nips nips2009 nips2009-11 nips2009-11-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Yao-liang Yu, Yuxi Li, Dale Schuurmans, Csaba Szepesvári
Abstract: Surjectivity of linear projections between distribution families with fixed mean and covariance (regardless of dimension) is re-derived by a new proof. We further extend this property to distribution families that respect additional constraints, such as symmetry, unimodality and log-concavity. By combining our results with classic univariate inequalities, we provide new worst-case analyses for natural risk criteria arising in classification, optimization, portfolio selection and Markov decision processes. 1
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