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Optimal sequential probability assignment for individual sequences

机译：单个序列的最佳顺序概率分配

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摘要

The problem of sequential probability assignment for individual sequences is investigated. The authors compare the probabilities assigned by any sequential scheme to the performance of the best "batch" scheme (model) in some class. For the class of finite-state schemes and other related families, they derive a deterministic performance bound, analogous to the classical (probabilistic) minimum description length (MDL) bound. It holds for "most" sequences, similarly to the probabilistic setting, where the bound holds for "most" sources in a class. It is shown that the bound can be attained both pointwise and sequentially for any model family in the reference class and without any prior knowledge of its order. This is achieved by a universal scheme based on a mixing approach. The bound and its sequential achievability establish a completely deterministic significance to the concept of predictive MDL.
机译：研究了单个序列的顺序概率分配问题。作者将任何顺序方案分配的概率与某个类中最佳“批处理”方案（模型）的性能进行比较。对于一类有限状态方案和其他相关族，它们派生出确定性性能范围，类似于经典（概率）最小描述长度（MDL）范围。它适用于“最”序列，与概率设置类似，其中界限适用于类中的“最”源。结果表明，对于参考类中的任何模型族，都可以逐点和顺序地获得边界，而无需事先知道其顺序。这是通过基于混合方法的通用方案来实现的。界限及其顺序可实现性对预测MDL概念建立了完全确定的意义。

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