Offline to Online Conversion
We consider the problem of converting offline estimators into an online predictor or estimator with small extra regret. Formally this is the problem of merging a collection of probability measures over strings of length 1,2,3,... into a single probability measure over infinite sequences. We describe various approaches and their pros and cons on various examples. As a side-result we give an elementary non-heuristic purely combinatoric derivation of Turing’s famous estimator. Our main technical contribution is to determine the computational complexity of online estimators with good guarantees in general.
KeywordsOffline online batch sequential probability estimation prediction time-consistency normalization tractable regret combinatorics Bayes Laplace Ristad Good-Turing
Unable to display preview. Download preview PDF.
- [AB09]Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press (2009)Google Scholar
- [AS74]Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions. Dover Publications (1974)Google Scholar
- [Grü07]Grünwald, P.D.: The Minimum Description Length Principle. The MIT Press, Cambridge (2007)Google Scholar
- [Hut05]Hutter, M.: Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Springer, Berlin (2005)Google Scholar
- [Hut09]Hutter, M.: Discrete MDL predicts in total variation. In: Advances in Neural Information Processing Systems 22 (NIPS 2009), pp. 817–825. Curran Associates, Cambridge (2009)Google Scholar
- [Hut14]Hutter, M.: Offline to online conversion. Technical report (2014), http://www.hutter1.net/publ/off2onx.pdf
- [Ris95]Ristad, E.S.: A natural law of succession. Technical Report CS-TR-495-95. Princeton University (1995)Google Scholar
- [San06]Santhanam, N.: Probability Estimation and Compression Involving Large Alphabets. PhD thesis, Univerity of California, San Diego, USA (2006)Google Scholar