I have tried to write some easy but formal definition of a machine learning model using a classification task as example and I need some review.
The goal of machine learning is:
$arg min_{\Theta}(c(\textbf y,\hat{\textbf y})|o)$
$c(.) \in C$ = Cost Function of a set of Cost Functions$
$f(.) \in F$ = Function (Machine Learning Model) of a set of Functions$
$o(.) \in O$ = Optimizer of a set of Optimizers$
$\hat{y} = f(\textbf x,\Theta) =$ Predicted Value
$y =$ True Value
$\textbf x \in \mathbb{R}^{d}$ = d-dimensional Datapoint$
$\Theta \in \mathbb{R}^{m}$ = m-dimensional Parameter Vector$
Here, given the dataset $\mathbf X$ for a chosen Classifier $f(.) \in F$ the Optimizer $o(.) \in O$ is used to find the Parameter Vector $\Theta \in \mathbb{R}^{m}$ for the $f(.) \in F$ such that the Cost function $c(.) \in C$ is minimized.
I am happy for any comments!