全变差中的离散MDL预测
Discrete MDL Predicts in Total Variation
摘要：
最小描述长度（MDL）原则选择具有最短代码的模型用于数据加模型。我们发现，对于可数的一类模型，MDL预测接近真实的分布在很强的意义上。结果是完全通用的。不需要对模型类进行独立性、遍历性、平稳性、可识别性或其他假设。更正式地说，我们表明，对于任何可数类的模型，由MDL（或MAP）选择的分布渐近预测（合并）在类中的真实措施在全变差的距离。对非i.i.d.的影响讨论了时间序列预测、判别学习和强化学习等领域。
英文摘要：
The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result is completely general. No independence, ergodicity, stationarity, identifiability, or other assumption on the model class need to be made. More formally, we show that for any countable class of models, the distributions selected by MDL (or MAP) asymptotically predict (merge with) the true measure in the class in total variation distance. Implications for non-i.i.d. domains like time-series forecasting, discriminative learning, and reinforcement learning are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
