Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Polynomial Time Algorithm for Maximum Likelihood Estimation of
  Multivariate Log-concave Densities   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.

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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int