# 2005 AnIntroForCRFs

Subject Headings: Conditional Random Fields, Literature Survey.

## Quotes

### Hidden Markov Model

• Cannot represent multiple interacting features or long range dependences between observed elements.

### Maximum Entropy Markov Model

• Label bias problem: the probability transitions leaving any given state must sum to one

### Conditional Random Field

• undirected graphical model globally conditioned on X
• Given an undirected graph G=(V, E) such that Y={Yv|v∈V}, if

• the probability of Yv given X and those random variables corresponding to nodes neighboring v in G. Then (X, Y) is a conditional random field.

### Definition

• CRF is a Markov Random Fields.
• By the Hammersley-Clifford theorem, the probability of a label can be expressed as a Gibbs distribution, so that

• What is clique?
• By only taking consideration of the one node and two nodes cliques, we have

### In Labeling

• In labeling, the task is to find the label sequence that has the largest probability
• Then the key is to estimate the parameter lambda

## References

,

volumeDate ValuetitletypejournaltitleUrldoinoteyear
2005 AnIntroForCRFsAn Introduction for Conditional Random FieldsLiterature Survey ¨Chttp://keg.cs.tsinghua.edu.cn/persons/tj/Reports/CRFs-Jie-Tang.ppt2005