On the website for CRF++ http://crfpp.sourceforge.net/ they mention that marginal probabilities can be output for each possible label. My question is, in CRF theory, what's the formula for this marginal probability? I think it's:
$$p_{_\theta}(Y_{_j} = y | X ) = \frac{\alpha_{_j}(y|X)\beta_{_j}(y|X)}{Z_{_\theta}(X)}$$
where Yj is a sebsequence of Y, which is the sequence of labels, conditioned on the observed variable X, and Z(X) is a normalization function of X, and α and β are the forward and backward probabilities used in forward-backward algorithms.
Is this correct?
