Compute bias and variance

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Problem

At a fixed input, the true value is $f(x)=3$ , and noise is ignored. Across three training sets, model A predicts $(1,1,1)$ and model B predicts $(1,3,5)$ . Using population variance, compute each model's bias, squared bias, variance, and expected squared error. Which model is better here?

Reveal answer or reference solution

Model A has mean $1$ , bias $-2$ , squared bias $4$ , variance $0$ , and MSE $4$ . Model B has mean $3$ , bias $0$ , squared bias $0$ , variance

\frac{(1-3)^2+0+(5-3)^2}{3}=\frac{8}{3},

and MSE $\frac{8}{3}$ . Model B is better here because $\frac{8}{3}<4$ , though it varies more across training sets.

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Compute bias and variance

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