Fused Density Estimation: Theory and Methods
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Authors
Bassett, Robert
Sharpnack, James
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Advisors
Date of Issue
2018-12
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Publisher
ArXiv
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Abstract
In this paper we introduce a method for nonparametric density estimation on infrastructure networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide theoretical support for fused density estimation by proving that the squared Hellinger rate of convergence for the estimator achieves the minimax bound over univariate densities of log-bounded variation. We reduce the original variational formulation in order to transform it into a tractable, finite-dimensional quadratic program. Because random variables the networks we consider generalizations of the univariate case, this method also provides a useful tool for univariate density estimation. Lastly, we apply this method and assess its performance on examples in the univariate and infrastructure network settings. We compare the performance of different optimization techniques to solve the problem, and use these results to inform recommendations for the computation of fused density estimators.
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Preprint
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Operations Research (OR)
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Sponsors
RB was supported in part by the U.S. Office of Naval Research grant N00014-17-2372. JS was supported in part by NSF grant DMS-1712996.
Funder
RB was supported in part by the U.S. Office of Naval Research grant N00014-17-2372. JS was supported in part by NSF grant DMS-1712996.
Format
50 p.
Citation
Bassett, Robert, and James Sharpnack. "Fused density estimation: theory and methods." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 81.5 (2019): 839-860.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.