- **General Discussion of Machine Learning**
(*http://book.caltech.edu/bookforum/forumdisplay.php?f=105*)

- - **example non-overlap hypothesis set H to make union bound equals vc bound**
(*http://book.caltech.edu/bookforum/showthread.php?t=4659*)

example non-overlap hypothesis set H to make union bound equals vc boundconsider the union bound, when H consists of only h1 and h2,
Pr[|Ein(g)-Eout(g)|>e] <=Pr[|Ein(h1)-Eout(h1)|>e or |Ein(h2)-Eout(h2)|>e] （eq.1） <=Pr[|Ein(h1)-Eout(h1)|>e] + Pr[|Ein(h2)-Eout(h2)|>e] (eq.2） =2exp(-2Ne^2) (eq.3) i wonder which kind of h1 and h2 can more "accurately" satisfy the union bound, maybe this means union bound equals vc bound. in other words, can i find h1 and h2 to let (eq.1)=(eq.2)? Pr[|Ein(h1)-Eout(h1)|>e or |Ein(h2)-Eout(h2)|>e] =Pr[|Ein(h1)-Eout(h1)|>e and |Ein(h2)-Eout(h2)|>e] (eq.a) +Pr[|Ein(h1)-Eout(h1)|>e and |Ein(h2)-Eout(h2)|<=e] (eq.b) +Pr[|Ein(h1)-Eout(h1)|<=e and |Ein(h2)-Eout(h2)|>e] (eq.c) if (eq.2)=(eq.1), then, sup(eq.a)=0 sup(eq.b)=sup(eq.c)=1/2(eq.3)=exp(-2Ne^2) but i cannot find the example h1&h2, which means h1 and h2 has no overlap when considering the union bound. can u help? :):D thanks. |

Re: example non-overlap hypothesis set H to make union bound equals vc bound |

Re: example non-overlap hypothesis set H to make union bound equals vc boundHi, htlin. I'm sorry for check the reply late.
Thanks for your proposition and it is a good institution. I want to find a more general way to build examples but I have not done it. I tried a small lab, when the loss function of h1 and h2 are same/or complementary, A=B;when increase the difference btw loss functions of h1 and h2, the overlap btw A&B increase also. keep in touch if u would like, i am new in Mearchine learning. https://www.facebook.com/wordchao |

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