STATISTICAL-INFERENCE UNDER MULTITERMINAL RATE RESTRICTIONS - A DIFFERENTIAL GEOMETRIC APPROACH
STATISTICAL-INFERENCE UNDER MULTITERMINAL RATE RESTRICTIONS - A DIFFERENTIAL GEOMETRIC APPROACH
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DOI：
10.1109/18.32118
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发表时间：
1989-03-01
影响因子：
2.5
通讯作者：
HAN, TS
中科院分区：
文献类型：
--
作者：
AMARI, SI;HAN, TS
处理发射相互相关信号X和Y的两端信息源的统计推断问题。让n个独立观察的序列X/sup n/和Y/sup n/分别以每个字母的速率R/sub 1/和R/sub 2/彼此独立地编码成消息集M/sub X/和M/sub Y/。这种压缩导致可用于测试有关X和Y的假设的统计信息的丢失。统计信息的丢失被评估为香农信息的量R/sub 1/和R/sub 2/的函数。在渐近完全数据压缩的情况下给出了完整的解决方案，R/sub 1/，R/sub 2/ 到0作为n到无穷大。结果表明，所有概率分布流形的微分几何在此类连接香农信息和统计信息的多终端问题中起着基础性作用。简要介绍了双耦合 e-仿射和 m-仿射连接以及 e-平坦度和 m-平坦度。<>
A statistical inference problem for a two-terminal information source emitting mutually correlated signals X and Y is treated. Let sequences X/sup n/ and Y/sup n/ of n independent observations be encoded independently of each other into message sets M/sub X/ and M/sub Y/ at rates R/sub 1/ and R/sub 2/ per letter, respectively. This compression causes a loss of the statistical information available for testing hypotheses concerning X and Y. The loss of statistical information is evaluated as a function of the amounts R/sub 1/ and R/sub 2/ of the Shannon information. A complete solution is given in the case of asymptotically complete data compression, R/sub 1/, R/sub 2/ to 0 as n to infinity . It is shown that the differential geometry of the manifold of all probability distributions plays a fundamental role in this type of multiterminal problem connecting Shannon information and statistical information. A brief introduction to the dually coupled e-affine and m-affine connections together with e-flatness and m-flatness is given.<>