Bandit-based Monte-Carlo structure learning of probabilistic logic programs

Abstract

Probabilistic logic programming can be used to model domains with complex and uncertain relationships among entities. While the problem of learning the parameters of such programs has been considered by various authors, the problem of learning the structure is yet to be explored in depth. In this work we present an approximate search method based on a one-player game approach, called LEMUR. It sees the problem of learning the structure of a probabilistic logic program as a multi-armed bandit problem, relying on the Monte-Carlo tree search UCT algorithm that combines the precision of tree search with the generality of random sampling. LEMUR works by modifying the UCT algorithm in a fashion similar to FUSE, that considers a finite unknown horizon and deals with the problem of having a huge branching factor. The proposed system has been tested on various real-world datasets and has shown good performance with respect to other state of the art statistical relational learning approaches in terms of classification abilities.

Probabilistic inductive constraint logic

“…• We performed tests on the datasets of Nguembang Fadja and Riguzzi (2018) plus the Bongard dataset (Bongard 1970), to which the Bongard Problem of Example 1 is inspired. Note that SLIPCOVER, LIFTCOVER and LEMUR can be seen as a baseline for comparison with respect to PASCAL, since they have already been compared with many stateof-art systems in our previous works (Bellodi and Riguzzi 2015;Di Mauro et al 2015), demonstrating that they were competitive or superior with respect to the MLNs learning systems.…”

“…LIFTCOVER can exploit either an expectation maximization (EM) algorithm (Dempster et al 1977) or L-BFGS (Nocedal 1980) to maximize the log-likelihood during parameter learning, so results show both variants. LEMUR settings can be found in subsection 7.1 of Di Mauro et al (2015) for the three datasets in common (Carcinogenesis, Mondial, Mutagenesis).…”

“…LSM and BUSL were also considered, but they are not included in the tables because they were not able to complete the task due to an out of memory error. LEMUR, MLN-BC, MLN-BT results are taken from Tables 3, 4 and 6 of Di Mauro et al (2015). Table 10 shows the p-value of a paired two-tailed t-test of the difference in AUC-PR and AUC-ROC between PASCAL and TILDE on all datasets, except for Carcinogenesis/Bongard, where we did not apply cross-validation, and Sisyb, where we got the same AUC values over all folds with both algorithms.…”

“…The head of each clause in a LPAD is composed of a disjunction of logical atoms, each annotated with the probability of being true when the body holds; probabilities in the head must sum up to 1. LEMUR (Di Mauro et al 2015) learns LPADs by means of a Monte Carlo tree search algorithm. LIFTCOVER (Nguembang Fadja and Riguzzi 2018) performs structure learning of liftable PLP programs, characterized by clauses all having a single atom of the same predicate in the head, annotated with a probability.…”

Using SWISH to Realize Interactive Web-based Tutorials for Logic-based Languages

“…EMBLEM (Bellodi and Riguzzi 2013) performs parameter learning in cplint on SWISH using a special dynamic programming algorithm operating on BDDs. For structure learning, cplint on SWISH includes SLIPCOVER (Bellodi and Riguzzi 2015), which performs a search in the space of clauses and scores them using the likelihood of the data after parameter learning by EMBLEM, and LEMUR (Di Mauro et al 2015), which is similar to SLIPCOVER but uses Monte Carlo tree search.…”