Thread: Exercise 1.10
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Old 05-22-2016, 02:23 AM
henry2015 henry2015 is offline
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Default 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!
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