CART Decision Tree Learning when some variables are ranges of continuous values

Question

Could anyone kindly give some practical advice on how to deal with predictors of a range of values?

For instance, I want to predict $Y$ based on features $X_{i}, \ i=1,2,...,N$. Some $X_{i}$s are of the form: $X_{i} \in [3,5]$ (ranges from 3 to 5) or $X_{j} \in \{2,3\} $. How would the decision tree learn where to split in between those integer ranges? In my particular application, these are all ranges of integer values. But advice on how to deal with real value ranges is appreciated too!

Follow-up: what formats would you advise to process such variables into when using, for instance, rpart package of R or sklearn from python? Do you simply discretize them into a matrix of binary variables, or better?

More follow-up: I am not asking how to process continuous or ordinal variables --- I already know that. I am asking how to preprocess instances of the form of a particular range. For instance,

id variable_x

0 3

1 [2,5]

2 {2,4}

3 [4,5]

Thanks!

Answer 1

As far as I know, in case of a decision tree model, it doesn't matter whether the variables are continuous or discrete. In any case, it tries to get the optimal split at any node (for any variable) so as to create an optimal set of decision rules for the correct prediction. In case of a discrete variable $X_{j} \in \{1,2,3,4\}$, the split could be of the form $\{1\}, \{2,3,4\}$ whereas in case of ordinal variables $X_i \in [3,5]$ the splits are of the form $\{x : 3<=x<4.2\}\{x : 4.2<=x<=5\} $ but the goal and method is generally the same in both cases.