# Linear-Chain Conditional Random Field

A Linear-Chain Conditional Random Field is a CRF instance that abides by a Linear-Chain CRFs Metamodel (in which the output nodes are linked by edges in a linear chain).

**AKA:**Linear-Chain CRF.**Context:**- It can be trained by a Linear-Chain CRF System (that implements a Linear-Chain CRF Algorithm.
- It can be associated with a Linear-Chain Confidence Score Function.
- It can (often) be used in a Supervised Segmentation Task, such as supervised text segmentation.
- …

**Counter-Example(s):****See:**Linear-CRF Training Algorithm.

## References

### 2013

- http://en.wikipedia.org/wiki/Conditional_random_field#Examples
- Linear-chain CRFs have many of the same applications as conceptually simpler hidden Markov models (HMMs), but relax certain assumptions about the input and output sequence distributions. An HMM can loosely be understood as a CRF with very specific feature functions that use constant probabilities to model state transitions and emissions. Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence.

### 2004

- (Wallach, 2004) ⇒ Wallach, 2004) ⇒ Hanna M. Wallach. (2004). “Conditional Random Fields: An introduction." Technical Report MS-CIS-04-21, University of Pennsylvania.

### 2003

- (McCallum & Li, 2003) ⇒ Andrew McCallum, and Wei Li. (2003). “Early Results for Named Entity Recognition with Conditional Random Fields, Feature Induction and Web-Enhanced Lexicons.” In: Proceedings of Seventh Conference on Natural Language Learning (CoNLL 2003). doi:10.3115/1119176.1119206
- QUOTE: In the special case in which the output nodes of the graphical model are linked by edges in a linear chain, CRFs make a first-order Markov independence assumption, and thus can be understood as conditionally-trained finite state machines (FSMs). In the remainder of this section we introduce the likelihood model, inference and estimation procedures for CRFs.