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:

$error_S(h)=\frac{1}{n}\sum _{x\in S}\delta (f(x)\neq h(x))$


$\delta (f(x)\neq h(x))=1$ 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?


The true error represents the probability that a randomly drawn instance from the entire distribution is misclassified while the sample error is the fraction of sample which is misclassified.

As true error represents entire population it becomes difficult to calculate hence we use sample to check our hypothesis and use evaluation methods to check it's confidence level. A sample might not be a true representation of population so the difference in results are sample error. We try different sampling methods so that there is no bias in choosing a sample like randomised and stratified sampling.

For more you can refer this

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.