Learning Markov Logic Networks Research Articles

Learning Mixtures of MLNs

Weight learning is a challenging problem in Markov Logic Networks (MLNs) due to the large size of the ground propositional probabilistic graphical model that underlies the first-order representation of MLNs. Though more sophisticated weight learning methods that use lifted inference have been proposed, such methods can typically scale up only in the absence of evidence, namely in generative weight learning. In discriminative learning, where the evidence typically destroys symmetries, existing approaches are lacking in scalability. In this paper, we propose a novel, intuitive approach for learning MLNs discriminatively by utilizing approximate symmetries. Specifically, we reduce the size of the training database by clustering approximately symmetric atoms together and selecting a representative atom from each cluster. However, each choice made from the clusters induces a different distribution, increasing the uncertainty in our learned model. To reduce this uncertainty, we learn a finite mixture model by stacking the different distributions, where the parameters of the model are learned using an EM approach. Our results on several benchmarks show that our approach is much more scalable and accurate as compared to existing state-of-the-art MLN learning methods.

Lifted generative learning of Markov logic networks

Markov logic networks (MLNs) are a well-known statistical relational learning formalism that combines Markov networks with first-order logic. MLNs attach weights to formulas in first-order logic. Learning MLNs from data is a challenging task as it requires searching through the huge space of possible theories. Additionally, evaluating a theory's likelihood requires learning the weight of all formulas in the theory. This in turn requires performing probabilistic inference, which, in general, is intractable in MLNs. Lifted inference speeds up probabilistic inference by exploiting symmetries in a model. We explore how to use lifted inference when learning MLNs. Specifically, we investigate generative learning where the goal is to maximize the likelihood of the model given the data. First, we provide a generic algorithm for learning maximum likelihood weights that works with any exact lifted inference approach. In contrast, most existing approaches optimize approximate measures such as the pseudo-likelihood. Second, we provide a concrete parameter learning algorithm based on first-order knowledge compilation. Third, we propose a structure learning algorithm that learns liftable MLNs, which is the first MLN structure learning algorithm that exactly optimizes the likelihood of the model. Finally, we perform an empirical evaluation on three real-world datasets. Our parameter learning algorithm results in more accurate models than several competing approximate approaches. It learns more accurate models in terms of test-set log-likelihood as well as prediction tasks. Furthermore, our tractable learner outperforms intractable models on prediction tasks suggesting that liftable models are a powerful hypothesis space, which may be sufficient for many standard learning problems.

Gradient-based boosting for statistical relational learning: the Markov logic network and missing data cases

Recent years have seen a surge of interest in Statistical Relational Learning (SRL) models that combine logic with probabilities. One prominent and highly expressive SRL model is Markov Logic Networks (MLNs), but the expressivity comes at the cost of learning complexity. Most of the current methods for learning MLN structure follow a two-step approach where first they search through the space of possible clauses (i.e. structures) and then learn weights via gradient descent for these clauses. We present a functional-gradient boosting algorithm to learn both the weights (in closed form) and the structure of the MLN simultaneously. Moreover most of the learning approaches for SRL apply the closed-world assumption, i.e., whatever is not observed is assumed to be false in the world. We attempt to open this assumption. We extend our algorithm for MLN structure learning to handle missing data by using an EM-based approach and show this algorithm can also be used to learn Relational Dependency Networks and relational policies. Our results in many domains demonstrate that our approach can effectively learn MLNs even in the presence of missing data.

Learning Markov logic networks with limited number of labeled training examples

Markov Logic Networks (MLN) is a unified framework integrating first-order logic and probabilistic inference. Most existing methods of MLN learning are supervised approaches requiring a large amount of training examples, leading to a substantial amount of human effort for preparing these training examples. To reduce such human effort, we have developed a semi-supervised framework for learning an MLN, in particular structure learning of MLN, from a set of unlabeled data and a limited number of labeled training examples. To achieve this, we aim at maximizing the expected pseudo-log-likelihood function of the observation from the set of unlabeled data, instead of maximizing the pseudo-log-likelihood function of the labeled training examples, which is commonly used in supervised learning of MLN. To evaluate our proposed method, we have conducted experiments on two different datasets and the empirical results demonstrate that our framework is effective, outperforming existing approach which considers labeled training examples alone.

Structure learning of probabilistic logic programs by searching the clause space

AbstractLearning 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.

Improving Scalability of Discriminative Learning Markov Logic Networks for Open Information Extraction

Improving Scalability of Discriminative Learning Markov Logic Networks for Open Information Extraction

Learning graphical models for relational data via lattice search

Many machine learning applications that involve relational databases incorporate first-order logic and probability. Relational extensions of graphical models include Parametrized Bayes Net (Poole in IJCAI, pp. 985---991, 2003), Probabilistic Relational Models (Getoor et al. in Introduction to statistical relational learning, pp. 129---173, 2007), and Markov Logic Networks (MLNs) (Domingos and Richardson in Introduction to statistical relational learning, 2007). Many of the current state-of-the-art algorithms for learning MLNs have focused on relatively small datasets with few descriptive attributes, where predicates are mostly binary and the main task is usually prediction of links between entities. This paper addresses what is in a sense a complementary problem: learning the structure of a graphical model that models the distribution of discrete descriptive attributes given the links between entities in a relational database. Descriptive attributes are usually nonbinary and can be very informative, but they increase the search space of possible candidate clauses. We present an efficient new algorithm for learning a Parametrized Bayes Net that performs a level-wise search through the table join lattice for relational dependencies. From the Bayes net we obtain an MLN structure via a standard moralization procedure for converting directed models to undirected models. Learning MLN structure by moralization is 200---1000 times faster and scores substantially higher in predictive accuracy than benchmark MLN algorithms on five relational databases.

Structure Learning for Markov Logic Networks with Many Descriptive Attributes

Many machine learning applications that involve relational databases incorporate first-order logic and probability. Markov Logic Networks (MLNs) are a prominent statistical relational model that consist of weighted first order clauses. Many of the current state-of-the-art algorithms for learning MLNs have focused on relatively small datasets with few descriptive attributes, where predicates are mostly binary and the main task is usually prediction of links between entities. This paper addresses what is in a sense a complementary problem: learning the structure of an MLN that models the distribution of discrete descriptive attributes on medium to large datasets, given the links between entities in a relational database. Descriptive attributes are usually nonbinary and can be very informative, but they increase the search space of possible candidate clauses. We present an efficient new algorithm for learning a directed relational model (parametrized Bayes net), which produces an MLN structure via a standard moralization procedure for converting directed models to undirected models. Learning MLN structure in this way is 200-1000 times faster and scores substantially higher in predictive accuracy than benchmark algorithms on three relational databases.