Prove that Memorize is a consistent learner for every class of (binary-valued) functions over any countable domain.

1. Prove that Memorize is a consistent learner for every class of (binary-valued) functions over any countable domain.

2. Let be the class of intervals on the line (formally equivalent to axis aligned rectangles in dimension = 1). Propose an implementation of the ERMlearning rule (in the agnostic case) that given a training set of size m, runs in time O(m2). Hint: Use dynamic programming.

3. Let H1,H2, . . . be a sequence of hypothesis classes for binary classification. Assume that there is a learning algorithm that implements the ERM rule in the realizable case such that the output hypothesis of the algorithm for each class Hn only depends on O(n) examples out of the training set. Furthermore, assume that such a hypothesis can be calculated given these O(n) examples in time O(n), and that the empirical risk of each such hypothesis can be evaluated in time O(mn). For example, if Hn is the class of axis aligned rectangles in Rn, we saw that it is possible to find an ERM hypothesis in the realizable case that is defined by at most 2examples. Prove that in such cases, it is possible to find an ERMhypothesis forHn in the unrealizable case in time O(mnmO(n)).

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Suggest a modification of the binary search algorithm that emulates this strategy for a list of names.

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Explain why insertion sort works well on partially sorted lists.

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Draw a class diagram that shows the relationships among the classes in this new version of the system

Jack decides to rework the banking system, which already includes the classes BankView, Bank, SavingsAccount, and RestrictedSavingsAccount. He wants to add another class for checking accounts. He sees that savings….