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