Sequential feature selection and inference using multi-variate random forests

Random forest (RF) has become a widely popular prediction generating mechanism. Its strength lies in its flexibility, interpretability and ability to handle large number of features, typically larger than the sample size. However, this methodology is of limited use if one wishes to identify statistically significant features. Several ranking schemes are available that provide information on the relative importance of the features, but there is a paucity of general inferential mechanism, particularly in a multi-variate set up. We use the conditional inference tree framework to generate a RF where features are deleted sequentially based on explicit hypothesis testing. The resulting sequential algorithm offers an inferentially justifiable, but model-free, variable selection procedure. Significant features are then used to generate predictive RF. An added advantage of our methodology is that both variable selection and prediction are based on conditional inference framework and hence are coherent.