# Is there a closed formula/function for decision trees?

i've been studying gradient boosting so realize the pure algorithm requires a function F/model to get boosted.What is the explicit F on gradient boosting trees?

• it is not (theoreticaly) necessary for $F$ to have a closed-form formula. Gradient can be numericaly computed Jan 15 '21 at 16:09
• gnosisda.gr/wp-content/uploads/2020/07/… Jan 15 '21 at 16:12
• Nikos M. even though it isn't necessary for F to have a closed formula, Can I express the functional form as sum of indicator terms and work to that? Feb 4 '21 at 0:33

## 1 Answer

It can be expressed as a linear combination of indicators, where the weights are the training averages on each partition of the space, and the indicator is the indicator for that partition.

Having said that, I haven't come across any software that automatically does it for you. I also think the analytic expressions might become very large when dealing with moderately wide trees.