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Online Bayesian Inference for the Parameters of PRISM Programs

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7207)

Abstract

This paper presents a method for approximating posterior distributions over the parameters of a given PRISM program. A sequential approach is taken where the distribution is updated one datapoint at a time. This makes it applicable to online learning situations where data arrives over time. The method is applicable whenever the prior is a mixture of products of Dirichlet distributions. In this case the true posterior will be a mixture of very many such products. An approximation is effected by merging products of Dirichlet distributions. An analysis of the quality of the approximation is presented. Due to the heavy computational burden of this approach, the method has been implemented in the Mercury logic programming language. Initial results using a hidden Markov model are presented.

Keywords

  • Posterior Distribution
  • Logic Program
  • Latent Dirichlet Allocation
  • Dirichlet Distribution
  • Ground Instance

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Blei, D.M., Ng, A.Y., Jordan, M.I.: Latent Dirichlet allocation. Journal of Machine Learning Research 3, 993–1022 (2003)

    MATH  Google Scholar 

  2. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley (1991)

    Google Scholar 

  3. Cowell, R.G., Dawid, A.P., Sebastiani, P.: A comparison of sequential learning methods for incomplete data. In: Bernado, J.M., Berger, J., Dawid, A.P., Smith, A.F.M. (eds.) Bayesian Statistics, vol. 5, pp. 533–541. Clarendon Press, Oxford (1995)

    Google Scholar 

  4. Cowell, R.G.: Mixture reduction via predictive scores. Statistics and Computing 8, 97–103 (1998)

    CrossRef  Google Scholar 

  5. Cowell, R.G., Philip Dawid, A., Lauritzen, S.L., Spiegelhalter, D.J.: Probabilistic Networks and Expert Systems. Springer, New York (1999)

    MATH  Google Scholar 

  6. Penny, W.D.: KL-divergences of Normal, Gamma, Dirichlet and Wishart densities. Technical report, University College London (2001)

    Google Scholar 

  7. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2011) ISBN 3-900051-07-0

    Google Scholar 

  8. Sato, T., Kameya, Y.: Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research 15, 391–454 (2001)

    MathSciNet  MATH  Google Scholar 

  9. Somogyi, Z., Henderson, F., Conway, T.: The execution algorithm of Mercury: an efficient purely declarative logic programming language. Journal of Logic Programming 29(1-3), 17–64 (1996)

    CrossRef  MATH  Google Scholar 

  10. West, M.: Modelling with mixtures. In: Bernado, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (eds.) Bayesian Statistics, vol. 4, pp. 503–524. Clarendon Press, Oxford (1992)

    Google Scholar 

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© 2012 Springer-Verlag Berlin Heidelberg

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Cussens, J. (2012). Online Bayesian Inference for the Parameters of PRISM Programs. In: Muggleton, S.H., Tamaddoni-Nezhad, A., Lisi, F.A. (eds) Inductive Logic Programming. ILP 2011. Lecture Notes in Computer Science(), vol 7207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31951-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-31951-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31950-1

  • Online ISBN: 978-3-642-31951-8

  • eBook Packages: Computer ScienceComputer Science (R0)