This paper describes how a functional-gradient-based boosting algorithm can be used to learn weights of Markov logic networks (MLN). As opposed to earlier methods, which learn the structure of the clauses and the weights in two separate learning steps, the authors’ algorithm learns both the weights for the clauses and the structure of the MLN at the same time. The authors also address the closed-world assumption that is usually used in statistical relational learning, where everything that is not known to be true is assumed false. They do this by extending their algorithm to handle missing data by using an expectation maximization (EM)-based approach.

The algorithms are described in some detail, although worked examples would have been helpful. The critical elements are the definitions of the squared error functions required to compute the gradients. In the case of missing data, which the authors also call “hidden data,” separate gradients are used for hidden and observed groundings. The algorithms are compared to four state-of-the-art MLN structural learning models. In the case where there is no hidden data, all the datasets are real-world data, for example, data on students and professors in computer science. In the case of missing data, use is made of synthetic datasets as well as real-world data by randomly hiding certain groundings. The experimental results show that the authors’ algorithms achieve performance superior to other algorithms on the standard datasets used.