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Chapter 6 & 7: Questions |
Q:
Why is the definition of $\mathcal{H}_0$ and $\mathcal{H}_1$ not exclusive?
A:
As we want to have $|\mathcal{H}_S| = |\mathcal{H}_0| + |\mathcal{H}_0|$, we have to count all the hypothesis, where "and" is true, twice.
Q:
Why do we use the term "convergence"?
A:
We use the term convergence in the calculus limit sense, as we can get $L_S(h)$ arbitrarily close to $L_{\mathcal{D}}(h)$ with a large enough sample size.
Q:
Is the $min$ in the definition of $\epsilon_n$ a problem?
A: (partial)
An $inf$ instead of $min$ should be more appropriate, as $\epsilon_n$ could converge to 0 or $\epsilon_n=0$ could happen. But if we would use the $inf$ and therefore allow $\epsilon_n=0$ we would get problems in later proofs, as we sometimes divide by $\epsilon_n$.
Q:
What is the meaning of the weight function wrt. regularization?
A:
Basic idea is to use some prior knowledge of the $\mathcal{H}_n$ to define the weight function. In that way, we can enforce a regularization during the learning to prefer simpler solutions.