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Bayesian Networks with Degenerate Gaussian Distributions

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  • Christopher Raphael

    (University of Massachusetts at Amherst)

Abstract

Bayesian networks compute marginal distributions through the “message passing” algorithm—a series of local calculations involving neighboring cliques of variables in a clique tree. In this work, these message passing computations are extended to the case of degenerate Gaussian potentials which are multivariate Gaussian densities that can have two different kinds of degeneracies corresponding to projections with zero variance and projections with infinite variance. The basic operations of the message passing algorithm, such as representing conditional distributions, extending potentials, and conditioning on observations, create or operate on potentials with various kinds of degeneracies thereby demonstrating the need for such methodology. Computer implementation of this scheme follows easily from the details within and some computational aspects are discussed. We also demonstrate an application of our methodology to automatic musical accompaniment.

Suggested Citation

  • Christopher Raphael, 2003. "Bayesian Networks with Degenerate Gaussian Distributions," Methodology and Computing in Applied Probability, Springer, vol. 5(2), pages 235-263, June.
    • Handle: RePEc:spr:metcap:v:5:y:2003:i:2:d:10.1023_a:1024565903746
    DOI: 10.1023/A:1024565903746
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    References listed on IDEAS

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