2.1 Minimizing a quadratic function and the curse of dimensionality Consider the simple quadratic function g(w)...

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2.1 Minimizing a quadratic function and the curse of dimensionality Consider the simple quadratic function g(w) = ww (2.33) whose minimum is always at the origin regardless of the input dimension N. (a) Create a range of these quadratics for input dimension N = 1 to N = 100, sample the input space of each P = 100 times uniformly on the hypercube [1,1]x[1,1]xx [-1, 1] (this hypercube has N sides), and plot the minimum value attained for each quadratic against the input dimension N. (b) Repeat part (a) using P = 100, P = 1000, and P = 10,000 samples, and plot all three curves in the same figure. What sort of trend can you see in this plot as N and P increase? (c) Repeat parts (a) and (b), this time replacing uniformly chosen samples with randomly selected ones. 2.1 Minimizing a quadratic function and the curse of dimensionality Consider the simple quadratic function g(w) = ww (2.33) whose minimum is always at the origin regardless of the input dimension N. (a) Create a range of these quadratics for input dimension N = 1 to N = 100, sample the input space of each P = 100 times uniformly on the hypercube [1,1]x[1,1]xx [-1, 1] (this hypercube has N sides), and plot the minimum value attained for each quadratic against the input dimension N. (b) Repeat part (a) using P = 100, P = 1000, and P = 10,000 samples, and plot all three curves in the same figure. What sort of trend can you see in this plot as N and P increase? (c) Repeat parts (a) and (b), this time replacing uniformly chosen samples with randomly selected ones.