GM-RKB: Conditional Random Field

AKA: CRF, Conditional Random Field, Conditional Random Field Graph, CRF-based Model, Trained CRF, Trained Conditional Random Field.
Context:
- It represents a ([[set of) conditional distribution p(y|x) such that for any fixed x and factor graph G over Y, p(y|x) factorizes according to G.
- Every conditional distribution p(y|x) is a CRF for some, perhaps trivial, factor graph.
- It can be produced/used by a CRF-based Learning System (that implements a CRF Training Algorithm and CRF Inference Algorithm)
- It can be a CRF-based Sequence Tagging Function/CRF-based Tagger (a Finite-State Sequence Tagging Model for a Sequence Labeling Task)
- It can be:
  - a Hidden CRF Model.
  - a Nonhidden CRF Model.
- It can use:
  - Interacting Features.
  - Long Range Dependencys between Observed Outcomes.
- It can be applied to:
  - Supervised Part-of-Speech Tagging (Lafferty & al, 2001).
  - Supervised High-level Activity Extraction (Liao & al, 2007).
  - Supervised Image Segmentation (Reynolds & Murphy, 2007); (Verbeek & Triggs, 2007).
  - Supervised Object Recognition (Quattoni & al, 2004).
  - Supervised Named Entity Recognition, (Sutton & McCallum, 2007); Stanford Named Entity Recognizer System.
  - Supervised Concept Mention Identification, (Melli, 2010b).
Counter-Example(s):
See: Label Bias, Joint Probability, CRF Modeling Task, CRF Inferencing Task.

References

(Sutton & McCallum, 2007) => Charles Sutton, and Andrew McCallum. (2007). "An Introduction to Conditional Random Fields for Relational Learning. In: (Getoor & Taskar, 2007).
- ... A conditional random field is simply a conditional distribution p(y|x) with an associated graphical structure. Because the model is conditional, dependencies among the input variables x do not need to be explicitly represented, affording the use of rich, global features of the input. ...
- ... We will occasionally use the term random field to refer to a particular distribution among those defined by an undirected model. To reiterate, we will consistently use the term model to refer to a family of distributions, and random field (or more commonly, distribution) to refer to a single one.
(Liao & al, 2007) => L. Liao, D. Fox, and H. Kautz. (2007). "Extracting Places and Activities from GPS Traces Using Hierarchical Conditional Random Fields." In: International Journal of Robotics Research.
(Verbeek & Triggs, 2007) => J. Verbeek and B. Triggs. (2007). "Scene Segmentation with Conditional Random Fields Learned from Partially Labeled Examples." In: Proceedings of Neural Information Processing Systems.

(Tasi & al, 2006) => Tzong-han Tsai, Wen-Chi Chou, Shih-Hung Wu, Ting-Yi Sung, Jieh Hsiang, and Wen-Lian Hsu. (2006). "Integrating Linguistic Knowledge into a Conditional Random Field Framework to Identify Biomedical Named Entities.' In: Expert Systems with Applications: An International Journal, 30(1). [doi>10.1016/j.eswa.2005.09.072]
- ... They are probabilistic tagging models that provide the conditional probability of a possible tag sequence y = y₁,...,y_n given the input token sequence x = x₁,...,x_n. We use two random variables X and Y to denote any input token sequences and tag sequences, respectively.
- A CRF on (X, Y) is specified by a vector f of local features and a corresponding weight vector λ. There are two kinds of local features: the state feature s(y_i, x_i) and the transition feature t(y_i-1, y_i, x, i), where y_i-1 and y_i are tags at positions i-1 and i in the tag sequence, respectively; i is the input position.

Hanna M. Wallach http://www.inference.phy.cam.ac.uk/hmw26/crf/
- This page contains material on, or relating to, conditional random fields.

(Quattoni & al, 2004) => Ariadna Quattoni, Michael Collins, and Trevor Darrel. (2004). "Conditional Random Fields for Object Recognition." In: Proceedings of Neural Information Processing Systems (NIPS 2004).