2
$\begingroup$

I'm studying theoretical machine learning at university, and I have this problem in textbook, that I have no Idea how to start. In space $X=R^2$ are given two models $H_1$ (rectangle with sides parallel to the coordinate axes) and $H_2$ (lines). We define a model $H_3$ such that every hypothesis is a combination of one hypothesis from $H_1$ and one from $H_2$. Prove or disprove that the model $H_3$ has a bigger VC dimension (Vapnik–Chervonenkis dimension) then the VC dimensions of the models $H_1$ and $H_2$.

I need to find VC of $H_1$, $H_2$, and combined of $H_3$.

Improve this question
$\endgroup$
6
  • $\begingroup$ examples of VC computation here but I fail to understand the $H_1$ and $H_2$ sets, in yout question $\endgroup$
    – Nikos M.
    Apr 20, 2021 at 7:15
  • $\begingroup$ @NikosM. so the first is rectangle with sides parallel to the coordinate axes and second are just straight lines. In textbook I found that VC (H2)=3 and VC(H1)=4 but I don't know how to get the VC dimension of H3? $\endgroup$
    – user779537
    Apr 20, 2021 at 8:28
  • $\begingroup$ If you understand how $VC(H_1)$ and $VC(H_2)$ are derived then it can help derive the combined VC $\endgroup$
    – Nikos M.
    Apr 20, 2021 at 15:57
  • 1
    $\begingroup$ Please credit the original source of all copied material: datascience.stackexchange.com/help/referencing. The same exercise is posted here, so something has been copied from somewhere: cs.stackexchange.com/q/139171/755, datascience.stackexchange.com/q/93279/8560. $\endgroup$
    – D.W.
    Apr 20, 2021 at 17:36
  • $\begingroup$ @NikosM. I understand and found that VC(H1)=3 and VC(H2)=4. But how can I combine them ? $\endgroup$
    – user779537
    Apr 20, 2021 at 20:42

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.