The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning
The aim of this paper is to develop a comprehensive study of the geometry involved in combining Bregman divergences with pooling operators over closed convex sets in a discrete probabilistic space. A particular connection we develop leads to an iterative procedure, which is similar to the alternatin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-12-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/12/6338 |
| _version_ | 1811303979961810944 |
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| author | Martin Adamčík |
| author_facet | Martin Adamčík |
| author_sort | Martin Adamčík |
| collection | DOAJ |
| description | The aim of this paper is to develop a comprehensive study of the geometry involved in combining Bregman divergences with pooling operators over closed convex sets in a discrete probabilistic space. A particular connection we develop leads to an iterative procedure, which is similar to the alternating projection procedure by Csiszár and Tusnády. Although such iterative procedures are well studied over much more general spaces than the one we consider, only a few authors have investigated combining projections with pooling operators. We aspire to achieve here a comprehensive study of such a combination. Besides, pooling operators combining the opinions of several rational experts allows us to discuss possible applications in multi-expert reasoning. |
| first_indexed | 2024-04-13T07:57:51Z |
| format | Article |
| id | doaj.art-297bdd9de89342899db4a21055b02ec5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T07:57:51Z |
| publishDate | 2014-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-297bdd9de89342899db4a21055b02ec52022-12-22T02:55:21ZengMDPI AGEntropy1099-43002014-12-0116126338638110.3390/e16126338e16126338The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert ReasoningMartin Adamčík0Martin de Tours School of Management and Economics, Assumption University, MSME Building, 4th Floor, 88 Moo 8 Bang Na-Trad Km. 26 Bangsaothong, 10540 Samuthprakarn, ThailandThe aim of this paper is to develop a comprehensive study of the geometry involved in combining Bregman divergences with pooling operators over closed convex sets in a discrete probabilistic space. A particular connection we develop leads to an iterative procedure, which is similar to the alternating projection procedure by Csiszár and Tusnády. Although such iterative procedures are well studied over much more general spaces than the one we consider, only a few authors have investigated combining projections with pooling operators. We aspire to achieve here a comprehensive study of such a combination. Besides, pooling operators combining the opinions of several rational experts allows us to discuss possible applications in multi-expert reasoning.http://www.mdpi.com/1099-4300/16/12/6338Bregman divergenceinformation geometrypooling operatordiscrete probability functionprobabilistic mergingmulti-expert reasoning |
| spellingShingle | Martin Adamčík The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning Entropy Bregman divergence information geometry pooling operator discrete probability function probabilistic merging multi-expert reasoning |
| title | The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning |
| title_full | The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning |
| title_fullStr | The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning |
| title_full_unstemmed | The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning |
| title_short | The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning |
| title_sort | information geometry of bregman divergences and some applications in multi expert reasoning |
| topic | Bregman divergence information geometry pooling operator discrete probability function probabilistic merging multi-expert reasoning |
| url | http://www.mdpi.com/1099-4300/16/12/6338 |
| work_keys_str_mv | AT martinadamcik theinformationgeometryofbregmandivergencesandsomeapplicationsinmultiexpertreasoning AT martinadamcik informationgeometryofbregmandivergencesandsomeapplicationsinmultiexpertreasoning |