What does an edge mean during a variable split in Random Forest?

Question

I am currently writing a blog where I plan to do a regression model using Random Forest. Random Forest averages the estimated prediction from many decision trees that are fitted on to a bootstrap from the dataset while choosing K<=M variables randomly from all the M dependent variables.

However, I recently came across this presentation. One of the slides says something like this:

Here, the author is building a regression model using Random Forest with Residual Sum of Squares as the splitting criterion. During the splitting process, it is stated that a split is "too close to the edge."

My question is, what does an "edge" mean in this case? And why not choose a split if it is too close to the "edge"?

Thanks in advance.

Answer 1

This is a worked out example of the recursive splitting done by tree-based models.

After going through the linked slides, I think what Cutler tries to say is that if you were to split at $3.07$, you would be rather close to the minimum value of that variable in the sample. Hence, a split near the 'edge' would yield one node containing almost all of the (remaining) observations and the other containing only one or a few. To avoid this imbalance, he suggests splitting slightly further away from the extremes.

Answer 2

The author probably means that the cut leaves only a small number of data points in one of the leaf nodes. It's hard to tell what he / she is thinking out of context, but it probably has to do with the fact that a split that hardly changes the data at all is almost the same as making no split, so you might as well stop there (or use a different variable). Essentially, if the "best" split occurs at the boundary of a variable's range, that indicates that the response is fairly homogeneous with respect to that variable and it probably shouldn't be used for splitting.