Generalized Gauss inequalities via semidefinite programming
نویسندگان
چکیده
منابع مشابه
Generalized Gauss inequalities via semidefinite programming
A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to be overly conservative since it is determined by a discrete worst-case distribution. In this paper we obtain a less pessimistic Gauss-type bo...
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A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result generalizes Chebyshev’s inequality for scalar random variables. Two semidefinite programming formulations are presented, with a constructive proof based on convex optimization duality and elementary...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2015
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-015-0878-1