I am a student and I am studying machine learning. I am focusing on the concept of evaluation of an hypotesis.
What I have seen is that there are two types of error: true error and sample error.
The true error of an hypotesis $h$ with respect to a target function $f$ and a distribution $D$ is the probability that an hypotesis $h$ misclassifies an instance $x$ drawn according to $D$, and it is computed as:
$error_D(h)=Pr_{x\in D}[f(x)\neq h(x)]$
while the sample error of an hypotesis $h$ with respect to a target function $f$ and data sample $S$ is the proportion of examples that $h$ misclassifies:
$error_S(h)=\frac{1}{n}\sum _{x\in S}\delta (f(x)\neq h(x))$
where
$\delta (f(x)\neq h(x))=1$ if $f(x)\neq h(x)$ and $0$ otherwise.
I ask this question because I have not clear what these errors are.
Moreover, I have seen that the true error cannot be computed, while we can compute only the sample error. I don't understand why.
Can somebody please help me understand?