Entanglement and Differentiable Information Gain Maximization

Decision forests can be thought of as a flexible optimization toolbox with many avenues to alter or recombine the underlying architectural components and improve recognition accuracy and efficiency. In this chapter, we present two fundamental approaches for re-architecting decision forests that yield higher prediction accuracy and shortened decision time. The first is entanglement, i.e. using the learned tree structure and intermediate probabilities computed in nodes closer to the root to affect the training of other nodes deeper in the trees. Unlike more conventional classifiers which assume that all data points (even those neighboring in space or time) are IID, the entanglement approach learns semantic correlation in non IID data. To demonstrate, we build an entangled decision forest (EDF) that exploits spatial correlation in human anatomy by simultaneously labeling voxels in computed tomography (CT) scans into 12 anatomical structures. The second contribution is the formulation of information gain as a function that is differentiable with respect to the parameters of the split node weak learner. This provides increased confidence and accuracy of maximum margin boundary localization and reduces classification time by using a few, shallow trees. We further extend the method to incorporate training label confidence, when available, into the information gain maximization. Due to bagging and random feature subset selection, we can retain decision forest virtues such as resiliency to overfitting. To demon-