Causal tree v. causal forest - when to use which for HTE? Would someone be able to explain the considerations for using a causal tree versus a causal forest to estimate heterogeneous treatment effects? Is it that a causal forest is less prone to overfitting? I've been reading over the papers but it wasn't clear to me. Thank you!
 A: As it stands at the moment in my mind, a causal forest is built using a combination of causal trees, my bare understanding is that when estimating for a group or cluster average treatment effects given a treatment assignment condition then a causal forest is the best choice, whereas if estimating treatment effect heterogeneity for an individual then the causal tree is more optimized for that. I may be wrong but that is how I get my head around it.
A: As usual, the short answer is: it depends.
From a methodological point of view, a causal tree estimates the CATE function $E \left[ Y (1) - Y(0) | X \right]$ (i.e., the treatment effects conditional on the covariates) by constructing a multi-variate step function. This means that you would be given groups of units and, for each group, an estimate of their average treatment effect, typically called GATE (Group Average Treatment Effect).
On the other hand, a causal forest is an ensemble of several causal trees (I assume we are talking about the causal forest proposed by Athey and Wager (2018)) The idea is to smooth over several step functions to get a smooth estimate of the CATE. This way, the causal forest yields treatment effects that vary across individuals - as opposed to groups of units.
This discussion abstracts from our belief about the true Data Generating Process. If for some reason, we believe that treatment effects are constant across groups, then a causal tree should work better than a causal forest. Moreover, one could also discuss the relative merits of interpretability vs explainability. A causal forest yields individual treatment effects for each unit in your data set. Thus, if you have 10,000 units, then you estimate 10,000 effects, and really nobody is able to look at each of them and make a coherent and strong story out of it (although there is now a vast literature on how to post-process CATEs estimates, starting from this wonderful paper). A causal tree is way more interpretable than a causal forest (this is generally true for any type of trees/forests). You get a particular number of groups (in my experience, no more than 10/12) and an estimate of the average effect of each group. This is highly interpretable, which is essential for understanding and communication.
