I am constructing a random forest model to predict a dependent variable Y
. Two features are X_1
and X_2
. However, from domain knowledge, I suspect that X_1
and X_2
don't strongly predict Y
on their own, and the feature that really matters is the ratio X_1/X_2
. (There are many other features X_i
as well.)
For example, suppose that Y
is the fraction of people in a given city that drive to work, while X_1
represents the number of cars in the city and X_2
represents the total population of the city. Clearly X_1
and X_2
would independently have at best a weak relationship with Y
, while the ratio X_1/X_2
would strongly predict Y
.
Can I expect a random forest model to automatically detect that Y
scales primarily with X_1/X_2
rather than with either variable independently? Or is it important to use domain knowledge to explicitly create the more relevant feature X_3 = X_1/X_2
before training?
(Maybe another way to say it is that the features X_1
and X_2
are highly correlated, while neither feature is highly correlated with X_1/X_2
. I am not a statistical sophisticate.)
I am interested in the answer for both random forest regressors (as in this setup) and classifiers, if they differ.