimation
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Global rates of convergence in log-concave density estimation
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Sample-optimal density estimation in nearly-linear time
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Learning multivariate log-concave distributions
I. Diakonikolas, D. M. Kane, and A. Stewart · 2017
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Geometry of Log-Concave Density Estimation
E. Robeva, B. Sturmfels, and C. Uhler · 2017
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Recent progress in log-concave density estimation
R. J. Samworth · 2017
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An efficient algorithm for high-dimensional log-concave maximum likelihood
B. Axelrod and G. Valiant · 2018
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Inference for a two-component mixture of symmetric distributions under log-concavity
F. Balabdaoui and C. R. Doss · 2018
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Near-optimal sample complexity bounds for maximum likelihood estimation of multivariate log-concave densities
T. Carpenter, I. Diakonikolas, A. Sidiropoulos, and A. Stewart · 2018
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Density estimation for shift-invariant multidimensional distributions
A. De, P. M. Long, and R. A. Servedio · 2018
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Fast and sample near-optimal algorithms for learning multidimensional histograms
I. Diakonikolas, J. Li, and L. Schmidt · 2018
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Fast multivariate log-concave density estimation
F. Rathke and C. Schnörr · 2018
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