Integrating Logic and Probability: Algorithmic Improvements in Markov Logic Networks

This dissertation proposes novel algorithms for learning and inference in Markov Logic Networks. Statistical Relational Learning challenges one of the most important problems of Machine Learning since its birth: integrating logic and probability in learning. Markov Logic is a powerful representation formalism that combines full first-order logic with probabilistic graphical models by attaching weights to first-order formulas and viewing these as templates for features of Markov Networks (MNs). Markov Logic Networks (MLNs) together with a set of constants define ground MNs. MLNs preserve the expressivity of first-order logic and take advantage of probabilistic graphical models algorithms being therefore a powerful model for dealing with structured, noisy and uncertain data. The rich expressivity of MLNs comes at the cost of learning and inference. Structure learning is the task of learning the logical clauses together with their weights and is a very computationally hard task involving a search in a huge space of hypothesis with many local optima for the evaluation function. Therefore robust algorithms for structure learning of MLNs are needed. This dissertation proposes a novel generative structure learning algorithm based on the iterated local search metaheuristic. Extensive empirical study using real-world benchmark datasets show that the algorithm improves predictive accuracy and learning time compared to the state-of-the-art algorithms. Generative structure learning algorithms optimize the joint distribution of all the variables. This can lead to suboptimal results for predictive tasks because of the mismatch between the objective function used (likelihood or a function thereof) and the goal of classification (maximizing accuracy or conditional likelihood). In contrast discriminative approaches maximize the conditional likelihood of a set of outputs given a set of inputs and this often produces better results for prediction problems. Unfortunately, the computational cost of optimizing structure and parameters for conditional likelihood is prohibitive. This disseratation proposes novel discriminative structure learning algorithms based on the simple approximation of choosing structures by maximizing conditional likelihood while setting parameters by maximum likelihood. Extensive experiments in real-world domains show that the proposed discriminative algorithms improve over state-of-the-art generative structure learning and discriminative weight learning algorithms. Inference in graphical models is NP-hard. For MLNs, MAP inference can be performed through SAT solvers. This dissertation proposes the IRoTS algorithm for MAP inference in MLNs and shows through experiments that it is a high performing algorithm by improving over the state-of-the-art existing algorithm in terms of solutions quality and inference running times. Moreover in statistical relational learning, probabilistic and deterministic dependencies must be handled. This dissertation extends IRoTS by proposing MC-IRoTS, an algorithm that combines MCMC methods and SAT solvers for the problem of conditional inference in MLNs. Empirical evaluation on real-world data shows good improvements towards the state-of-the-art algorithm for conditional inference in MLNs.