两部分MDL码的逼近
Approximation of the Two-Part MDL Code
摘要：
对于给定的数据，通过连续的长度单调递减的两部分MDL码来逼近最优的两部分MDL码，具有以下性质：（i）每一步的计算可能需要任意长的时间;（ii）我们可能不知道何时达到最优，或者我们是否会达到最优;（iii）生成的模型序列可能不会单调地改善拟合优度;但是（iv）与最优值相关联的模型具有（几乎）最佳拟合优度。为了表达单个数据集的单个模型的实际有趣的拟合优度，我们必须依赖Kolmogorov复杂性。
英文摘要：
Approximation of the optimal two-part MDL code for given data, through successive monotonically length-decreasing two-part MDL codes, has the following properties: (i) computation of each step may take arbitrarily long; (ii) we may not know when we reach the optimum, or whether we will reach the optimum at all; (iii) the sequence of models generated may not monotonically improve the goodness of fit; but (iv) the model associated with the optimum has (almost) the best goodness of fit. To express the practically interesting goodness of fit of individual models for individual data sets we have to rely on Kolmogorov complexity.
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