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Extra resources for Boosted Statistical Relational Learners: From Benchmarks to Data-Driven Medicine
Our algorithm for imitation learning using functional gradient boosting is called as TBRIL and is presented in Algorithm 7. Note that this is very similar to boosting RDNs, except that instead of going through each predicate in turn, we go through each parameterized action in turn and boost its conditional distribution. Algorithm TBoost is the main algorithm that iterates over all actions. For each action (k), it generates the examples for our regression tree learner (called using function FitRRT ) to get the new regression tree and updates its model (Λkm ).
The training time does not change for the different test-sets. As can be seen, for the complete dataset both boosting approaches (MLN-BT and MLN-BC) perform significantly better than other MLN learning techniques on the AUC-PR values. Current MLN learning algorithms on the other hand are able to achieve lower CLL values over the complete dataset by pushing the probabilities to 0, but are not able to differentiate between positive and negative examples as shown by the low AUC-PR values. We could not get BUSL to run on this data set.
As far as we are aware, this is the first work on combining EM with FGB for relational domains. 2 Structural EM for Relational Functional Gradients Recall that the Expectation-Maximization (EM) algorithm for standard graphical models proceeds in two steps. In the first “E” step, the expected values of the missing attributes are computed based on the current structure and parameters. These expected values are used in “M” step where the parameters (and possibly structure) are determined that maximize the loglikelihood.