论文标题
贝叶斯高参数的非平凡信息封闭
Non-trivial informational closure of a Bayesian hyperparameter
论文作者
论文摘要
我们研究了贝叶斯高参数的非平凡信息闭合（NTIC），这些律师参数推断出相同和独立分布的有限随机变量的潜在分布。为此，我们将贝叶斯高参数更新过程和随机数据过程嵌入到马尔可夫链中。 Bertschinger等人的原始出版物。 （2006年）提到，NTIC可能能够捕获建模的抽象概念，该概念对建模过程中的特定内部结构和存在的特定内部结构不可知。贝叶斯超参数是感兴趣的，因为它具有明确的解释为数据过程的模型，同时可以指定其动态，而无需参考这种解释。一方面，我们明确地表明，随着时间的流逝，高参数的NTIC无限期增加。另一方面，我们试图在数量之间建立一种连接，该数量是解释超参数为模型的特征，即信息增益和一个步骤的NTIC，这是一个不取决于这种解释的数量。我们发现通常，我们不能将一步的NTIC用作信息增益的指标。我们希望这项探索性工作可以进一步对NTIC与建模之间的关系进行进一步的严格研究。
We investigate the non-trivial informational closure (NTIC) of a Bayesian hyperparameter inferring the underlying distribution of an identically and independently distributed finite random variable. For this we embed both the Bayesian hyper-parameter updating process and the random data process into a Markov chain. The original publication by Bertschinger et al. (2006) mentioned that NTIC may be able to capture an abstract notion of modeling that is agnostic to the specific internal structure of and existence of explicit representations within the modeling process. The Bayesian hyperparameter is of interest since it has a well defined interpretation as a model of the data process and at the same time its dynamics can be specified without reference to this interpretation. On the one hand we show explicitly that the NTIC of the hyperparameter increases indefinitely over time. On the other hand we attempt to establish a connection between a quantity that is a feature of the interpretation of the hyperparameter as a model, namely the information gain, and the one-step pointwise NTIC which is a quantity that does not depend on this interpretation. We find that in general we cannot use the one-step pointwise NTIC as an indicator for information gain. We hope this exploratory work can lead to further rigorous studies of the relation between NTIC and modeling.
