I have been trying to understand EM and I am having a hard time understanding what a latent variable is. In particular, I am having issues in identifying whether in a particular model that I am using, a particular variable is a latent variable or not.
So, basically I observe two images $x$ and $y$ and I am trying to estimate a transformation $t$ between them which is parameterised by a set of parameters $w$. So the model is: $$ y = t(x, w) + e $$ So, $y$ is a transformed version of $x$ according to some transformation parameters $w$. Graphically, I can represent it as follows.
Please ignore the prior distributions on $w$ and $\phi$ and all the hyper parameters.
So, my understanding is that $x$ and $y$ are two random variables but they are not latent as we actually observe and measure particular instances of them (hence they are shaded in the PGM diagram).
However, the parameters of the transformation $w$ can be treated as a random variable and since we do not observe it but rather want to infer it, they are the latent variables in my model.
Is my understanding/reasoning correct?