Skip to content
Last Dictionary
Plane
Symbolic & Classical AIMachine Learning

Markov logic network

nounAlso: MLN, Markov logic, statistical relational learning, StarAI

In plain wordsA way of combining logical rules with probabilities, so that a rule like 'friends usually like the same music' can sometimes be broken, with each rule given a weight saying how strongly it holds.

  1. A probabilistic logic in which every formula of first-order logicfirst-order logic, n.: A precise formal language for statements about objects and their relations, using 'for all' and 'there exists', such as 'every person has a mother'. It is the standard logic of mathematics and of classic AI. carries a real-valued weight expressing how strongly it should hold. Instantiating the formulas for every combination of a finite set of constants turns the weighted theory into a Markov random fieldMarkov random field, n.: A model of many linked uncertain quantities, such as neighboring pixels in a photo, in which each one depends directly only on its neighbors, with no notion of which one causes which. — a binary variable for each ground atom, a feature for each ground formula — in which a possible world's probability is proportional to the exponential of the weighted count of formulas it satisfies. Hard logical constraints are the limit of infinite weights; a world that violates a soft formula becomes less probable rather than impossible. Weights are learned from relational data, and inference uses Markov chain Monte CarloMarkov chain Monte Carlo, n.: A family of methods for drawing random examples from a complicated probability distribution by taking a long, carefully designed random walk that eventually visits each region in proportion to its probability., belief propagationbelief propagation, n.: A way for a network of uncertain quantities to reach conclusions by having each node pass short messages to its neighbors about what it currently believes, until the beliefs settle down. or weighted satisfiability (MaxSAT). Markov logic networks are a central formalism of statistical relational learning, alongside probabilistic logic programs such as ProbLog, and a precursor of neuro-symbolicneuro-symbolic AI, n.: AI that combines neural networks, which learn patterns from data, with symbolic methods, which follow explicit rules and logic, aiming for systems that both learn flexibly and reason reliably. methods that soften logic so that it can be learned.

P(X=x)=1Zexp⁡(∑iwi ni(x))P(X = x) = \frac{1}{Z} \exp\Big(\sum_i w_i \, n_i(x)\Big)

Origin

Introduced by Matthew Richardson and Pedro Domingos at the University of Washington and published in Machine Learning in 2006, together with the open-source Alchemy system.

Usage note

In the formula, n_i(x) is the number of true groundings of formula i in world x and w_i its weight.

Related

See also
  • Markov random fieldMarkov random field, n.: A model of many linked uncertain quantities, such as neighboring pixels in a photo, in which each one depends directly only on its neighbors, with no notion of which one causes which.
  • first-order logicfirst-order logic, n.: A precise formal language for statements about objects and their relations, using 'for all' and 'there exists', such as 'every person has a mother'. It is the standard logic of mathematics and of classic AI.
  • probabilistic graphical modelprobabilistic graphical model, n.: A way of describing how many uncertain quantities depend on one another by drawing them as a network, which makes it practical for a computer to reason about all of them together.
  • inductive logic programminginductive logic programming, n.: A kind of machine learning that discovers general logical rules — such as 'X is a grandparent of Z if X is a parent of a parent of Z' — from examples and background knowledge.
  • neuro-symbolic AIneuro-symbolic AI, n.: AI that combines neural networks, which learn patterns from data, with symbolic methods, which follow explicit rules and logic, aiming for systems that both learn flexibly and reason reliably.
  • probabilistic programmingprobabilistic programming, n.: Writing a statistical model as an ordinary-looking program that includes random choices, and letting the system work out automatically which hidden values best explain the observed data.

Sources

  1. Richardson, M. & Domingos, P. (2006). Markov Logic Networks. Machine Learning 62(1–2), 107–136.

Mentioned in

neuro-symbolic AIneuro-symbolic AI, n.: AI that combines neural networks, which learn patterns from data, with symbolic methods, which follow explicit rules and logic, aiming for systems that both learn flexibly and reason reliably., inductive logic programminginductive logic programming, n.: A kind of machine learning that discovers general logical rules — such as 'X is a grandparent of Z if X is a parent of a parent of Z' — from examples and background knowledge.