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Bias-Variance Trade-off

E(y0 - f-hat(x0))2 = Var(f-hat(x0)) + [Bias(f-hat(x0))]2 + Var(ɛ)

Quoted: It is possible to show that the expected test MSE, for a given value x0, can always be decomposed into the sum of three fundamental quantities;
  • Variance of f-hat(x0)
  • Squared bias of f-hat(x0)
  • Variance of the error terms ɛ

There are some situations where allowing a little bias can provide a useful reduction in variance.