Learning Parameters for Relational Probabilistic Models with Noisy-Or Combining Rule

Languages that combine predicate logic with probabilities are needed to succinctly represent knowledge in many real-world domains. We consider a formalism based on universally quantified conditional influence statements that capture local interactions between object attributes. The effects of different conditional influence statements can be combined using rules such as Noisy-OR. To combine multiple instantiations of the same rule we need other combining rules at a lower level. In this paper we derive and implement algorithms based on gradient-descent and EM for learning the parameters of these multi-level combining rules. We compare our approaches to learning in Markov Logic Networks and show superior performance in multiple domains.