Exercise 5.2

Answers

(a): There are $2^{5}$ possible predictions of win-lose for 5 games.
(b): If the sender wants to make sure that at least one person receives correct predictions on all 5 games from him, he should begin with $2^{5}$ people.
(c): After the first letter ’predicting’ the outcome of the first game, he only need target $2^{4}$ of the original recipients.
(d): There are total $2^{5} + 2^{4} + \dots + 2^{1} = 31$ letters been sent.
(e): He will make $50 - 31 * 0.50 = 34.5$ dollars.
(f): This is similar to the growth function that if our hypothesis set is large enough, it can possibly contain all the possible dichotomies for the training data set, and if we are lucky, the training algorithm may find a hypothesis function that can predict correctly for each of the training data (this hypothesis is the guy who receives correct predictions for each of 5 games). This doesn’t mean that our model can predict new data very well. So the credibility of fitting the data is not conceivable.

niuers

2021-12-08 09:33