Title: End-to-end Learning of Deterministic Decision Trees,
Abstract: Conventional decision trees have a number of favorable properties, including
interpretability, a small computational footprint and the ability to learn from
little training data. However, they lack a key quality that has helped fuel the
deep learning revolution: that of being end-to-end trainable, and to learn from
scratch those features that best allow to solve a given supervised learning
problem. Recent work (Kontschieder 2015) has addressed this deficit, but at the
cost of losing a main attractive trait of decision trees: the fact that each
sample is routed along a small subset of tree nodes only. We here propose a
model and Expectation-Maximization training scheme for decision trees that are
fully probabilistic at train time, but after a deterministic annealing process
become deterministic at test time. We also analyze the learned oblique split
parameters on image datasets and show that Neural Networks can be trained at
each split node. In summary, we present the first end-to-end learning scheme
for deterministic decision trees and present results on par with or superior to
published standard oblique decision tree algorithms.