Location of Repository

Inner Product Spaces for Bayesian Networks

By Atsuyoshi Nakamura, Michael Schmitt, Niels Schmitt, Hans Ulrich Simon, Ruhr-universität Bochum and Tommi Jaakkola


Bayesian networks have become one of the major models used for statistical inference. We study the question whether the decisions computed by a Bayesian network can be represented within a low-dimensional inner product space. We focus on two-label classification tasks over the Boolean domain. As main results we establish upper and lower bounds on the dimension of the inner product space for Bayesian networks with an explicitly given (full or reduced) parameter collection. In particular, these bounds are tight up to a factor of 2. For some nontrivial cases of Bayesian networks we even determine the exact values of this dimension. We further consider logistic autoregressive Bayesian networks and show that every sufficiently expressive inner product space must have dimension at least Ω(n 2), where n is the number of network nodes. We also derive the bound 2 Ω(n) for an artificial variant of this network, thereby demonstrating the limits of our approach and raising an interesting open question. As a major technical contribution, this work reveals combinatorial and algebraic structures within Bayesian networks such that known methods for the derivation of lower bounds on the dimension of inner product spaces can be brought into play. Keywords: dimension Bayesian network, inner product space, embedding, linear arrangement, Euclidean 1

Year: 2005
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://jmlr.org/papers/volume6... (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.