To preface this question, I am building a Random Forest model using the randomForest package in R. I am not sure if this question is dependent upon my program, or if it can be answered based on the inherent properties of the algorithm. I felt this question was more appropriate for "Cross Validated" versus "Overflow", please let me know if you think otherwise.
A Random Forest model creates many decision trees which contain a subset of variables and data. Is there any guarantee that every possible combination of variables are accounted for across all of the decision trees?
For example, I have 4 variables that I am feeding into the RF model. Three of those variables are binary (X1, X2, Y1, Y2, Z1, Z2). The other variable (of ordinal type) contains 8 unique values.(A1...A8). This leaves me with 56 possible variable combinations.
How can I guarantee that all possible unique combinations of variables are accounted for across trees? I understand that simply increasing the number of trees would increase the likelihood of this. I also realize that my example contains a relatively small number of variables, however consider a situation with many variables and unique combinations.