LFD Book Forum

LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Chapter 1 - The Learning Problem (http://book.caltech.edu/bookforum/forumdisplay.php?f=108)
-   -   Exercise 1.10 (http://book.caltech.edu/bookforum/showthread.php?t=4676)

henry2015 05-22-2016 02:23 AM

Exercise 1.10
 
Hi,

Right before exercise 1.10, the book states, "The next exercise considers a simple coin experiment that further illustrates the difference between a fixed h and the final hypothesis g selected by the learning algorithm".

That statement confuses me a bit because:
1. I don't really see any function (no target function f and no hypothesis h) but the real probability of getting head of a fair coin. No?
2. Cmin illustrates that "if the sample was not randomly selected but picked in a particular way, we would lose the benefit of the probabilistic analysis (Hoeffding Inequality?)" (quoted from page 20). No?

Last question, although Cmin is picked in a particular way, if we treat each v from each 10 flips of each coin in each trial from one unique bin (such that the v's from 10 flips from the same coin in 2 different trials come from 2 bins). Then, we can still apply non vanilla version Hoeffding Inequality --P[|Ein(g)-Eout(g)| > ε] <= 2M*e^-2N*(ε^2).

Hope I can get some clarification.

Thanks!

henry2015 05-26-2016 07:05 AM

Re: Exercise 1.10
 
Small modification to #1:
1. I don't really see any function (no target function f and no hypothesis h) but the *expected* probability of getting head of a fair coin. No?


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