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• W2904306058 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 $epsilon>0$, it runs in time $text{poly}(n, d, 1/epsilon)$, and outputs a log-concave density that with high probability maximizes the log-likelihood up to an additive $epsilon$. Our approach relies on a natural convex optimization formulation of the underlying problem that can be efficiently solved by a projected stochastic subgradient method. The main challenge lies in showing that a stochastic subgradient of our objective function can be efficiently approximated. To achieve this, we rely on structural results on approximation of log-concave densities and leverage classical algorithmic tools on volume approximation of convex bodies and uniform sampling from convex sets." @default.
• W2904306058 created "2018-12-22" @default.
• W2904306058 creator A5013188587 @default.
• W2904306058 creator A5054966819 @default.
• W2904306058 creator A5083699810 @default.
• W2904306058 date "2018-12-13" @default.
• W2904306058 modified "2023-09-27" @default.
• W2904306058 title "A Polynomial Time Algorithm for Maximum Likelihood Estimation of Multivariate Log-concave Densities." @default.
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• W2904306058 hasPublicationYear "2018" @default.
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