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_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.
@cite_27 @cite_25 @cite_7
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In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data, and strong local models are needed to make good predictions. Addressing these problems, we propose a binary tree-structured hierarchical routing mixture of experts (HRME) model that has classifiers as non-leaf node experts and simple regression models as leaf node experts. The classifier nodes jointly soft-partition the input-output space based on the natural separateness of multimodal data. This enables simple leaf experts to be effective for prediction. Further, we develop a probabilistic framework for the HRME model, and propose a recursive Expectation-Maximization (EM) based algorithm to learn both the tree structure and the expert models. Experiments on a collection of regression tasks validate the effectiveness of our method compared to a variety of other regression models. 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. 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). Randomized decision trees and forests have a rich history in machine learning and have seen considerable success in application, perhaps particularly so for computer vision. However, they face a fundamental limitation: given enough data, the number of nodes in decision trees will grow exponentially with depth. For certain applications, for example on mobile or embedded processors, memory is a limited resource, and so the exponential growth of trees limits their depth, and thus their potential accuracy. This paper proposes decision jungles, revisiting the idea of ensembles of rooted decision directed acyclic graphs (DAGs), and shows these to be compact and powerful discriminative models for classification. Unlike conventional decision trees that only allow one path to every node, a DAG in a decision jungle allows multiple paths from the root to each leaf. We present and compare two new node merging algorithms that jointly optimize both the features and the structure of the DAGs efficiently. During training, node splitting and node merging are driven by the minimization of exactly the same objective function, here the weighted sum of entropies at the leaves. Results on varied datasets show that, compared to decision forests and several other baselines, decision jungles require dramatically less memory while considerably improving generalization. Deep neural networks and decision trees operate on largely separate paradigms; typically, the former performs representation learning with pre-specified architectures, while the latter is characterised by learning hierarchies over pre-specified features with data-driven architectures. We unite the two via adaptive neural trees (ANTs) that incorporates representation learning into edges, routing functions and leaf nodes of a decision tree, along with a backpropagation-based training algorithm that adaptively grows the architecture from primitive modules (e.g., convolutional layers). We demonstrate that, whilst achieving competitive performance on classification and regression datasets, ANTs benefit from (i) lightweight inference via conditional computation, (ii) hierarchical separation of features useful to the task e.g. learning meaningful class associations, such as separating natural vs. man-made objects, and (iii) a mechanism to adapt the architecture to the size and complexity of the training dataset. Conventional appearance-based gaze estimation methods employ local or global features as eye gaze appearance descriptor. But these methods don't work well under natural light with free head movement. To solve this problem, we present an appearance-based gaze estimation method using deep feature representation and feature forest regression. The deep feature is learned through hierarchical extraction of deep Convolutional Neural Network (CNN). And random forest regression with cluster-to-classify node splitting rules is used to take advantage of data distribution in sparse feature space. Experimental results demonstrate that the deep feature has a better performance than local features on calibrated gaze regression. The combination of deep features and random forest regression provides an effective solution for gaze estimation in a natural environment. 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. We give a (ln n+ 1)-approximation for the decision tree (DT) problem. An instance of DT is a set of mbinary tests T= (T 1 , ..., T m ) and a set of nitems X= (X 1 , ..., X n ). The goal is to output a binary tree where each internal node is a test, each leaf is an item and the total external path length of the tree is minimized. Total external path length is the sum of the depths of all the leaves in the tree. DT has a long history in computer science with applications ranging from medical diagnosis to experiment design. It also generalizes the problem of finding optimal average-case search strategies in partially ordered sets which includes several alphabetic tree problems. Our work decreases the previous upper bound on the approximation ratio by a constant factor. We provide a new analysis of the greedy algorithm that uses a simple accounting scheme to spread the cost of a tree among pairs of items split at a particular node. We conclude by showing that our upper bound also holds for the DT problem with weighted tests. 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. This paper proposes a learning-based approach to scene parsing inspired by the deep Recursive Context Propagation Network (RCPN). RCPN is a deep feed-forward neural network that utilizes the contextual information from the entire image, through bottom-up followed by top-down context propagation via random binary parse trees. This improves the feature representation of every super-pixel in the image for better classification into semantic categories. We analyze RCPN and propose two novel contributions to further improve the model. We first analyze the learning of RCPN parameters and discover the presence of bypass error paths in the computation graph of RCPN that can hinder contextual propagation. We propose to tackle this problem by including the classification loss of the internal nodes of the random parse trees in the original RCPN loss function. Secondly, we use an MRF on the parse tree nodes to model the hierarchical dependency present in the output. Both modifications provide performance boosts over the original RCPN and the new system achieves state-of-the-art performance on Stanford Background, SIFT-Flow and Daimler urban datasets. We present OctNet, a representation for deep learning with sparse 3D data. In contrast to existing models, our representation enables 3D convolutional networks which are both deep and high resolution. Towards this goal, we exploit the sparsity in the input data to hierarchically partition the space using a set of unbalanced octrees where each leaf node stores a pooled feature representation. This allows to focus memory allocation and computation to the relevant dense regions and enables deeper networks without compromising resolution. We demonstrate the utility of our OctNet representation by analyzing the impact of resolution on several 3D tasks including 3D object classification, orientation estimation and point cloud labeling. Deep neural networks (DNNs) have become the dominant technique for acoustic-phonetic modeling due to their markedly improved performance over other models. Despite this, little is understood about the computation they implement in creating phonemic categories from highly variable acoustic signals. In this paper, we analyzed a DNN trained for phoneme recognition and characterized its representational properties, both at the single node and population level in each layer. At the single node level, we found strong selectivity to distinct phonetic features in all layers. Node selectivity to specific manners and places of articulation appeared from the first hidden layer and became more explicit in deeper layers. Furthermore, we found that nodes with similar phonetic feature selectivity were differentially activated to different exemplars of these features. Thus, each node becomes tuned to a particular acoustic manifestation of the same feature, providing an effective representational basis for the formation of invariant phonemic categories. This study reveals that phonetic features organize the activations in different layers of a DNN, a result that mirrors the recent findings of feature encoding in the human auditory system. These insights may provide better understanding of the limitations of current models, leading to new strategies to improve their performance. Index Terms: Deep neural networks, deep learning, automatic speech recognition. We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are built from pre-mined association rules. They have a logical structure that is a sequence of IF-THEN rules, identical to a decision list or one-sided decision tree. Instead of using greedy splitting and pruning like decision tree algorithms, we aim to fully optimize over rule lists, striking a practical balance between accuracy, interpretability, and computational speed. The algorithm presented here uses a mixture of theoretical bounds (tight enough to have practical implications as a screening or bounding procedure), computational reuse, and highly tuned language libraries to achieve computational efficiency. Currently, for many practical problems, this method achieves better accuracy and sparsity than decision trees, with practical running times. The predictions in each leaf are probabilistic. We propose a compact and efficient index structure for massive data sets. Several indexing techniques are widely-used and well-known such as binary trees and B+trees. Unfortunately, we find that these techniques suffer major two shortcomings when applied to massive sets; first, their indices are so large they could overflow regular main memory, and, second, they suffer from a variety of penalties (e.g., conditional branches, low cache hits, and TLB misses), which restricts the number of instructions executed per processor cycle. Our state-of-the-art index structure, called VAST-Tree, classifies branch nodes into multiple layers. It applies existing techniques such as cache-conscious, aligned, and branch-free structures to the top layers of branch nodes in trees. Next, it applies the adaptive compression technique to save space and harness data parallelism with SIMD instructions to the middle and bottom layers of branch nodes. Moreover, a processor-friendly compression technique is applied to leaf nodes. The end result is that trees are much more compact and traversal efficiency is high. We implement a prototype and show its resulting index size and performance as compared to binary trees, and the hardware-conscious technique called FAST which currently offers the highest performance. Compared to current alternatives, VAST-Tree compacts the branch nodes by more than 95 , and the overall index size by 47-84 given that there are 230 keys. With 228 keys, it has roughly 6.0-times and 1.24-times throughput and saves the memory consumption by more than 94.7 and 40.5 as compared to binary trees and FAST, respectively. The availability of large-scale annotated data and the uneven separability of different data categories have become two major impediments of deep learning for image classification. In this paper, we present a semi-supervised hierarchical convolutional neural network (SS-HCNN) to address these two challenges. A large-scale unsupervised maximum margin clustering technique is designed, which splits images into a number of hierarchical clusters iteratively to learn cluster-level CNNs at parent nodes and category-level CNNs at leaf nodes. The splitting uses the similarity of CNN features to group visually similar images into the same cluster, which relieves the uneven data separability constraint. With the hierarchical cluster-level CNNs capturing certain high-level image category information, the category-level CNNs can be trained with a small amount of labeled images, and this relieves the data annotation constraint. A novel cluster splitting criterion is also designed, which automatically terminates the image clustering in the tree hierarchy. The proposed SS-HCNN has been evaluated on the CIFAR-100 and ImageNet classification datasets. The experiments show that the SS-HCNN trained using a portion of labeled training images can achieve comparable performance with other fully trained CNNs using all labeled images. Additionally, the SS-HCNN trained using all labeled images clearly outperforms other fully trained CNNs. Display Omitted Deep convolutional neural network (CNN) for plant identification focusing on leaf vein patterns.No task-specific feature extractors needed.Improved the state of the art accuracy on a legume species recognition task.Visualization of relevant vein patterns. We propose using a deep convolutional neural network (CNN) for the problem of plant identification from leaf vein patterns. In particular, we consider classifying three different legume species: white bean, red bean and soybean. The introduction of a CNN avoids the use of handcrafted feature extractors as it is standard in state of the art pipeline. Furthermore, this deep learning approach significantly improves the accuracy of the referred pipeline. We also show that the reported accuracy is reached by increasing the model depth. Finally, by analyzing the resulting models with a simple visualization technique, we are able to unveil relevant vein patterns. Many researchers have introduced tag information to recommender systems to improve the performance of traditional recommendation techniques. However, user-defined tags will usually suffer from many problems, such as sparsity, redundancy, and ambiguity. To address these problems, we propose a new recommendation algorithm based on deep neural networks. In the proposed algorithm, users' profiles are initially represented by tags and then a deep neural network model is used to extract the in-depth features from tag space layer by layer. In this way, representations of the raw data will become more abstract and advanced, and therefore the unique structure of tag space will be revealed automatically. Based on those extracted abstract features, users' profiles are updated and used for making recommendations. The experimental results demonstrate the usefulness of the proposed algorithm and show its superior performance over the clustering based recommendation algorithms. In addition, the impact of network depth on the algorithm performance is also investigated. Extreme learning machine (ELM) is an emerging learning algorithm for the generalized single hidden layer feedforward neural networks, of which the hidden node parameters are randomly generated and the output weights are analytically computed. However, due to its shallow architecture, feature learning using ELM may not be effective for natural signals (e.g., images videos), even with a large number of hidden nodes. To address this issue, in this paper, a new ELM-based hierarchical learning framework is proposed for multilayer perceptron. The proposed architecture is divided into two main components: 1) self-taught feature extraction followed by supervised feature classification and 2) they are bridged by random initialized hidden weights. The novelties of this paper are as follows: 1) unsupervised multilayer encoding is conducted for feature extraction, and an ELM-based sparse autoencoder is developed via l 1 constraint. By doing so, it achieves more compact and meaningful feature representations than the original ELM; 2) by exploiting the advantages of ELM random feature mapping, the hierarchically encoded outputs are randomly projected before final decision making, which leads to a better generalization with faster learning speed; and 3) unlike the greedy layerwise training of deep learning (DL), the hidden layers of the proposed framework are trained in a forward manner. Once the previous layer is established, the weights of the current layer are fixed without fine-tuning. Therefore, it has much better learning efficiency than the DL. Extensive experiments on various widely used classification data sets show that the proposed algorithm achieves better and faster convergence than the existing state-of-the-art hierarchical learning methods. Furthermore, multiple applications in computer vision further confirm the generality and capability of the proposed learning scheme. The skyline of a set of d-dimensional points contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive (or online) algorithms that can quickly return the first skyline points without having to read the entire data file. Currently, the most efficient algorithm is NN ( n earest n eighbors), which applies the divide -and-conquer framework on datasets indexed by R-trees. Although NN has some desirable features (such as high speed for returning the initial skyline points, applicability to arbitrary data distributions and dimensions), it also presents several inherent disadvantages (need for duplicate elimination if d>2, multiple accesses of the same node, large space overhead). In this paper we develop BBS ( b ranch-and- b ound s kyline), a progressive algorithm also based on nearest neighbor search, which is IO optimal, i.e., it performs a single access only to those R-tree nodes that may contain skyline points. Furthermore, it does not retrieve duplicates and its space overhead is significantly smaller than that of NN. Finally, BBS is simple to implement and can be efficiently applied to a variety of alternative skyline queries. An analytical and experimental comparison shows that BBS outperforms NN (usually by orders of magnitude) under all problem instances.