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The only explanations I've seen of the bias/variance tradeoff rely on rewriting the squared error of an estimator as the sum of bias and variance terms. How does the bias/variance tradeoff work if the loss function is not squared error? Thanks in advance!

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MSE=bias$^2$ +variance So the tradeoff is obvious for MSE. If your loss function is some other function of bias and variance then there will be a variance-bias tradeoff for it too. Otherwise there is none for varying the expected loss.

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Typically, we can't minimize bias and variance at the same time, can we? –  loganecolss Dec 24 '13 at 1:44

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