Learning From Data – A Short Course: Exercise 4.9

Page 142:

Referring to Figure 4.10, why are both curves increasing with K? Why do they converge to each other with increasing K?

For the first question, as we use more data to validate, we use less data to train. Less data to train will output worse final hypothesis, hence the increase of both curves.

For the second question, please refer to (4.11) page 143 as M is fixed while K increases:

    \[ E_{out}(g^{-}_{m*}) \leq E_{val}(g^{-}_{m*}) + O\left (\sqrt{\frac{\ln {M}}{K}} \right ) \]


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