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Markov Logic Networks

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Markov Logic Networks, by Matthew Richardson and Pedro Domingos.

Department of Computer Science and Engineering, University of Washington, Seattle.

Main Themes

  • Combining first-order logic and probabilistic graphical models to create a powerful representation for uncertain knowledge.
  • Introducing Markov logic networks (MLNs), a framework for representing and reasoning with this type of knowledge.
  • Describing algorithms for inference and learning in MLNs.
  • Illustrating the capabilities of MLNs on a real-world dataset.
  • Positioning MLNs as a general framework for statistical relational learning.

    • Most Important Ideas/Facts

    • MLNs bridge the gap between first-order logic, which is expressive but brittle, and probabilistic graphical models, which are good at handling uncertainty but not as expressive.
    • An MLN is a set of first-order logic formulas with associated weights, which define a probability distribution over possible worlds.
    • Higher weights correspond to stronger constraints, making worlds that satisfy the associated formulas more probable.
    • MLNs subsume both propositional probabilistic models and first-order logic as special cases.
    • Inference in MLNs can be performed using Markov Chain Monte Carlo (MCMC) methods, taking advantage of the logical structure to improve efficiency.
    • Weights can be learned from relational databases using maximum pseudo-likelihood estimation, which is more tractable than maximum likelihood estimation.
    • Inductive logic programming techniques, such as CLAUDIEN, can be used to learn the structure of MLNs.

      • Key Results

      • In experiments on a real-world dataset, MLNs outperformed purely logical and purely probabilistic methods on a link prediction task.
      • MLNs successfully combined human-provided knowledge with information learned from data.
      • Inference and learning in MLNs were shown to be computationally feasible for the dataset used.

        • Supporting Quotes

        • "Combining probability and first-order logic in a single representation has long been a goal of AI. Probabilistic graphical models enable us to efficiently handle uncertainty. First-order logic enables us to compactly represent a wide variety of knowledge. Many (if not most) applications require both."
        • "A Markov logic network is a first-order knowledge base with a weight attached to each formula, and can be viewed as a template for constructing Markov networks."
        • "From the point of view of probability, MLNs provide a compact language to specify very large Markov networks, and the ability to flexibly and modularly incorporate a wide range of domain knowledge into them."

          • Future Directions

          • Develop more efficient inference and learning algorithms for MLNs.
          • Explore the use of MLNs for other statistical relational learning tasks, such as collective classification, link-based clustering, social network modeling, and object identification.
          • Apply MLNs to a wider range of real-world problems in areas such as information extraction, natural language processing, vision, and computational biology.

            • Link

            https://homes.cs.washington.edu/~pedrod/papers/mlj05.pdf

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            One Paper a WeekBy Simón Muñoz