Discrete MDL Predicts in Total Variation

Details Discrete MDL Predicts in Total Variation Discrete MDL Predicts in Total Variation

2009-09-25

arxiv.org/abs/0909.4588v1

Advances in Neural Information Processing Systems 22 (NIPS 2009) pages 817-825

Mathematics

Probability

15 LaTeX pages

Scientific paper

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.

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