GradTree: Learning Axis-Aligned Decision Trees with Gradient Descent

Sascha Marton, Stefan Lüdtke, Christian Bartelt, Heiner Stuckenschmidt

Keywords: Decision Trees, Gradient Descent

TL;DR: A novel approach to learn hard, axis-aligned decision trees with gradient descent using the straight-through operator on a dense decision tree representation

Abstract:

Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable. Therefore, common approaches learn DTs using a greedy growth algorithm that minimizes the impurity locally at each internal node. Unfortunately, this greedy procedure can lead to inaccurate trees.
In this paper, we present a novel approach for learning hard, axis-aligned DTs with gradient descent. The proposed method uses backpropagation with a straight-through operator on a dense DT representation, to jointly optimize all tree parameters.
Our approach outperforms existing methods on a wide range of binary classification benchmarks and is available under: https://github.com/s-marton/GradTree

Submission Number: 1