text: We propose Deep Hierarchical Machine (DHM), a model inspired from the divide-and-conquer strategy while emphasizing representation learning ability and flexibility. A stochastic routing framework as used by recent deep neural decision regression forests is incorporated, but we remove the need to evaluate unnecessary computation paths by utilizing a different topology and introducing a probabilistic pruning technique. We also show a specified version of DHM (DSHM) for efficiency, which inherits the sparse feature extraction process as in traditional decision tree with pixel-difference feature. To achieve sparse feature extraction, we propose to utilize sparse convolution operation in DSHM and show one possibility of introducing sparse convolution kernels by using local binary convolution layer. DHM can be applied to both classification and regression problems, and we validate it on standard image classification and face alignment tasks to show its advantages over past architectures.
  @cite_27: 
  @cite_25: 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).
  @cite_7: This paper presents a novel deep architecture, called neural regression forest (NRF), for depth estimation from a single image. NRF combines random forests and convolutional neural networks (CNNs). Scanning windows extracted from the image represent samples which are passed down the trees of NRF for predicting their depth. At every tree node, the sample is filtered with a CNN associated with that node. Results of the convolutional filtering are passed to left and right children nodes, i.e., corresponding CNNs, with a Bernoulli probability, until the leaves, where depth estimations are made. CNNs at every node are designed to have fewer parameters than seen in recent work, but their stacked processing along a path in the tree effectively amounts to a deeper CNN. NRF allows for parallelizable training of all "shallow" CNNs, and efficient enforcing of smoothness in depth estimation results. Our evaluation on the benchmark Make3D and NYUv2 datasets demonstrates that NRF outperforms the state of the art, and gracefully handles gradually decreasing training datasets.
summary: @cite_25 @cite_27 proposed to extract deep features to divide the problem space and use simple probabilistic distribution at leaf nodes. These models enabled traditional decision regression trees with deep representation learning ability. Leaf node update rules were proposed based on convex optimization techniques, and they out-performed deep models without divide-and-conquer strategy. However, since the last layer of a deep model was used to divide the problem space, every path in the tree needs to be computed. Even when a branch of computation contributes little to the final prediction, it stills need evaluation because each splitting node requires the full forward-pass of the deep neural network. A model structure where each splitting node is separately evaluated was used @cite_7 for depth estimation, but a general framework was missing and the effect of computation path pruning was not investigated.