Information Geometry of Generalized Bayesian Prediction Using $\alpha$ -Divergences as Loss Functions
In this paper, the methods of information geometry are employed to investigate a generalized Bayes rule for prediction. Taking α-divergences as the loss functions, optimality, and asymptotic properties of the generalized Bayesian predictive densities are considered. We show that the Bayesian predict...
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| Veröffentlicht in: | IEEE transactions on information theory 2018-03, Vol.64 (3), p.1812-1824 |
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| container_title | IEEE transactions on information theory |
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| creator | Zhang, Fode Shi, Yimin Ng, Hon Keung Tony Wang, Ruibing |
| description | In this paper, the methods of information geometry are employed to investigate a generalized Bayes rule for prediction. Taking α-divergences as the loss functions, optimality, and asymptotic properties of the generalized Bayesian predictive densities are considered. We show that the Bayesian predictive densities minimize a generalized Bayes risk. We also find that the asymptotic expansions of the densities are related to the coefficients of the α-connections of a statistical manifold. In addition, we discuss the difference between two risk functions of the generalized Bayesian predictions based on different priors. Finally, using the non-informative priors (i.e., Jeffreys and reference priors), uniform prior, and conjugate prior, two examples are presented to illustrate the main results. |
| doi_str_mv | 10.1109/TIT.2017.2774820 |
| format | Article |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Asymptotic properties Asymptotic series Bayesian analysis Predictions |
| title | Information Geometry of Generalized Bayesian Prediction Using $\alpha$ -Divergences as Loss Functions |
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