Learning Bayesian Networks with Restricted Causal Interactions
This work addresses computational efficiency issues for researchers and practitioners in probabilistic graphical modeling, but appears incremental as it builds on existing log-linear models and MML metrics.
The paper tackles the problem of exponential parameter growth in Bayesian network learning by proposing a method using log-linear local models and Minimum Message Length for structure learning of first-order networks with causal independence, achieving unspecified improvements in model complexity.
A major problem for the learning of Bayesian networks (BNs) is the exponential number of parameters needed for conditional probability tables. Recent research reduces this complexity by modeling local structure in the probability tables. We examine the use of log-linear local models. While log-linear models in this context are not new (Whittaker, 1990; Buntine, 1991; Neal, 1992; Heckerman and Meek, 1997), for structure learning they are generally subsumed under a naive Bayes model. We describe an alternative interpretation, and use a Minimum Message Length (MML) (Wallace, 1987) metric for structure learning of networks exhibiting causal independence, which we term first-order networks (FONs). We also investigate local model selection on a node-by-node basis.