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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Information Science and Technology / Faculty of Information Science and Technology >
Peer-reviewed Journal Articles, etc >
MDL convergence speed for Bernoulli sequences
| Title: | MDL convergence speed for Bernoulli sequences |
| Authors: | Poland, Jan Browse this author | | Hutter, Marcus Browse this author |
| Issue Date: | Jun-2006 |
| Publisher: | Springer |
| Journal Title: | Statistics and Computing |
| Volume: | 16 |
| Issue: | 2 |
| Start Page: | 161 |
| End Page: | 175 |
| Publisher DOI: | 10.1007/s11222-006-6746-3 |
| Abstract: | The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is finitely bounded, implying convergence with probability one, and (b) it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound (comparable to the one for Bayes mixtures) for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models. |
| Rights: | The original publication is available at www.springerlink.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/14562 |
| Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: Jan Poland
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