Rewriting Decision Trees with Differentiable Programming: A Neural Network Approach"

Title: "Rewriting Decision Trees with Differentiable Programming: A Neural Network Approach"

In this LinkedIn article, I discuss the concept of rewriting decision trees using a Differentiable Programming approach, inspired by the NODE paper. By reformulating decision trees within the mathematical framework of Neural Networks, we can address common issues encountered when building and training Custom Neural Networks.

The article begins by highlighting the limitations of traditional methods like XGBoost, LightGBM, or CatBoost, which rely on brute force approaches for constructing ensembles of decision trees. To overcome these limitations, Differentiable Programming offers a more efficient and flexible approach.

However, traditional decision tree construction is non-differentiable, making it challenging to incorporate within a differentiable framework. The article introduces a differentiable formulation of decision trees proposed by Popov, Morozov, and Babenko in 2019, which enables seamless integration with Differentiable Programming.

The article then delves into the reformulation process, addressing key questions such as avoiding the vanishing gradient problem, choosing appropriate initial weights, and utilizing batch normalization. The reformulated decision tree is presented in the context of feature selection and threshold determination, with Python code examples using Jax.

For feature selection, a differentiable function is introduced, using the entmax function to ensure the weights sum up to 1. This enables learning the vector selection_weights, which determines the features to retain for optimal gain.

Regarding threshold determination, a similar approach is employed, utilizing a dot product and the entmax function to generate a 1 if the value is above the threshold or a -1 if it is below. This enables the model to follow the appropriate path in the decision tree.

The article concludes by outlining future steps, including extending the method to support multi-level decision trees and addressing the challenge of learning the parameters. Additionally, the importance of staying within the linear part of the entmax function to prevent gradient vanishing is highlighted.

Overall, this article provides insights into the exciting possibility of integrating decision trees into the realm of Differentiable Programming, opening up new avenues for optimization and model development.

#XGBoost #GradientBoosting #DecisionTrees #DeepLearning #DifferentiableProgramming #MachineLearning #DataScience #NeuralNetworks #LinkedIn