Conditional Random Fields

This is a method discussed in Information Extraction 10-707 in Fall 2010.

Linear-chain Conditional Random Fields

The paper focuses on conditional random fields on sequences. Such CRFs define conditional probability distributions p(Y|X) of label sequences given input sequences. The label and input sequences are assumed to have the same length.

A CRF on (X, Y) is specified by a local feature vector and a weight vector, the local features are defined as follows:

And the global feature vector is thus an aggregate of the local features:

The conditional probability distribution defined by CRF is then defined as

In sequential labeling task, we would like to find the most probable label sequence for input sequence, thus we use the following formula

The decoding process can be done with the Viterbi algorithm.