Markov logic networks (MLNs) combine logic and probability by attaching weights to first-order clauses, and viewing these as templates for features of Markov networks. Learning MLN structure from a relational database involves learning the clauses and weights. The state-of-the-art MLN structure learners all involve some element of greedily generating candidate clauses, and are susceptible to local optima. To address this problem, we present an approach that directly utilizes the data in constructing candidates. A relational database can be viewed as a hypergraph with constants as nodes and relations as hyperedges. We find paths of true ground atoms in the hypergraph that are connected via their arguments. To make this tractable (there are exponentially many paths in the hypergraph), we lift the hypergraph by jointly clustering the constants to form higherlevel concepts, and find paths in it. We variabilize the ground atoms in each path, and use them to form clauses, which are evaluated using a pseudolikelihood measure. In our experiments on three real-world datasets, we find that our algorithm outperforms the state-of-the-art approaches. 1.

Abstract. Markov logic networks (MLNs) are an expressive representation for statistical relational learning that generalizes both first-order logic and graphical models. Existing discriminative weight learning methods for MLNs all try to learn weights that optimize the Conditional Log Likelihood (CLL) of the training examples. In this work, we present a new discriminative weight learning method for MLNs based on a max-margin framework. This results in a new model, Max-Margin Markov Logic Networks (M3LNs), that combines the expressiveness of MLNs with the predictive accuracy of structural Support Vector Machines (SVMs). To train the proposed model, we design a new approximation algorithm for lossaugmented inference in MLNs based on Linear Programming (LP). The experimental result shows that the proposed approach generally achieves higher F1 scores than the current best discriminative weight learner for MLNs. 1

Markov logic networks (MLNs) use firstorder formulas to define features of Markov networks. Current MLN structure learners can only learn short clauses (4-5 literals) due to extreme computational costs, and thus are unable to represent complex regularities in data. To address this problem, we present LSM, the first MLN structure learner capable of efficiently and accurately learning long clauses. LSM is based on the observation that relational data typically contains patterns that are variations of the same structural motifs. By constraining the search for clauses to occur within motifs, LSM can greatly speed up the search and thereby reduce the cost of finding long clauses. LSM uses random walks to identify densely connected objects in data, and groups them and their associated relations into a motif. Our experiments on three real-world datasets show that our approach is 2-5 orders of magnitude faster than the state-of-the-art ones, while achieving the same or better predictive performance. 1.

Abstract—Recent years have seen a surge of interest in Statistical Relational Learning (SRL) models that combine logic with probabilities. One prominent example is Markov Logic Networks (MLNs). While MLNs are indeed highly expressive, this expressiveness comes at a cost. Learning MLNs is a hard problem and therefore has attracted much interest in the SRL community. Current methods for learning MLNs follow a twostep approach: first, perform a search through the space of possible clauses and then learn appropriate weights for these clauses. We propose to take a different approach, namely to learn both the weights and the structure of the MLN simultaneously. Our approach is based on functional gradient boosting where the problem of learning MLNs is turned into a series of relational functional approximation problems. We use two kinds of representations for the gradients: clausebased and tree-based. Our experimental evaluation on several benchmark data sets demonstrates that our new approach can learn MLNs as good or better than those found with state-ofthe-art methods, but often in a fraction of the time.

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Statistical relational learning (SRL) is an emerging area of research that addresses the problem of learning from noisy structured/relational data. Markov logic networks (MLNs), sets of weighted clauses, are a simple but powerful SRL formalism that combines the expressivity of first-order logic with the flexibility of probabilistic reasoning. Most of the existing learning algorithms for MLNs are in the generative setting: they try to learn a model that maximizes the likelihood of the training data. However, most of the learning problems in relational data are discriminative. So to utilize the power of MLNs, we need discriminative learning methods that well match these discriminative tasks. In this proposal, we present two new discriminative learning algorithms for MLNs. The first one is a discriminative structure and weight learner for MLNs with non-recursive clauses. We use a variant of ALEPH, an off-the-shelf Inductive Logic Programming (ILP) system, to learn a large set of Horn clauses from the training data, then we apply an L1-regularization weight learner to select a small set of non-zero weight clauses that maximizes the conditional log-likelihood (CLL) of the training data. The experimental results show that our proposed algorithm outperforms existing learning methods for MLNs and traditional ILP systems in term of predictive accuracy, and its performance is comparable to stateof-the-art

Abstract Statistical Relational Learning (SRL) is a growing field in Machine Learning that aims at the integration of logic-based learning approaches with probabilistic graphical models. Markov Logic Networks (MLNs) are one of the state-of-the-art SRL models that combine first-order logic and Markov networks (MNs) by attaching weights to first-order formulas and viewing these as templates for features of MNs. Learning models in SRL consists in learning the structure (logical clauses in MLNs) and the parameters (weights for each clause in MLNs). Structure learning of MLNs is performed by maximizing a likelihood function (or a function thereof) over relational databases and MLNs have been successfully applied to problems in relational and uncertain domains. However, most complex domains are characterized by incomplete data. Until now SRL models have mostly used Expectation-Maximization (EM) for learning statistical parameters under missing values. Multistrategic learning in the relational setting has been a successful approach to dealing with complex problems where multiple inference mechanisms can help solve different subproblems. Abduction is an inference strategy that has been proven useful for completing missing values in observations. In this paper we propose two frameworks for integrating abduction in SRL models. The first tightly integrates logical abduction with structure and parameter learning of MLNs in a single step. During structure search guided by conditional likelihood, clause evaluation is performed by first trying to logically abduce missing values in the data and then by learning optimal pseudo-likelihood parameters using the completed data. The second approach integrates abduction with Structural EM of [17] by performing logical abductive inference in the E-step and then by trying to maximize parameters in the M-step.

In this paper we present a new algorithm for generatively learning the structure of Markov Logic Networks. This algorithm relies on a graph of predicates, which summarizes the links existing between predicates and on relational information between ground atoms in the training database. Candidate clauses are produced by means of a heuristical variabilization technique. According to our first experiments, this approach appears to be promising. 1

In recent years, there has been a surge of interest in combining statistical and relational learning approaches (Getoor & Taskar, 2007), driven by the realization that many applications require both. Recently,

Abstract. Most existing learning methods for Markov Logic Networks (MLNs) use batch training, which becomes computationally expensive and eventually infeasible for large datasets with thousands of training examples which may not even all fit in main memory. To address this issue, previous work has used online learning to train MLNs. However, they all assume that the model’s structure (set of logical clauses) is given, and only learn the model’s parameters. However, the input structure is usually incomplete, so it should also be updated. In this work, we present OSL—the first algorithm that performs both online structure and parameter learning for MLNs. Experimental results on two realworld datasets for natural-language field segmentation show that OSL outperforms systems that cannot revise structure. 1