# Hidden states in hidden conditional random fields

I am trying to study hidden conditional random fields but I still have some fundamental questions about those methods. I would be immensely grateful if someone could provide some clarification over the notation used on most papers about the topic.

In several papers the most common form of the the HCRF model is given as:

$p(w|o;\theta) = \frac{1}{z(o; \theta)} \sum_{s} \exp{ \Psi(w, s, o; \theta) }$

In which $\theta$ is the parameter vector, $w$ is the class label, $o$ is the observation sequence, $s$ is the hidden state sequence and $\Psi$ is the potential function. However, I still could't figure out what $s$ means. Is it just a sequence of integer numbers, or is it actually a sequence of nodes in a graph? How one actually computes this summation?

Most papers I have read mention only that each $s_i \in S$ captures certain underlying structure of each class ($S$ being the set of hidden states in the model). But I still couldn't figure out what this actually means.

• not a full answer, but what may help you is to "go backwards" and learn a more basic model, and then how this one "generalises" that more basic model. You may need to do this in several steps. do you get to choose $S$? like in a mixture model? This does look like a mixture model, where each "s" defines a "component". Kind of like saying "I have $S$ models, but I don't know the state which each individual observation is in. So I will average over these states" – probabilityislogic Mar 10 '11 at 11:17