TreeGrad: Transferring Tree Ensembles to Neural Networks

Gradient Boosting Decision Tree (GBDT) are popular machine learning algorithms with implementations such as LightGBM and in popular machine learning toolkits like Scikit-Learn. Many implementations can only produce trees in an offline manner and in a greedy manner. We explore ways to convert existing GBDT implementations to known neural network architectures with minimal performance loss in order to allow decision splits to be updated in an online manner and provide extensions to allow splits points to be altered as a neural architecture search problem. We provide learning bounds for our neural network.Comment: Technical Report on Implementation of Deep Neural Decision Forests Algorithm. To accompany implementation here: https://github.com/chappers/TreeGrad. Update: Please cite as: Siu, C. (2019). "Transferring Tree Ensembles to Neural Networks". International Conference on Neural Information Processing. Springer, 2019. arXiv admin note: text overlap with arXiv:1909.1179

Deep Neural Decision Forests

Abstract We present Deep Neural Decision Forests -a novel approach that unifies classification trees with the representation learning functionality known from deep convolutional networks, by training them in an end-to-end manner. To combine these two worlds, we introduce a stochastic and differentiable decision tree model, which steers the representation learning usually conducted in the initial layers of a (deep) convolutional network. Our model differs from conventional deep networks because a decision forest provides the final predictions and it differs from conventional decision forests since we propose a principled, joint and global optimization of split and leaf node parameters. We show experimental results on benchmark machine learning datasets like MNIST and ImageNet and find onpar or superior results when compared to state-of-the-art deep models. Most remarkably, we obtain Top5-Errors of only 7.84%/6.38% on ImageNet validation data when integrating our forests in a single-crop, single/seven model GoogLeNet architecture, respectively. Thus, even without any form of training data set augmentation we are improving on the 6.67% error obtained by the best GoogLeNet architecture (7 models, 144 crops)

Comparison of the Representational Power of Random Forests, Binary Decision Diagrams, and Neural Networks

In this letter, we compare the representational power of random forests, binary decision diagrams (BDDs), and neural networks in terms of the number of nodes. We assume that an axis-aligned function on a single variable is assigned to each edge in random forests and BDDs, and the activation functions of neural networks are sigmoid, rectified linear unit, or similar functions. Based on existing studies, we show that for any random forest, there exists an equivalent depth-3 neural network with a linear number of nodes. We also show that for any BDD with balanced width, there exists an equivalent shallow depth neural network with a polynomial number of nodes. These results suggest that even shallow neural networks have the same or higher representation power than deep random forests and deep BDDs. We also show that in some cases, an exponential number of nodes are required to express a given random forest by a random forest with a much fewer number of trees, which suggests that many trees are required for random forests to represent some specific knowledge efficiently