Stochastic Complexity
本文提出随机复杂度概念，定义为数据的最短描述长度，并证明其能提取观测数据中的所有有用信息，同时决定预测误差的下界。给出了抽象定义和两个基本定理，并描述了三种近似随机复杂度的模型选择准则。
SUMMARY It is argued that all the useful information in observed data that can be extracted with a selected class of modeled distributions, will be obtained if we calculate the stochastic complexity, defined to be the shortest description length of the data. The same quantity also determines the greatest lower bound for prediction errors when the data are sequentially predicted. An abstract definition of stochastic complexity is given along with two fundamental theorems which justify the notion. Further, three explicit model selection criteria to approximate the stochastic complexity are described and the associated optimal models are interpreted to define asymptotically sufficient statistics for the data.