  Dependency networks (Heckerman et al., 2000) are potential probabilistic
graphical models for systems comprising a large number of variables. Like
Bayesian networks, the structure of a dependency network is represented by a
directed graph, and each node has a conditional probability table. Learning and
inference are realized locally on individual nodes; therefore, computation
remains tractable even with a large number of variables. However, the
dependency network's learned distribution is the stationary distribution of a
Markov chain called pseudo-Gibbs sampling and has no closed-form expressions.
This technical disadvantage has impeded the development of dependency networks.
In this paper, we consider a certain manifold for each node. Then, we can
interpret pseudo-Gibbs sampling as iterative m-projections onto these
manifolds. This interpretation provides a theoretical bound for the location
where the stationary distribution of pseudo-Gibbs sampling exists in
distribution space. Furthermore, this interpretation involves structure and
parameter learning algorithms as optimization problems. In addition, we compare
dependency and Bayesian networks experimentally. The results demonstrate that
the dependency network and the Bayesian network have roughly the same
performance in terms of the accuracy of their learned distributions. The
results also show that the dependency network can learn much faster than the
Bayesian network.
