# How to split nodes in regression trees

I am looking for a comparison of different regression tree node splitting approaches within the random forest framework. I am looking at the trade-off between ensemble accuracy/reliability (holding forest size constant) and computational complexity of the split since I deal with large datasets.

The standard approach is to minimise $\sum_{i \in Region_1} (y_i - mean(y_i)_{Region1})^2$ +$\sum_{i \in Region_2} (y_i - mean(y_i)_{Region2})^2$. But another approach I have seen in a PhD thesis which drastically reduces the computational complexity is to look at the average of $(\sum_{i \in Region_1} y_i)^2/(Cardinality of Region_1)$ versus the same for $Region_2$; this allows me to use a running sum of $y_i$.

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