Define the loss function as follows.

1. Consider the problem of learning halfspaces with the hinge loss. We limit our domain to the Euclidean ball with radius R. That is, ={x :    x2 ≤ R}. The label set is = {±1} and the loss function        is defined by     (w(xy)) = max{0,1− y_w,x_}. We already know that the loss function is convex. Show that it is R-Lipschitz.

2.  (*) Convex-Lipschitz-Boundedness Is Not Sufficient for Computational Efficiency: In the next chapter we show that from the statistical perspective, all convex- Lipschitz-bounded problems are learnable (in the agnostic PAC model). However, our main motivation to learn such problems resulted from the computational perspective – convex optimization is often efficiently solvable. Yet the goal of this exercise is to show that convexity alone is not sufficient for efficiency. We show that even for the case = 1, there is a convex-Lipschitz-bounded problem which cannot be learned by any computable learner. Let the hypothesis class be H=[01] and let the example domain, Z, be the set of all Turing machines. Define the loss function as follows. For every Turing machine

∈ Z, let               (0,)=1 if halts on the input 0 and         (0,)=0 if doesn’t halt on the input 0. Similarly, let        (1,)=0 if halts on the input 0 and                (1,)=1 if doesn’t halt on the input 0. Finally, for ∈ (01), let                 (h,) = h              (0,)+(1−h) (1,).

 

find the cost of your paper

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

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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….