无限参数复杂性下MDL模型选择的实证研究
An Empirical Study of MDL Model Selection with Infinite Parametric Complexity
摘要：
参数复杂性是MDL模型选择的核心概念。在实践中，它经常被证明是无限的，即使是非常简单的模型，如泊松和几何家庭。在这种情况下，不能使用基于NML的MDL模型选择和基于Jeffreys先验的贝叶斯推理。已经提出了几种解决这个问题的方法。我们进行实验，以比较和评估其行为的小样本量。我们发现插件预测代码的行为非常糟糕;限制NML模型表现得很好，但如果结果验证了其理论动机，则值得怀疑。Jeffreys先验不适当的贝叶斯模型是最可靠的。
英文摘要：
Parametric complexity is a central concept in MDL model selection. In practice it often turns out to be infinite, even for quite simple models such as the Poisson and Geometric families. In such cases, MDL model selection as based on NML and Bayesian inference based on Jeffreys' prior can not be used. Several ways to resolve this problem have been proposed. We conduct experiments to compare and evaluate their behaviour on small sample sizes. We find interestingly poor behaviour for the plug-in predictive code; a restricted NML model performs quite well but it is questionable if the results validate its theoretical motivation. The Bayesian model with the improper Jeffreys' prior is the most dependable.
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