Learning probabilistic logic programming languages is receiving an increasing attention, and systems are available for learning the parameters (PRISM, LeProbLog, LFI-ProbLog and EMBLEM) or both structure and parameters (SEM-CP-logic and SLIPCASE) of these languages. In this paper we present the algorithm SLIPCOVER for “Structure LearnIng of Probabilistic logic programs by searChing OVER the clause space.” It performs a beam search in the space of probabilistic clauses and a greedy search in the space of theories using the log likelihood of the data as the guiding heuristics. To estimate the log likelihood, SLIPCOVER performs Expectation Maximization with EMBLEM. The algorithm has been tested on five real world datasets and compared with SLIPCASE, SEM-CP-logic, Aleph and two algorithms for learning Markov Logic Networks (Learning using Structural Motifs (LSM) and ALEPH++ExactL1). SLIPCOVER achieves higher areas under the precision-recall and receiver operating characteristic curves in most cases.
SEM-CP-logic @cite_46 learns parameters and structure of ground CP-logic programs. It performs learning by considering the Bayesian networks equivalent to CP-logic programs and by applying techniques for learning Bayesian networks. In particular, it applies the Structural Expectation Maximization (SEM) algorithm @cite_57 : it iteratively generates refinements of the equivalent Bayesian network and it greedily chooses the one that maximizes the BIC score @cite_5 . In SLIPCOVER, we used the LL as a score because experiments with BIC were giving inferior results. Moreover, SLIPCOVER differs from SEM-CP-logic also because it searches the clause space and it refines clauses with standard ILP refinement operators, which allow to learn non ground theories.
@cite_57 @cite_5 @cite_46
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Causal relations are present in many application domains. Causal Probabilistic Logic (CP-logic) is a probabilistic modeling language that is especially designed to express such relations. This paper investigates the learning of CP-logic theories (CP-theories) from training data. Its first contribution is SEM-CP-logic, an algorithm that learns CP-theories by leveraging Bayesian network (BN) learning techniques. SEM-CP-logic is based on a transformation between CP-theories and BNs. That is, the method applies BN learning techniques to learn a CP-theory in the form of an equivalent BN. To this end, certain modifications are required to the BN parameter learning and structure search, the most important one being that the refinement operator used by the search must guarantee that the constructed BNs represent valid CP-theories. The paper's second contribution is a theoretical and experimental comparison between CP-theory and BN learning. We show that the most simple CP-theories can be represented with BNs consisting of noisy-OR nodes, while more complex theories require close to fully connected networks (unless additional unobserved nodes are introduced in the network). Experiments in a controlled artificial domain show that in the latter cases CP-theory learning with SEM-CP-logic requires fewer training data than BN learning. We also apply SEM-CP-logic in a medical application in the context of HIV research, and show that it can compete with state-of-the-art methods in this domain. We propose a logical mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm. Markov Logic Networks (MLNs) combine Markov networks and first-order logic by attaching weights to first-order formulas and viewing these as templates for features of Markov networks. Learning the structure of MLNs is performed by state-of-the-art methods by maximizing the likelihood of a relational database. This can lead to suboptimal results given prediction tasks. On the other hand better results in prediction problems have been achieved by discriminative learning of MLNs weights given a certain structure. In this paper we propose an algorithm for learning the structure of MLNs discriminatively by maximimizing the conditional likelihood of the query predicates instead of the joint likelihood of all predicates. The algorithm chooses the structures by maximizing conditional likelihood and sets the parameters by maximum likelihood. Experiments in two real-world domains show that the proposed algorithm improves over the state-of-the-art discriminative weight learning algorithm for MLNs in terms of conditional likelihood. We also compare the proposed algorithm with the state-of-the-art generative structure learning algorithm for MLNs and confirm the results in [22] showing that for small datasets the generative algorithm is competitive, while for larger datasets the discriminative algorithm outperfoms the generative one. Relational learning can be described as the task of learning first-order logic rules from examples. It has enabled a number of new machine learning applications, e.g. graph mining and link analysis. Inductive Logic Programming (ILP) performs relational learning either directly by manipulating first-order rules or through propositionalization, which translates the relational task into an attribute-value learning task by representing subsets of relations as features. In this paper, we introduce a fast method and system for relational learning based on a novel propositionalization called Bottom Clause Propositionalization (BCP). Bottom clauses are boundaries in the hypothesis search space used by ILP systems Progol and Aleph. Bottom clauses carry semantic meaning and can be mapped directly onto numerical vectors, simplifying the feature extraction process. We have integrated BCP with a well-known neural-symbolic system, C-IL2P, to perform learning from numerical vectors. C-IL2P uses background knowledge in the form of propositional logic programs to build a neural network. The integrated system, which we call CILP++, handles first-order logic knowledge and is available for download from Sourceforge. We have evaluated CILP++ on seven ILP datasets, comparing results with Aleph and a well-known propositionalization method, RSD. The results show that CILP++ can achieve accuracy comparable to Aleph, while being generally faster, BCP achieved statistically significant improvement in accuracy in comparison with RSD when running with a neural network, but BCP and RSD perform similarly when running with C4.5. We have also extended CILP++ to include a statistical feature selection method, mRMR, with preliminary results indicating that a reduction of more than 90 of features can be achieved with a small loss of accuracy.