Source
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
