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.
Deep Neural Decision Forests @cite_7 demonstrates how neural decision tree forests can replace a fully connected layer using stochastic and differential decision trees which assume the node split structure fixed and the node split is learned.
@cite_7
2220384803 2059424674 2578395343 2179503016
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 on-par 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). In this work we present Neural Decision Forests, a novel approach to jointly tackle data representation- and discriminative learning within randomized decision trees. Recent advances of deep learning architectures demonstrate the power of embedding representation learning within the classifier--An idea that is intuitively supported by the hierarchical nature of the decision forest model where the input space is typically left unchanged during training and testing. We bridge this gap by introducing randomized Multi- Layer Perceptrons (rMLP) as new split nodes which are capable of learning non-linear, data-specific representations and taking advantage of them by finding optimal predictions for the emerging child nodes. To prevent overfitting, we i) randomly select the image data fed to the input layer, ii) automatically adapt the rMLP topology to meet the complexity of the data arriving at the node and iii) introduce an l1-norm based regularization that additionally sparsifies the network. The key findings in our experiments on three different semantic image labelling datasets are consistently improved results and significantly compressed trees compared to conventional classification trees. We present a novel approach to enrich classification trees with the representation learning ability of deep (neural) networks within an end-to-end trainable architecture. We combine these two worlds via a stochastic and differentiable decision tree model, which steers the formation of latent representations within the hidden layers of a deep network. The proposed model differs from conventional deep networks in that a decision forest provides the final predictions and it differs from conventional decision forests by introducing a principled, joint and global optimization of split and leaf node parameters. Our approach compares favourably to other state-of-the-art deep models on a large-scale image classification task like ImageNet. Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy procedure often leads to suboptimal trees. In this paper, we present an algorithm for optimizing the split functions at all levels of the tree jointly with the leaf parameters, based on a global objective. We show that the problem of finding optimal linear-combination (oblique) splits for decision trees is related to structured prediction with latent variables, and we formulate a convex-concave upper bound on the tree's empirical loss. Computing the gradient of the proposed surrogate objective with respect to each training exemplar is O(d2), where d is the tree depth, and thus training deep trees is feasible. The use of stochastic gradient descent for optimization enables effective training with large datasets. Experiments on several classification benchmarks demonstrate that the resulting non-greedy decision trees outperform greedy decision tree baselines.