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I am using a RandomForestRegressor as an estimator in the SelectFromModel object (sklearn) in a variable selection problem where I have about 200 variables approximately.

Since this number of variables is very easy to grow in an exaggerated way, I would like to know if there is some theoretical number of trees inside the RandomForest that makes that selection of variables acceptable in relation to the number of input variables (and I am looking for something deeper than putting the largest number of estimators that my system accepts and the time that I can be training), since each tree will choose one of the variables randomly as root.

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