Abstract
Current methods to estimate conditional probabilities from incomplete data rely on iterative algorithms, such as the EM algorithm and Gibbs Sampling, which, although very reliable, pose convergence problems and assume that data are missing at random. This paper describes a deterministic method, called Bound and Collapse (BC), which relaxes the assumption that data are missing at random, does not pose problem of convergence rate and detection, and has a computational cost independent of the number of missing data.
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References
Cooper, G.F. & Herskovitz, E. (1992). A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9, 309–347.
Dempster, A., Laird, D. & and Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1–38.
Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.
Little, R.J.A. & Rubin, D.B. (1987). Statistical Analysis with Missing Data. New York: Wiley
Ramoni, M. & Sebastiani, P. (1996). Robust learning with missing data. Technical Report KMi-TR-28, Knowledge Media Institute, The Open University.
Thiesson, B. (1995). Accelerated quantification of Bayesian networks with incomplete data. In: Proceedings of first international conference on knowledge discovery and data mining, 306–11. San Mateo: Morgan Kaufman
Thomas, A., Spiegelhalter, D.J., & Gilks, W.D. (1992). Bugs: A program to perform Bayesian inference using Gibbs Sampling. In: Bayesian Statistics 4, 837–42. Oxford: Clarendon Press.
Whittaker, J. (1990). Graphical Models in Applied Multivariate Statistics. New York: Wiley.
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© 1998 Springer-Verlag Berlin Heidelberg
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Sebastiani, P., Ramoni, M. (1998). Induction of Graphical Models from Incomplete Samples. In: Payne, R., Green, P. (eds) COMPSTAT. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-01131-7_63
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DOI: https://doi.org/10.1007/978-3-662-01131-7_63
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1131-5
Online ISBN: 978-3-662-01131-7
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