Intrinsic Losses Based on Information Geometry and Their Applications
One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the framework of Riemannian geometry an...
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| Format: | Article |
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MDPI AG
2017-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/8/405 |
| _version_ | 1798004969535700992 |
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| author | Yao Rong Mengjiao Tang Jie Zhou |
| author_facet | Yao Rong Mengjiao Tang Jie Zhou |
| author_sort | Yao Rong |
| collection | DOAJ |
| description | One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the framework of Riemannian geometry and dual geometry, we revisit two commonly-used intrinsic losses which are respectively given by the squared Rao distance and the symmetrized Kullback–Leibler divergence (or Jeffreys divergence). For an exponential family endowed with the Fisher metric and α -connections, the two loss functions are uniformly described as the energy difference along an α -geodesic path, for some α ∈ { − 1 , 0 , 1 } . Subsequently, the two intrinsic losses are utilized to develop Bayesian analyses of covariance matrix estimation and range-spread target detection. We provide an intrinsically unbiased covariance estimator, which is verified to be asymptotically efficient in terms of the intrinsic mean square error. The decision rules deduced by the intrinsic Bayesian criterion provide a geometrical justification for the constant false alarm rate detector based on generalized likelihood ratio principle. |
| first_indexed | 2024-04-11T12:31:54Z |
| format | Article |
| id | doaj.art-07c80a23a2e6430b8a08e3b65dd754e4 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:31:54Z |
| publishDate | 2017-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-07c80a23a2e6430b8a08e3b65dd754e42022-12-22T04:23:43ZengMDPI AGEntropy1099-43002017-08-0119840510.3390/e19080405e19080405Intrinsic Losses Based on Information Geometry and Their ApplicationsYao Rong0Mengjiao Tang1Jie Zhou2College of Mathematics, Sichuan University, Chengdu 610064, ChinaCollege of Mathematics, Sichuan University, Chengdu 610064, ChinaCollege of Mathematics, Sichuan University, Chengdu 610064, ChinaOne main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the framework of Riemannian geometry and dual geometry, we revisit two commonly-used intrinsic losses which are respectively given by the squared Rao distance and the symmetrized Kullback–Leibler divergence (or Jeffreys divergence). For an exponential family endowed with the Fisher metric and α -connections, the two loss functions are uniformly described as the energy difference along an α -geodesic path, for some α ∈ { − 1 , 0 , 1 } . Subsequently, the two intrinsic losses are utilized to develop Bayesian analyses of covariance matrix estimation and range-spread target detection. We provide an intrinsically unbiased covariance estimator, which is verified to be asymptotically efficient in terms of the intrinsic mean square error. The decision rules deduced by the intrinsic Bayesian criterion provide a geometrical justification for the constant false alarm rate detector based on generalized likelihood ratio principle.https://www.mdpi.com/1099-4300/19/8/405intrinsic lossinformation geometryexponential familycovariance matrix estimationrange-spread target detection |
| spellingShingle | Yao Rong Mengjiao Tang Jie Zhou Intrinsic Losses Based on Information Geometry and Their Applications Entropy intrinsic loss information geometry exponential family covariance matrix estimation range-spread target detection |
| title | Intrinsic Losses Based on Information Geometry and Their Applications |
| title_full | Intrinsic Losses Based on Information Geometry and Their Applications |
| title_fullStr | Intrinsic Losses Based on Information Geometry and Their Applications |
| title_full_unstemmed | Intrinsic Losses Based on Information Geometry and Their Applications |
| title_short | Intrinsic Losses Based on Information Geometry and Their Applications |
| title_sort | intrinsic losses based on information geometry and their applications |
| topic | intrinsic loss information geometry exponential family covariance matrix estimation range-spread target detection |
| url | https://www.mdpi.com/1099-4300/19/8/405 |
| work_keys_str_mv | AT yaorong intrinsiclossesbasedoninformationgeometryandtheirapplications AT mengjiaotang intrinsiclossesbasedoninformationgeometryandtheirapplications AT jiezhou intrinsiclossesbasedoninformationgeometryandtheirapplications |