Margin-based first-order rule learning

We present a new margin-based approach to first-order rule learning. The approach addresses many of the prominent challenges in first-order rule learning, such as the computational complexity of optimization and capacity control. Optimizing the mean of the margin minus its variance, we obtain an algorithm linear in the number of examples and a handle for capacity control based on error bounds. A useful parameter in the optimization problem tunes how evenly the weights are spread among the rules. Moreover, the search strategy for including new rules can be adjusted flexibly, to perform variants of propositionalization or relational learning. The implementation of the system includes plugins for logical queries, graphs and mathematical terms. In extensive experiments, we found that, at least on the most commonly used toxicological datasets, overfitting is hardly an issue. In another batch of experiments, a comparison with margin-based ILP approaches using kernels turns out to be favorable. Finally, an experiment shows how many features are needed by propositionalization and relational learning approaches to reach a certain predictive performance.