Hinge-Loss Markov Random Field

A Hinge-Loss Markov Random Field is a Markov random field that …

• Context:
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• Example(s):
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• Counter-Example(s):
  • Boolean MRF.
• See: Probabilistic Soft Logic, Probabilistic Logic Language.

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References

2016

• (Nickel et al., 2016) ⇒ Maximilian Nickel, Kevin Murphy, Volker Tresp, and Evgeniy Gabrilovich. (2016). “A Review of Relational Machine Learning for Knowledge Graphs.” In: Proceedings of the IEEE, 104(1). doi:10.1109/JPROC.2015.2483592
  • QUOTE: … If one restricts the class of potential functions to be just disjunctions (using or and not, but no and), then one obtains a (special case of) hinge loss MRF (HL-MRFs) (Bach et al., 2015), for which efficient convex algorithms can be applied, based on a continuous relaxation of the binary random variables. Probabilistic soft logic (PSL) (Kimming et al, 2012) provides a convenient form of ‘‘syntactic sugar’’ for defining HL-MRFs, just as MLNs provide a form of syntactic sugar for regular (boolean) MRFs. HL-MRFs have been shown to scale to fairly large knowledge bases (Pujara et al., 2015). …

2016

• https://github.com/linqs/psl/wiki/Glossary
  • Hinge-loss Markov random field: A factor graph defined over continuous variables in the [0,1] interval with (log) factors that are hinge-loss functions. Many classes in PSL work together to implement the functionality of HL-MRFs, but the class for storing collections of hinge-loss potentials, which define HL-MRFs, is GroundRuleStore.java.

2015

• (Bach et al., 2015) ⇒ Stephen H Bach, Matthias Broecheler, Bert Huang, and Lise Getoor. (2015). “Hinge-loss Markov Random Fields and Probabilistic Soft Logic.” In: arXiv preprint arXiv:1505.04406.
  • QUOTE: A fundamental challenge in developing high-impact machine learning technologies is balancing the ability to model rich, structured domains with the ability to scale to big data. …

    … The second new formalism, probabilistic soft logic (PSL), is a probabilistic programming language that makes HL-MRFs easy to define using a syntax based on first-order logic.

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