1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….
Show how to express h(x) on the basis of the kernel function, and without accessing individual entries of ψ(x) or w.
1. Let w = c+ −c− and let b = 12 ( c− 2 − c+ 2). Show that h(x) = sign(_w,ψ(x)_+b).
2. Show how to express h(x) on the basis of the kernel function, and without accessing individual entries of ψ(x) or w.
3. Consider a set S of examples in Rn × [k] for which there exist vectors μ1, . . .,μk such that every example (x, y) ∈ S falls within a ball centered at μy whose radius is r ≥ 1. Assume also that for every i _= j , μi −μj ≥ 4r . Consider concatenating each instance by the constant 1 and then applying the multivector construction, namely, _(x, y)= [ :0, .;.. ,0= ∈R(y−1)(n+1) , :x1, . .;., xn ,1= ∈Rn+1 , :0, .;.. ,0= ∈R(k−y)(n+1) ].
Show that there exists a vector w ∈ Rk(n+1) such that (w, (x, y)) = 0 for every (x, y) ∈ S.
Hint: Observe that for every example (x, y) ∈ S we can write x = μy +v for some v ≤r. Now, take w = [w1, . . .,wk ], where wi = [μi , − μi 2/2].