Near-Optimal Sample Complexity Bounds for Maximum Likelihood Estimation of Multivariate Log-concave Densities

COLT, pp. 1234-1262, 2018.

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Abstract:

We study the problem of learning multivariate log-concave densities with respect to a global loss function. We obtain the emph{first} upper bound on the sample complexity of the maximum likelihood estimator (MLE) for a log-concave density on (mathbb{R}^d), for all (d geq 4). Prior to this work, no finite sample upper bound was known for ...More

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