 Solution

ID: past-exam-of-the-advanced-topics-in-statistical-machine-learning-course-of-the-university-of-oxford/2025/2/b/ii/solution

Choose two inputs

0 < a < b

. Their proposed kernel matrix is

K = (a b b b) .

α = (1, - 1)^{T}

gives

α^{T} K α = a - b < 0.

Thus

K

k_{2} (x, x^{'}) = max (x, x^{'}) is not a positive-semidefinite kernel .

Equivalently, its determinant

ab - b^{2} = b (a - b)

is negative.

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