A Polynomial Time Algorithm for Maximum Likelihood Estimation of Multivariate Log-concave Densities

arXiv: Data Structures and Algorithms, Volume abs/1812.05524, 2018.

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Abstract:

We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on input a set of $n$ points in $mathbb{R}^d$ and an accuracy parameter $epsilonu003e0$, it runs in ti...More

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