A Polynomial Time Algorithm for Log-Concave Maximum Likelihood via Locally Exponential Families

ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 32 (NIPS 2019), pp. 7721-7733, 2019.

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Keywords:
exponential familiesset of pointsnovel connection

Abstract:

We consider the problem of computing the maximum likelihood multivariate log-concave distribution for a set of points. Specifically, we present an algorithm which, given n points in R-d and an accuracy parameter epsilon > 0, runs in time poly(n, d, 1/epsilon), and returns a log-concave distribution which, with high probability, has the pr...More

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