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2 Support Vector Machine [ 3 0 pts ] Suppose we use suppor vector machines with the kernel: K ( x , x ' )
Support Vector Machine pts
Suppose we use suppor vector machines with the kernel:
As we discussed in class, this corresponds to mapping each to a vector in some high
dimensional space that need not be specified so that
As usual, we are given examples cdots, where Assume for
simplicity that all the s are distinctie for
Recall that the weight vector used in SVMs has the form
Compute the s explicitly that would be found using SVMs with this kernel.
pts Recall that the SVM algorithm outputs a classifier that, on input computes the sign of
What is the value of this inner product on training example What is the value of this
inner product on any example not seen during training? Based on these answers, what kind of
generalization error do you expect will be achieved by SVMs using this kernel?
pts Recall that the generalization error of SVMs can be bounded using the margin which is
equal to or using the number of support vectors. What is in this case? How many support
vectors are there in this case? How are these answers consistent with your answer in part b
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