Recurrent Neural Networks (RNNs) are designed to handle sequential data but suffer from vanishing or exploding gradients. Recent work on Unitary Recurrent Neural Networks (uRNNs) have been used to address this issue and in some cases, exceed the capabilities of Long Short-Term Memory networks (LSTMs). We propose a simpler and novel update scheme to maintain orthogonal recurrent weight matrices without using complex valued matrices. This is done by parametrizing with a skew-symmetric matrix using the Cayley transform. Such a parametrization is unable to represent matrices with negative one eigenvalues, but this limitation is overcome by scaling the recurrent weight matrix by a diagonal matrix consisting of ones and negative ones. The proposed training scheme involves a straightforward gradient calculation and update step. In several experiments, the proposed scaled Cayley orthogonal recurrent neural network (scoRNN) achieves superior results with fewer trainable parameters than other unitary RNNs.

* 12 pages
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Deep Convolution Neural Networks (DCNNs) are capable of learning unprecedentedly effective image representations. However, their ability in handling significant local and global image rotations remains limited. In this paper, we propose Active Rotating Filters (ARFs) that actively rotate during convolution and produce feature maps with location and orientation explicitly encoded. An ARF acts as a virtual filter bank containing the filter itself and its multiple unmaterialised rotated versions. During back-propagation, an ARF is collectively updated using errors from all its rotated versions. DCNNs using ARFs, referred to as Oriented Response Networks (ORNs), can produce within-class rotation-invariant deep features while maintaining inter-class discrimination for classification tasks. The oriented response produced by ORNs can also be used for image and object orientation estimation tasks. Over multiple state-of-the-art DCNN architectures, such as VGG, ResNet, and STN, we consistently observe that replacing regular filters with the proposed ARFs leads to significant reduction in the number of network parameters and improvement in classification performance. We report the best results on several commonly used benchmarks.

* Accepted in CVPR 2017. Source code available at http://yzhou.work/ORN
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Recurrent neural networks (RNNs) have been successfully used on a wide range of sequential data problems. A well known difficulty in using RNNs is the \textit{vanishing or exploding gradient} problem. Recently, there have been several different RNN architectures that try to mitigate this issue by maintaining an orthogonal or unitary recurrent weight matrix. One such architecture is the scaled Cayley orthogonal recurrent neural network (scoRNN) which parameterizes the orthogonal recurrent weight matrix through a scaled Cayley transform. This parametrization contains a diagonal scaling matrix consisting of positive or negative one entries that can not be optimized by gradient descent. Thus the scaling matrix is fixed before training and a hyperparameter is introduced to tune the matrix for each particular task. In this paper, we develop a unitary RNN architecture based on a complex scaled Cayley transform. Unlike the real orthogonal case, the transformation uses a diagonal scaling matrix consisting of entries on the complex unit circle which can be optimized using gradient descent and no longer requires the tuning of a hyperparameter. We also provide an analysis of a potential issue of the modReLU activiation function which is used in our work and several other unitary RNNs. In the experiments conducted, the scaled Cayley unitary recurrent neural network (scuRNN) achieves comparable or better results than scoRNN and other unitary RNNs without fixing the scaling matrix.

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Weakly supervised instance segmentation with image-level labels, instead of expensive pixel-level masks, remains unexplored. In this paper, we tackle this challenging problem by exploiting class peak responses to enable a classification network for instance mask extraction. With image labels supervision only, CNN classifiers in a fully convolutional manner can produce class response maps, which specify classification confidence at each image location. We observed that local maximums, i.e., peaks, in a class response map typically correspond to strong visual cues residing inside each instance. Motivated by this, we first design a process to stimulate peaks to emerge from a class response map. The emerged peaks are then back-propagated and effectively mapped to highly informative regions of each object instance, such as instance boundaries. We refer to the above maps generated from class peak responses as Peak Response Maps (PRMs). PRMs provide a fine-detailed instance-level representation, which allows instance masks to be extracted even with some off-the-shelf methods. To the best of our knowledge, we for the first time report results for the challenging image-level supervised instance segmentation task. Extensive experiments show that our method also boosts weakly supervised pointwise localization as well as semantic segmentation performance, and reports state-of-the-art results on popular benchmarks, including PASCAL VOC 2012 and MS COCO.

* Accepted in CVPR 2018 (Spotlight)
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Weakly supervised object localization remains challenging, where only image labels instead of bounding boxes are available during training. Object proposal is an effective component in localization, but often computationally expensive and incapable of joint optimization with some of the remaining modules. In this paper, to the best of our knowledge, we for the first time integrate weakly supervised object proposal into convolutional neural networks (CNNs) in an end-to-end learning manner. We design a network component, Soft Proposal (SP), to be plugged into any standard convolutional architecture to introduce the nearly cost-free object proposal, orders of magnitude faster than state-of-the-art methods. In the SP-augmented CNNs, referred to as Soft Proposal Networks (SPNs), iteratively evolved object proposals are generated based on the deep feature maps then projected back, and further jointly optimized with network parameters, with image-level supervision only. Through the unified learning process, SPNs learn better object-centric filters, discover more discriminative visual evidence, and suppress background interference, significantly boosting both weakly supervised object localization and classification performance. We report the best results on popular benchmarks, including PASCAL VOC, MS COCO, and ImageNet.

* ICCV 2017
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In this paper, a self-learning approach is proposed towards solving scene-specific pedestrian detection problem without any human' annotation involved. The self-learning approach is deployed as progressive steps of object discovery, object enforcement, and label propagation. In the learning procedure, object locations in each frame are treated as latent variables that are solved with a progressive latent model (PLM). Compared with conventional latent models, the proposed PLM incorporates a spatial regularization term to reduce ambiguities in object proposals and to enforce object localization, and also a graph-based label propagation to discover harder instances in adjacent frames. With the difference of convex (DC) objective functions, PLM can be efficiently optimized with a concave-convex programming and thus guaranteeing the stability of self-learning. Extensive experiments demonstrate that even without annotation the proposed self-learning approach outperforms weakly supervised learning approaches, while achieving comparable performance with transfer learning and fully supervised approaches.

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Thompson Sampling algorithm is a well known Bayesian algorithm for solving stochastic multi-armed bandit. At each time step the algorithm chooses each arm with probability proportional to it being the current best arm. We modify the strategy by introducing a paramter h which alters the importance of the probability of an arm being the current best arm. We show that the optimality of Thompson sampling is robust to this perturbation within a range of parameter values for two arm bandits.

* 12 pages,0 figures
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In this paper, we propose an auto-encoder based generative neural network model whose encoder compresses the inputs into vectors in the tangent space of a special Lie group manifold: upper triangular positive definite affine transform matrices (UTDATs). UTDATs are representations of Gaussian distributions and can straightforwardly generate Gaussian distributed samples. Therefore, the encoder is trained together with a decoder (generator) which takes Gaussian distributed latent vectors as input. Compared with related generative models such as variational auto-encoder, the proposed model incorporates the information on geometric properties of Gaussian distributions. As a special case, we derive an exponential mapping layer for diagonal Gaussian UTDATs which eliminates matrix exponential operator compared with general exponential mapping in Lie group theory. Moreover, we derive an intrinsic loss for UTDAT Lie group which can be calculated as l-2 loss in the tangent space. Furthermore, inspired by the Lie group theory, we propose to use the Lie algebra vectors rather than the raw parameters (e.g. mean) of Gaussian distributions as compressed representations of original inputs. Experimental results verity the effectiveness of the proposed new generative model and the benefits gained from the Lie group structural information of UTDATs.

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The developments of deep neural networks (DNN) in recent years have ushered a brand new era of artificial intelligence. DNNs are proved to be excellent in solving very complex problems, e.g., visual recognition and text understanding, to the extent of competing with or even surpassing people. Despite inspiring and encouraging success of DNNs, thorough theoretical analyses still lack to unravel the mystery of their magics. The design of DNN structure is dominated by empirical results in terms of network depth, number of neurons and activations. A few of remarkable works published recently in an attempt to interpret DNNs have established the first glimpses of their internal mechanisms. Nevertheless, research on exploring how DNNs operate is still at the initial stage with plenty of room for refinement. In this paper, we extend precedent research on neural networks with piecewise linear activations (PLNN) concerning linear regions bounds. We present (i) the exact maximal number of linear regions for single layer PLNNs; (ii) a upper bound for multi-layer PLNNs; and (iii) a tighter upper bound for the maximal number of liner regions on rectifier networks. The derived bounds also indirectly explain why deep models are more powerful than shallow counterparts, and how non-linearity of activation functions impacts on expressiveness of networks.

* Counting linear regions of neural networks
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Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a unified framework that includes low, moderate and high dimensions, we study multidimensional scaling in the setting of clustering noisy data. Our results suggest that, in order to achieve consistent estimation of the embedding scheme, the classical multidimensional scaling needs to be modified, especially when the noise level increases. To this end, we propose {\it modified multidimensional scaling} which applies a nonlinear transformation to the sample eigenvalues. The nonlinear transformation depends on the dimensionality, sample size and unknown moment. We show that modified multidimensional scaling followed by various clustering algorithms can achieve exact recovery, i.e., all the cluster labels can be recovered correctly with probability tending to one. Numerical simulations and two real data applications lend strong support to our proposed methodology. As a byproduct, we unify and improve existing results on the $\ell_{\infty}$ bound for eigenvectors under only low bounded moment conditions. This can be of independent interest.

* 31 pages, 4 figures
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Edge features contain important information about graphs. However, current state-of-the-art neural network models designed for graph learning do not consider incorporating edge features, especially multi-dimensional edge features. In this paper, we propose an attention mechanism which combines both node features and edge features. Guided by the edge features, the attention mechanism on a pair of graph nodes will not only depend on node contents, but also ajust automatically with respect to the properties of the edge connecting these two nodes. Moreover, the edge features are adjusted by the attention function and fed to the next layer, which means our edge features are adaptive across network layers. As a result, our proposed adaptive edge features guided graph attention model can consolidate a rich source of graph information that current state-of-the-art graph learning methods cannot. We apply our proposed model to graph node classification, and experimental results on three citaion network datasets and a biological network dataset show that out method outperforms the current state-of-the-art methods, testifying to the discriminative capability of edge features and the effectiveness of our adaptive edge features guided attention model. Additional ablation experimental study further shows that both the edge features and adaptiveness components contribute to our model.

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The locations of the fiducial facial landmark points around facial components and facial contour capture the rigid and non-rigid facial deformations due to head movements and facial expressions. They are hence important for various facial analysis tasks. Many facial landmark detection algorithms have been developed to automatically detect those key points over the years, and in this paper, we perform an extensive review of them. We classify the facial landmark detection algorithms into three major categories: holistic methods, Constrained Local Model (CLM) methods, and the regression-based methods. They differ in the ways to utilize the facial appearance and shape information. The holistic methods explicitly build models to represent the global facial appearance and shape information. The CLMs explicitly leverage the global shape model but build the local appearance models. The regression-based methods implicitly capture facial shape and appearance information. For algorithms within each category, we discuss their underlying theories as well as their differences. We also compare their performances on both controlled and in the wild benchmark datasets, under varying facial expressions, head poses, and occlusion. Based on the evaluations, we point out their respective strengths and weaknesses. There is also a separate section to review the latest deep learning-based algorithms. The survey also includes a listing of the benchmark databases and existing software. Finally, we identify future research directions, including combining methods in different categories to leverage their respective strengths to solve landmark detection "in-the-wild".

* International Journal on Computer Vision, 2017
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Feature learning with deep models has achieved impressive results for both data representation and classification for various vision tasks. Deep feature learning, however, typically requires a large amount of training data, which may not be feasible for some application domains. Transfer learning can be one of the approaches to alleviate this problem by transferring data from data-rich source domain to data-scarce target domain. Existing transfer learning methods typically perform one-shot transfer learning and often ignore the specific properties that the transferred data must satisfy. To address these issues, we introduce a constrained deep transfer feature learning method to perform simultaneous transfer learning and feature learning by performing transfer learning in a progressively improving feature space iteratively in order to better narrow the gap between the target domain and the source domain for effective transfer of the data from the source domain to target domain. Furthermore, we propose to exploit the target domain knowledge and incorporate such prior knowledge as a constraint during transfer learning to ensure that the transferred data satisfies certain properties of the target domain. To demonstrate the effectiveness of the proposed constrained deep transfer feature learning method, we apply it to thermal feature learning for eye detection by transferring from the visible domain. We also applied the proposed method for cross-view facial expression recognition as a second application. The experimental results demonstrate the effectiveness of the proposed method for both applications.

* International Conference on Computer Vision and Pattern Recognition, 2016
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We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of functional gradient descent that minimizes the KL divergence. Empirical studies are performed on various real world models and datasets, on which our method is competitive with existing state-of-the-art methods. The derivation of our method is based on a new theoretical result that connects the derivative of KL divergence under smooth transforms with Stein's identity and a recently proposed kernelized Stein discrepancy, which is of independent interest.

* To appear in NIPS 2016
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The importance of accurate recommender systems has been widely recognized by academia and industry. However, the recommendation quality is still rather low. Recently, a linear sparse and low-rank representation of the user-item matrix has been applied to produce Top-N recommendations. This approach uses the nuclear norm as a convex relaxation for the rank function and has achieved better recommendation accuracy than the state-of-the-art methods. In the past several years, solving rank minimization problems by leveraging nonconvex relaxations has received increasing attention. Some empirical results demonstrate that it can provide a better approximation to original problems than convex relaxation. In this paper, we propose a novel rank approximation to enhance the performance of Top-N recommendation systems, where the approximation error is controllable. Experimental results on real data show that the proposed rank approximation improves the Top-$N$ recommendation accuracy substantially.

* SDM 2016. arXiv admin note: text overlap with arXiv:1601.04800
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Concept hierarchy is the backbone of ontology, and the concept hierarchy acquisition has been a hot topic in the field of ontology learning. this paper proposes a hyponymy extraction method of domain ontology concept based on cascaded conditional random field(CCRFs) and hierarchy clustering. It takes free text as extracting object, adopts CCRFs identifying the domain concepts. First the low layer of CCRFs is used to identify simple domain concept, then the results are sent to the high layer, in which the nesting concepts are recognized. Next we adopt hierarchy clustering to identify the hyponymy relation between domain ontology concepts. The experimental results demonstrate the proposed method is efficient.

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Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the intractable inference. To address this problem, most existing algorithms make assumptions to render the latent variables independent of each other, either by designing specific priors, or by approximating the true posterior using a factorized distribution. We believe the correlations among latent variables are crucial for faithful data representation. Driven by this idea, we propose an inference method based on the conditional pseudo-likelihood that preserves the dependencies among the latent variables. For learning, we propose to employ the hard Expectation Maximization (EM) algorithm, which avoids the intractability of the traditional EM by max-out instead of sum-out to compute the data likelihood. Qualitative and quantitative evaluations of our model against state of the art deep models on benchmark datasets demonstrate the effectiveness of the proposed algorithm in data representation and reconstruction.

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Bayesian networks are a useful tool in the representation of uncertain knowledge. This paper proposes a new algorithm called ACO-E, to learn the structure of a Bayesian network. It does this by conducting a search through the space of equivalence classes of Bayesian networks using Ant Colony Optimization (ACO). To this end, two novel extensions of traditional ACO techniques are proposed and implemented. Firstly, multiple types of moves are allowed. Secondly, moves can be given in terms of indices that are not based on construction graph nodes. The results of testing show that ACO-E performs better than a greedy search and other state-of-the-art and metaheuristic algorithms whilst searching in the space of equivalence classes.

* Journal Of Artificial Intelligence Research, Volume 35, pages 391-447, 2009
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Recognizing group activities is challenging due to the difficulties in isolating individual entities, finding the respective roles played by the individuals and representing the complex interactions among the participants. Individual actions and group activities in videos can be represented in a common framework as they share the following common feature: both are composed of a set of low-level features describing motions, e.g., optical flow for each pixel or a trajectory for each feature point, according to a set of composition constraints in both temporal and spatial dimensions. In this paper, we present a unified model to assess the similarity between two given individual or group activities. Our approach avoids explicit extraction of individual actors, identifying and representing the inter-person interactions. With the proposed approach, retrieval from a video database can be performed through Query-by-Example; and activities can be recognized by querying videos containing known activities. The suggested video matching process can be performed in an unsupervised manner. We demonstrate the performance of our approach by recognizing a set of human actions and football plays.

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Variational inference with {\alpha}-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using {\alpha}-divergences (with positive {\alpha} values) is their mass-covering property. However, estimating and optimizing {\alpha}-divergences require to use importance sampling, which could have extremely large or infinite variances due to heavy tails of importance weights. In this paper, we propose a new class of tail-adaptive f-divergences that adaptively change the convex function f with the tail of the importance weights, in a way that theoretically guarantees finite moments, while simultaneously achieving mass-covering properties. We test our methods on Bayesian neural networks, as well as deep reinforcement learning in which our method is applied to improve a recent soft actor-critic (SAC) algorithm. Our results show that our approach yields significant advantages compared with existing methods based on classical KL and {\alpha}-divergences.

* Conference on Neural Information Processing Systems (NIPS) 2018
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