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In machine learning, why does bagging increase bias? I've read that using less data would lead to a worse estimate of the parameters, but isn't the expected value of the parameter constant regardless of sample size?

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In principle bagging is performed to reduce variance of fitted values as it increases the stability of the fitted values. In addition, as a rule of thumb I would say that: "the magnitudes of the bias are roughly the same for the bagged and the original procedure" (Bühlmann & Yu, 2002). That is because bagging allows us to approximate relative complex response surfaces by practically smoothing over the learners' decision boundaries.

That said, you raise a good point about bagging "using less data"; my understanding is that this is a problem when the learners are potentially weak. Having less data makes the learning task more difficult. An obvious example would be an imbalanced dataset where a positive example is rather rare; in that case a simple majority rule for the bagging ensemble will probably be more harmful than helpful as indeed it will be more likely to misclassify the rare class - Berk's "Statistical Learning from a Regression Perspective", Sect. 4.4. on "Some Limitations of Bagging" touches upon this too. Let me note that this deteriorated performance is not totally surprising; bagging or any other procedure is not a silver bullet so it is expected that there will be cases that an otherwise helpful procedure (here bagging) makes things worse.

I think that the Bühlmann & Yu, 2002 paper: "Analyzing bagging" is a canonical reference on the matter if you want to explore further. I also liked the Strobl et al., 2007 paper: "Bias in random forest variable importance measures: Illustrations, sources and a solution", it focuses mostly on variable selection but makes a good point about how bagging affects the bias in that task.

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  • $\begingroup$ BTW, welcome to the CV community! $\endgroup$ – usεr11852 Oct 18 '18 at 23:03

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