Context-specific independence in Bayesian networks

  • Authors:

  • Craig Boutilier;Nir Friedman;Moises Goldszmidt;Daphne Koller

  • Affiliations:

  • Dept. of Computer Science, University of British Columbia, Vancouver, BC;Dept. of Computer Science, Stanford University, Stanford, CA;SRI International, Menlo Park, CA;Dept. of Computer Science, Stanford University, Stanford, CA

  • Venue:
  • UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
  • Year:
  • 1996

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Abstract

Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution, This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables, In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme--tree-structured CPTs-- for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms, in particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on outset conditioning.