Computational and Statistical Learning Theory
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چکیده
{0, 1}-valued random variables X1, . . . , Xn are drawn independently each from Bernoulli distribution with parameter p = 0.1. Define Pn := P( 1 n ∑n i=1Xi ≤ 0.2). (a) For n = 1 to 30 calculate and plot the below in the same plot (see [1, section 6.1] for definition of Hoeffding and Bernstein inequalities): i. Exact value of Pn (binomial distribution). ii. Normal approximation for Pn. iii. Hoeffding inequality bound on Pn. iv. Bernstein inequality bound on Pn. (b) For n = 30 to 300 calculate and plot the below in the same plot : i. Normal approximation for Pn. ii. Hoeffding inequality bound on Pn. iii. Bernstein inequality bound on Pn. 2. VC Bound: Given a set C = {x1, . . . , xm} let Hx1,...,xm = {(h(x1), . . . , h(xm)) ∈ {±1} : h ∈ H}. Recall that we say that such a set is shattered by H if |Hx1,...,xm| = 2, and that the VC
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