Following this answer and this, I am trying to understand what can be meant by $P(z|x, y; k)$ notation. How to interpret this with examples in terms of machine learning?
As I understand, $P(z|x, y)$ used for conditional probability. For examples, z is height, x is gender, y is wealth, k is country. With $P(z|woman, rich)$, we are trying to find the height given the person is woman and rich.
In the first link, $f(x; y)$ says $y$ is chosen or implied value and we are interested in the value of $x$. So as I understand $y$ is fixed like hyperparameter(or input data?) and $x$ is the parameter in terms of neural networks.
In the 2nd link, it says $P(X; h)$ finding $h$ that best explains the data $X$. So $X$ is fixed as input data and $h$ is neural network parameters.
In first link the part after semicolon is fixed, but in second link the part before semicolon is fixed. In both cases the positions are different. How to explain this?
Edit
If $x$ is image, $y$ is text caption, $k$ is network parameters like weights and biases and with $z$ we are trying to find if the text caption matches the image. Is it a correct explanation of $P(z|x, y; k)$?