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4. (5 points) This exercise tries to show that the radial kernel K (x, r') = exp (-ylx - x'|2) has an infinite-dimensional feature space in the following steps. (i) Express K (x, x') = exp (27 (x, r') ) exp (-v lla||2) exp (-7 lla'll?). (ii) Express exp (27 (x, x)) = > Ent.to-i (21 )1/2 151..2.P 1(27) 312 ( 2 1) " 1 .(1; ) Vni!onp! Vn1!-.np! (iii) Conclude that K (x, x') = (h (x) , h (x')), where h(x) = exp (-ylx2) (1,h,"(x) , .., h; (x), . . ha (x), . . . h, (x), ) with h," (x) = (2y)1/2 n1 . np Vn1!--np! , nj + .. + np = j and 1