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I am looking at various implementations of the Isolation Forest in python and R. Both sklearn in python and solitude in R use a y variable with the ExtraTrees regressor.
Since, Isolation Forest is unsupervised, I am wondering why it is being turned into a supervised problem? Wouldnt this be an issue when scoring on previously unseen data sets?
For example sklearn (python) line 248 has this.
And in solitude line 144 as well.
Extra-random Trees needs a target variable, so Isolation Forest generates a random target (sklearn, solitude). At prediction time, no y values are used, and the ExtraTrees doesn't actually make a prediction; instead, the samples are propagated to the leaves and the depth is extracted (sklearn).
As for the tree-building process, sklearn at least doesn't make use of the y values, because the ExtraTrees model has max_features=1 and splitter='random' (source). I'm not so sure about solitude, since it has mtry=ncol-1 (source); maybe further down, using splitrule='extratrees' takes care of that? Otherwise, the splits chosen will try to optimize on the random y, though since those are random it maybe doesn't matter (certainly I wouldn't call it a supervised model, anyway).
