Difficulty of singularity in population coding
Difficulty of singularity in population coding
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DOI：
10.1162/0899766053429426
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发表时间：
2005-04-01
影响因子：
2.9
通讯作者：
Nakahara, H
中科院分区：
文献类型：
--
作者：
Amari, S;Nakahara, H
Fisher信息已被用来分析神经群体编码的准确性。当Fisher信息不退化时，这很有效，但是当两个刺激被呈现给神经元群体时，通过它们的相互作用出现奇异结构。在这种情况下，Fisher信息矩阵退化，并且违反了确保Cramer-Rao统计范式的正则性条件。动物在这种情况下表现出病态行为。我们提出了一种新的统计分析方法来理解人口编码中的信息，其中代数奇异性起着重要作用。该方法通过计算Fisher信息来阐明病理病例的性质。然后，我们建议，同步发射可以解决奇异性，并显示一种方法来分析绑定问题的Fisher信息。我们的方法集成了各种学科的人口编码，如非正规统计，贝叶斯统计，奇异性代数几何，同步发射，主题下的Fisher信息。
Fisher information has been used to analyze the accuracy of neural population coding. This works well when the Fisher information does not degenerate, but when two stimuli are presented to a population of neurons, a singular structure emerges by their mutual interactions. In this case, the Fisher information matrix degenerates, and the regularity condition ensuring the Cramer-Rao paradigm of statistics is violated. An animal shows pathological behavior in such a situation. We present a novel method of statistical analysis to understand information in population coding in which algebraic singularity plays a major role. The method elucidates the nature of the pathological case by calculating the Fisher information. We then suggest that synchronous firing can resolve singularity and show a method of analyzing the binding problem in terms of the Fisher information. Our method integrates a variety of disciplines in population coding, such as nonregular statistics, Bayesian statistics, singularity in algebraic geometry, and synchronous firing, under the theme of Fisher information.