Skip to main content

Offline to Online Conversion

  • Conference paper
Algorithmic Learning Theory (ALT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8776))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press (2009)

    Google Scholar 

  2. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions. Dover Publications (1974)

    Google Scholar 

  3. Barron, A.R., Cover, T.M.: Minimum complexity density estimation. IEEE Transactions on Information Theory 37, 1034–1054 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, S.F., Goodman, J.: An empirical study of smoothing techniques for language modeling. Computer Speech and Language 13, 359–394 (1999)

    Article  Google Scholar 

  5. Good, I.J.: The population frequencies of species and the estimation of population parameters. Biometrika 40(3/4), 237–264 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  6. GrĂĽnwald, P.D.: The Minimum Description Length Principle. The MIT Press, Cambridge (2007)

    Google Scholar 

  7. Hutter, M.: Optimality of universal Bayesian prediction for general loss and alphabet. Journal of Machine Learning Research 4, 971–1000 (2003)

    MathSciNet  Google Scholar 

  8. Hutter, M.: Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Springer, Berlin (2005)

    Google Scholar 

  9. 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 

  10. Hutter, M.: Offline to online conversion. Technical report (2014), http://www.hutter1.net/publ/off2onx.pdf

  11. Nadas, A.: On Turing’s formula for word probabilities. IEEE Transactions on Acoustics, Speech, and Signal Processing 33(6), 1414–1416 (1985)

    Article  MATH  Google Scholar 

  12. Poland, J., Hutter, M.: Asymptotics of discrete MDL for online prediction. IEEE Transactions on Information Theory 51(11), 3780–3795 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ryabko, D., Hutter, M.: On sequence prediction for arbitrary measures. In: Proc. IEEE International Symposium on Information Theory (ISIT 2007), pp. 2346–2350. IEEE, Nice (2007)

    Chapter  Google Scholar 

  14. Ristad, E.S.: A natural law of succession. Technical Report CS-TR-495-95. Princeton University (1995)

    Google Scholar 

  15. Santhanam, N.: Probability Estimation and Compression Involving Large Alphabets. PhD thesis, Univerity of California, San Diego, USA (2006)

    Google Scholar 

  16. Solomonoff, R.J.: Complexity-based induction systems: Comparisons and convergence theorems. IEEE Transactions on Information Theory IT-24, 422–432 (1978)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Hutter, M. (2014). Offline to Online Conversion. In: Auer, P., Clark, A., Zeugmann, T., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2014. Lecture Notes in Computer Science(), vol 8776. Springer, Cham. https://doi.org/10.1007/978-3-319-11662-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11662-4_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11661-7

  • Online ISBN: 978-3-319-11662-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics