Hi,
If you are using SAS software like Enterprise Miner or HPSLIT, default settings on these parameters, more often than not, serve you a fairly good baseline deccision tree model.
In the case of Enterprise Miner where you can do what we call interactive tree, you can inject any variable based rules to stop, expand or prune a tree. You can also combine this kind of 'manual' tree with machine built trees. Machine trees are trees most predictive modelers mean when they talk about decision tree modeling. I believe your question is about machine-built tree (DT).
Best this, best that, the key is one word: validation. Where to stop, how many trees, how many variables to try (in other words, if you have 500K variables, it is not good idea to pump them all in at once to the tree engine), pruning guidance, surrogates... should all be decided on hold-out samples. As for deciding criteria (which I believe is what you are asking, literally), cost-complexity, balance between training and validation, outweighs so-called accuracy. Best practice typically involves rounds of rounds of tweaking.
In the latest and the great SAS Viya ML suite, you have access to a facility called Auto Tuning that allows you to set ranges on (hyper) parameters, like those mentioned in your question, and let Viya tell which are the optimal combination. The search routine goes beyond brute force nature of grid search (Latin Hypercube, anyone). It is directly and immediately scalabe for the modeler to run it against huge data set in-memory.
So what is the best of this and that? Go to work. Decision tree is unlike many other methods and algorithms. In many cases, the best is when you see it, like gardening. Because there is a visual tree for you to see.
Hope this helps?
Best Regards
Jason Xin
