Neural Random Forests

Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of Breiman (2001) into a neural network setting, and in turn propose two new hybrid procedures that we call neural random forests. Both predictors exploit prior knowledge of regression trees for their architecture, have less parameters to tune than standard networks, and less restrictions on the geometry of the decision boundaries. Consistency results are proved, and substantial numerical evidence is provided on both synthetic and real data sets to assess the excellent performance of our methods in a large variety of prediction problems. Index Terms — Random forests, neural networks, ensemble methods, randomization, sparse networks. 2010 Mathematics Subject Classification: 62G08, 62G20, 68T05.