 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability/6/c/i/solution

Use a column gradient. By the multivariable chain rule,

\nabla l (x) = i = 1 \sum n y_{i} f^{'} (a_{i}^{T} x) a_{i} .

The scalar coefficients multiply the constant vectors

a_{i}

. In particular

f^{'} (t) = - t e^{- t^{2} /2}

, although explicit differentiation of

f

is not required.

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