CRF and HMM

CRF formulation

• A CRF model consists of
• F = \(<f_1, \ldots, f_k>\), a vector of "feature functions"
• \(\bf{\theta} = <\theta_1, \ldots, \theta_k>\), a vector of weights for each feature function
• Let O = \(<o_1, \ldots, o_T>\) be an observed sequence
• Let A = \(<a_1, \ldots, a_T>\) be the latent variables

$$p(A = y | O) = \frac{\exp (\theta \cdot F(y, O))}{\sum_{y'} \exp (\theta\cdot F(y', O))}$$

Reference

http://knight.cis.temple.edu/~yates/cis8538/sp11/slides/conditional-random-fields.ppt