Show how to run the Perceptron algorithm while only accessing the instances via the kernel function.

1.Variable step size (*): Prove an analog of Theorem 14.8 for SGD with a variable step size, ηB Ρ √ . 16.1 Consider the task of finding a sequence of characters in a file, as described in Section 16.2.1. Show that every member of the classHcan be realized by composing a linear classifier over ψ(x), whose norm is 1 and that attains a margin of 1.

2 Kernelized Perceptron: Show how to run the Perceptron algorithm while only accessing the instances via the kernel function. Hint: The derivation is similar to the derivation of implementing SGD with kernels.

3 Kernel Ridge Regression: The ridge regression problem, with a feature mapping

ψ, is the problem of finding a vector w that minimizes the function (w)= λ         w            2 + 1 2_m i=1 (_w(x)_− yi )2(16.8) and then returning the predictor h(x) = _w,x_. Show how to implement the ridge regression algorithm with kernels. _Hint: The representer theorem tells us that there exists a vector α ∈ Rsuch that mi =1 αiψ(x) is a minimizer of Equation (16.8).

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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….