Representer Theorem Weight Solve

Problem

Solve the regularized kernel system (K + lam*I) * alpha = y for the 2x2 kernel matrix K.

Return the coefficient vector alpha as floats; these are the weights the representer theorem assigns to the training points.

Hint

The ridge penalty lam keeps the kernel system well-conditioned.

case 1

in: [[[1,0],[0,1]],[1,2],0]

expected: [1,2]

case 2

in: [[[1,0.5],[0.5,1]],[1,0],1]

expected: [0.5333333333333333,-0.13333333333333333]

case 3

in: [[[2,0],[0,2]],[2,4],2]

expected: [0.5,1]

case 4

in: [[[1,0],[0,1]],[0,0],1]

expected: [0,0]

Starter codePython

def representer_weights(K, y, lam):
    # Your code here
    pass

4 test cases · run your code against them in the editor