I have a question regarding interpretation of results of a random forest that I created. First, some background regarding the data:
I have a dataset that consists of 100 true instances and 1000 instances of a negative set. I have 20,000 features, thus giving me a matrix of 1100 x 20,000. (These features are sparsely distributed throughout the matrix. Of the 22,000,000 values of the matrix, 21 million are 0's and only about 1 million have values greater than 0).From this sparse data I created a random forest of 500 trees (using the default settings in package RandomForest in R).
After this training, I tested the random forest on a testing set consisting of another gold standard and negative standard that the RF was not trained on to see how well it performed. The final output for this testing set for each 1100 instances is a probability from zero to 1, of it being in the gold standard. The results were excellent,with ROC curves showing that the Random Forest classifier had a true positive rate of 60% and a false positive rate of less than 5%, which is excellent in this context and outperforms other methods I used previously for this problem.
The problem that I have is I need to justify in this context why each prediction is being made, which I am not sure how to do. For example, if instance 212 is predicted to be part of the gold standard with a probability of 63%, how do I justify why, as concretely as possible, this is being predicted?
By way of comparison, for Naive Bayes Classifiers, this is easily done, since for "instance 212" each feature is associated with an odds ratio (or posterior probability) of that instance being in the gold standard, which makes interpretation easy. Is there an analog of this for Random Forests? I know that there is variable importance, but that does not directly bear on any individual instance.
EDIT:My question does overlap somewhat with How to make Random Forests more interpretable?. However, it sounds like some people there are just saying the answer is no, while others are saying there might be a way to interpret the probability distributions for each tree in a way that is logical, but I am not sure how that would be done.