Random Regression for Bayes Nets Applied to Relational Data

Bayes nets (BNs) for relational databases are a major research topic in machine learning and artificial intelligence. When the database exhibits cyclic probabilistic dependencies, the usual Bayes net product formula does not define valid inferences. In this paper we describe and evaluate a new approach to defining Bayes net relational inference in the presence of cyclic dependencies. The key idea is to define the random regression logprobability of a target node value (unnormalized) as the expected log-probability (unnormalized) associated with a random instantiation of the node’s Markov blanket. We provide a tractable closed form for random regression, which is equivalent to a loglinear model, but with the predictors scaled to be instance frequencies of relational patterns (features), rather than instance counts. Instance counts are used in inference models based on Markov networks. We carried out an empirical comparison on five benchmark databases with (i) weights as log-conditional probabilities using maximum likelihood estimates vs. (ii) general weights learned with Markov net methods. Maximum likelihood estimates took seconds to compute in comparison to hours for Markov net learning. With the frequency scaling, predictive accuracy for the conditional probability weights was competitive with the general weights.