[olooney]

Individual trees are high variance. The random forest itself is an ensemble of many trees - a "forest" if we've being cute. Each tree in the forest is randomized training on a bootstrap sample. This is sometimes called "bagging", a portmanteau of "bootstrap" and "aggregating." Each tree may be further randomized by selecting a different subset of dimensions to consider each time we split a node. The end result is that each tree uses very different rules to make its prediction. When all of these predictions are combined (by voting for classification, or by averaging for regression) error due to overfitting tends to cancel out, while signal due to the same true pattern being discovered independently by many trees is amplified. Thus we can continue to add trees indefinitely without worrying about over-fitting. Other hyperparameters of random forest, such as max tree depth or the minimum number of samples in a node necessary for splitting, can result in overfitting or underfitting so need to be tuned. However, because forest will eventually fit the data set even if we use so-called "stump" learners (max tree depth=1) we can choose very conservative parameters like max-depth=3 which makes trees less likely to overfit. And if they underfit, well, that's not a problem, the ensemble will take care of that. The number of trees in a forest can be cranked up as high as we want without worrying about overfitting; the only downside is that training takes longer, the model takes more space on disk and in memory, and predictions take longer to run.

[rq1]

Yes that’s exactly overfitting the bootstrapped samples, thus the high variance.

The « variance » won’t just magically vanish as you average things out[1], you need to change the scale and check out the asymptotic law of your estimator (CLT, Kolmogorov-Smirnov… etc.) and confront it to your data.

[1] the variance of the estimator itself vanishes thanks to LLN (in case of convergence), but that’s not actually the quantity of interest

Edit: don't get me wrong, I'm not saying that RFs are good or bad, just reacting to the bias/variance thing.

[yters]

Based on the downvotes, it seems people think reducing variance is the same as reducing overfitting.

Think of the bias/variance tradeoff as a spotlight, and we are shining the spotlight on a bunch of cats, who reflect back the spotlight when their eyes are open. Eyes are open or closed randomly. Cat eyes are either green or brown. We want to know the distribution of cat eyes in parts of the population, which in general is an even 50/50 split. We determine the distribution in a certain location by taking the average of the eyes we see.

If variance is large, then the spotlight is very large, and we don't learn anything because we just average the entire population.

If the spotlight is small, then we can learn something, but only if there are enough samples in the region we shine the light.

So, what if we start with a large spotlight, and then when we see a region with a large number of open eyes of one color, we narrow the light down to just that region? Won't that allow us to avoid overfitting, while maximizing our ability to learn?

It unfortunately does not, because with a large enough population that is evenly distributed, there will always be pockets that exhibit what appear to be a pattern, but is just an accident of which cats happened to open their eyes.

This scenario of starting with the spotlight large and then zooming into a patterned region is the same as reducing variance with the training data. With a large enough dataset it is always possible to find these accidental patterns and then zoom into them by reducing variance.

[yters]

More thoughts on this seemingly controversial claim.

https://stats.stackexchange.com/questions/20714/does-ensembl...

[yters]

Ensemble models increase VC dimension so they are more prone to overfitting.

Example, you could have a tree that individually segments each data point and memorize your dataset. That's the definition of overfitting.