Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones
The Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appear...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-10-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/18/11/383 |
| _version_ | 1811183960148934656 |
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| author | Hideyuki Ishi |
| author_facet | Hideyuki Ishi |
| author_sort | Hideyuki Ishi |
| collection | DOAJ |
| description | The Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appearing in statistics. Furthermore, we discuss an application to maximum likelihood estimation for a certain exponential family over a cone of this class. |
| first_indexed | 2024-04-11T13:05:26Z |
| format | Article |
| id | doaj.art-e5aef887eb664de78870809d6c2f4b00 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:05:26Z |
| publishDate | 2016-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e5aef887eb664de78870809d6c2f4b002022-12-22T04:22:48ZengMDPI AGEntropy1099-43002016-10-01181138310.3390/e18110383e18110383Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex ConesHideyuki Ishi0Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, JapanThe Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appearing in statistics. Furthermore, we discuss an application to maximum likelihood estimation for a certain exponential family over a cone of this class.http://www.mdpi.com/1099-4300/18/11/383convex conehomogeneous conegraphical modelKoszul–Vinberg characteristic function |
| spellingShingle | Hideyuki Ishi Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones Entropy convex cone homogeneous cone graphical model Koszul–Vinberg characteristic function |
| title | Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones |
| title_full | Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones |
| title_fullStr | Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones |
| title_full_unstemmed | Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones |
| title_short | Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones |
| title_sort | explicit formula of koszul vinberg characteristic functions for a wide class of regular convex cones |
| topic | convex cone homogeneous cone graphical model Koszul–Vinberg characteristic function |
| url | http://www.mdpi.com/1099-4300/18/11/383 |
| work_keys_str_mv | AT hideyukiishi explicitformulaofkoszulvinbergcharacteristicfunctionsforawideclassofregularconvexcones |