Markov logic: theory, algorithms and applications

AI systems need to reason about complex objects and explicitly handle uncertainty. First-order logic handles the first and probability the latter. Combining the two has been a longstanding goal of AI research. Markov logic [86] combines the power of first-order logic and Markov networks by attaching real-valued weights to formulas in first-order logic. Markov logic can be seen as defining templates for ground Markov networks.For any representation language to be useful, it should be (a) sufficiently expressive, (b) amenable to the design of fast learning and inference algorithms and, (c) easy to use in real-world domains. In this dissertation, we address all these three aspects in the context of Markov logic.On the theoretical front, we extend Markov logic semantics to handle infinite domains. The original formulation of Markov logic deals only with finite domains. This is a limitation on the full first-order logic semantics. Borrowing ideas from the physics literature, we generalize Markov logic to the case of infinite domains.On the algorithmic side, we provide efficient inference and learning algorithms for Markov logic. The naive approach to inference in Markov logic is to ground out the domain theory and then apply propositional inference techniques. This leads to an explosion in time and memory. We present two algorithms: LazySAT (lazy WalkSAT) and lifted inference, which exploit the structure of the network to significantly improve the time and memory cost of inference. LazySAT, as the name suggests, grounds out the theory lazily, thereby saving very large amounts of memory without compromising speed. Lifted inference is a first-order (lifted) version of ground inference, where inference is carried out over clusters of nodes about which we have the same information. This yields significant improvements in both time and memory. For learning the parameters (weights) of a Markov logic network, we propose a novel method based on the voted perceptron algorithm of Collins (2002).On the application side, we demonstrate the effective use of Markov logic to two real-world problems: (a) providing a unified solution to the problem of entity resolution, and (b) identifying social relationships in image collections.