Bagging random forest9/12/2023 ![]() Seems to be a contradiction which I have not sorted out yet. Your answer however seems to make sense, and in the right plot of Fig 15.10 we can see that the green horizontal line, which is the squared bias of a single tree, is way below the bias of a random forest. Elements of Statistical Learning 2nd Ed, Chapter 9.2.3. Both limitations leads to higher bias in each tree, but often the variance reduction in the model overshines the bias increase in each tree, and thus Bagging and Random Forests tend to produce a better model than just a single decision tree.Īccording to the authors of "Elements of Statistical Learning" (see proof below):Īs in bagging, the bias of a random forest is the same as the bias of Again, higher bias occurs in each tree.Ĭonclusion: Both situations are a matter of limiting our ability to explain the population: First we limit the number of observations, then we limit the number of variables to split on in each split. we limit the number of variables to explain our data with. I will accept the answer on 1) from Kunlun, but just to close this case, I will here give the conclusions on the two questions that I reached in my thesis (which were both accepted by my Supervisor):ġ) More data produces better models, and since we only use part of the whole training data to train the model (bootstrap), higher bias occurs in each tree (Copy from the answer by Kunlun)Ģ) In the Random Forests algorithm, we limit the number of variables to split on in each split - i.e. But why does this lead to an increase in bias of the individual trees in Bagging / Random Forests?Ģ) Furthermore, why does the limit on available variables to split on in each split lead to higher bias in the individual trees in Random Forests? This leads me to the two following questions:ġ) I know that with bootstrap sampling, we will (almost always) have some of the same observations in the bootstrap sample. Thus, the prediction accuracy is only increased, if the increase in bias of the single trees in Bagging and Random Forests is not "overshining" the variance reduction. Both Bagging and Random Forests use Bootstrap sampling, and as described in "Elements of Statistical Learning", this increases bias in the single tree.įurthermore, as the Random Forest method limits the allowed variables to split on in each node, the bias for a single random forest tree is increased even more. an unpruned decision tree) it has high variance and low bias.īagging and Random Forests use these high variance models and aggregate them in order to reduce variance and thus enhance prediction accuracy. If we consider a full grown decision tree (i.e.
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