A General Projection Property for Distribution Families

A General Projection Property for Distribution Families. Yu, Y., Li, Y., Schuurmans, D., & Szepesvári, C. In Advances in Neural Information Processing Systems, 2009.

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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.

@inproceedings{yu2009,
	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.},
	acceptrate = {263 out of 1105=24\%},
	author = {Yu, Y.-L. and Li, Y. and Schuurmans, D. and Szepesv{\'a}ri, Cs.},
	booktitle = {Advances in Neural Information Processing Systems},
	keywords = {theory, value at risk, stochastic programming},
	title = {A General Projection Property for Distribution Families},
	url_paper = {CVAR-NeurIPS09.pdf},
	year = {2009}}

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