In this paper, we study the problem of semi-supervised structured output prediction, which aims to learn predictors for structured outputs, such as sequences, tree nodes, vectors, etc., from a set of data points of both inputoutput pairs and single inputs without outputs. The traditional methods to solve this problem usually learns one single predictor for all the data points, and ignores the variety of the different data points. Different parts of the data set may have different local distributions, and requires different optimal local predictors. To overcome this disadvantage of existing methods, we propose to learn different local predictors for neighborhoods of different data points, and the missing structured outputs simultaneously. In the neighborhood of each data point, we proposed to learn a linear predictor by minimizing both the complexity of the predictor and the upper bound of the structured prediction loss. The minimization is conducted by gradient descent algorithms. Experiments over four benchmark data sets, including DDSM mammography medical images, SUN natural image data set, Cora research paper data set, and Spanish news wire article sentence data set, show the advantages of the proposed method.
Brefeld and Scheffer @cite_10 proposed to solve the problem of semi-supervised structured output prediction by learning in the space of input-output space, and using co-training method. This method is based on the assumption that the multiple structured output predictors should be consent with each other. Based on this assumption, the structural support vector machine is extended to the argued input-output space.
@cite_10
2137450504
Structured output prediction aims to learn a predictor to predict a structured output from a input data vector . The structured outputs include vector, tree, sequence, etc. We usually assume that we have a training set of input---output pairs to train the predictor. However, in many real-world applications, it is difficult to obtain the output for a input, and thus for many training input data points, the structured outputs are missing. In this paper, we discuss how to learn from a training set composed of some input---output pairs and some input data points without outputs. This problem is called semi-supervised structured output prediction. We propose a novel method for this problem by constructing a nearest neighbor graph from the input space to present the manifold structure and use it to regularize the structured output space directly. We define a slack structured output for each training data point and propose to predict it by learning a structured output predictor. The learning of both slack structured outputs and the predictor are unified within one single minimization problem. In this problem, we propose to minimize the structured loss between the slack structured outputs of neighboring data points and the prediction error measured by the structured loss. The problem is optimized by an iterative algorithm. Experiment results over three benchmark data sets show its advantage. The problem of learning a mapping between input and structured, interdependent output variables covers sequential, spatial, and relational learning as well as predicting recursive structures. Joint feature representations of the input and output variables have paved the way to leveraging discriminative learners such as SVMs to this class of problems. We address the problem of semi-supervised learning in joint input output spaces. The co-training approach is based on the principle of maximizing the consensus among multiple independent hypotheses; we develop this principle into a semi-supervised support vector learning algorithm for joint input output spaces and arbitrary loss functions. Experiments investigate the benefit of semi-supervised structured models in terms of accuracy and F1 score. Learning general functional dependencies is one of the main goals in machine learning. Recent progress in kernel-based methods has focused on designing flexible and powerful input representations. This paper addresses the complementary issue of problems involving complex outputs such as multiple dependent output variables and structured output spaces. We propose to generalize multiclass Support Vector Machine learning in a formulation that involves features extracted jointly from inputs and outputs. The resulting optimization problem is solved efficiently by a cutting plane algorithm that exploits the sparseness and structural decomposition of the problem. We demonstrate the versatility and effectiveness of our method on problems ranging from supervised grammar learning and named-entity recognition, to taxonomic text classification and sequence alignment. Many problems in machine learning and computer vision consist of predicting multi-dimensional output vectors given a specific set of input features. In many of these problems, there exist inherent temporal and spatial dependencies between the output vectors, as well as repeating output patterns and input-output associations, that can provide more robust and accurate predictors when modeled properly. With this intrinsic motivation, we propose a novel Output-Associative Relevance Vector Machine (OA-RVM) regression framework that augments the traditional RVM regression by being able to learn non-linear input and output dependencies. Instead of depending solely on the input patterns, OA-RVM models output covariances within a predefined temporal window, thus capturing past, current and future context. As a result, output patterns manifested in the training data are captured within a formal probabilistic framework, and subsequently used during inference. As a proof of concept, we target the highly challenging problem of dimensional and continuous prediction of emotions, and evaluate the proposed framework by focusing on the case of multiple nonverbal cues, namely facial expressions, shoulder movements and audio cues. We demonstrate the advantages of the proposed OA-RVM regression by performing subject-independent evaluation using the SAL database that constitutes naturalistic conversational interactions. The experimental results show that OA-RVM regression outperforms the traditional RVM and SVM regression approaches in terms of accuracy of the prediction (evaluated using the Root Mean Squared Error) and structure of the prediction (evaluated using the correlation coefficient), generating more accurate and robust prediction models. Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary issue of designing classification algorithms that can deal with more complex outputs, such as trees, sequences, or sets. More generally, we consider problems involving multiple dependent output variables, structured output spaces, and classification problems with class attributes. In order to accomplish this, we propose to appropriately generalize the well-known notion of a separation margin and derive a corresponding maximum-margin formulation. While this leads to a quadratic program with a potentially prohibitive, i.e. exponential, number of constraints, we present a cutting plane algorithm that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval extraction, and optical character recognition. Experiments from various domains involving different types of output spaces emphasize the breadth and generality of our approach. Many machine learning algorithms assume that all input samples are independently and identically distributed from some common distribution on either the input space X, in the case of unsupervised learning, or the input and output space XxY in the case of supervised and semi-supervised learning. In the last number of years the relaxation of this assumption has been explored and the importance of incorporation of additional information within machine learning algorithms became more apparent. Traditionally such fusion of information was the domain of semi-supervised learning. More recently the inclusion of knowledge from separate hypothetical spaces has been proposed by Vapnik as part of the supervised setting. In this work we are interested in exploring Vapnik's idea of 'master-class' learning and the associated learning using 'privileged' information, however within the unsupervised setting. Adoption of the advanced supervised learning paradigm for the unsupervised setting instigates investigation into the difference between privileged and technical data. By means of our proposed aRi-MAX method stability of the K-Means algorithm is improved and identification of the best clustering solution is achieved on an artificial dataset. Subsequently an information theoretic dot product based algorithm called P-Dot is proposed. This method has the ability to utilize a wide variety of clustering techniques, individually or in combination, while fusing privileged and technical data for improved clustering. Application of the P-Dot method to the task of digit recognition confirms our findings in a real-world scenario. We consider a framework for structured prediction based on search in the space of complete structured outputs. Given a structured input, an output is produced by running a time-bounded search procedure guided by a learned cost function, and then returning the least cost output uncovered during the search. This framework can be instantiated for a wide range of search spaces and search procedures, and easily incorporates arbitrary structured-prediction loss functions. In this paper, we make two main technical contributions. First, we define the limited-discrepancy search space over structured outputs, which is able to leverage powerful classification learning algorithms to improve the search space quality. Second, we give a generic cost function learning approach, where the key idea is to learn a cost function that attempts to mimic the behavior of conducting searches guided by the true loss function. Our experiments on six benchmark domains demonstrate that using our framework with only a small amount of search is sufficient for significantly improving on state-of-the-art structured-prediction performance. Structured prediction is the problem of learning a function from structured inputs to structured outputs. Inspired by the recent successes of search-based structured prediction, we introduce a new framework for structured prediction called HC-Search. Given a structured input, the framework uses a search procedure guided by a learned heuristic H to uncover high quality candidate outputs and then uses a separate learned cost function C to select a final prediction among those outputs. We can decompose the regret of the overall approach into the loss due to H not leading to high quality outputs, and the loss due to C not selecting the best among the generated outputs. Guided by this decomposition, we minimize the overall regret in a greedy stagewise manner by first training H to quickly uncover high quality outputs via imitation learning, and then training C to correctly rank the outputs generated via H according to their true losses. Experiments on several benchmark domains show that our approach significantly outperforms the state-of-the-art methods. In this paper, we present a simple and efficient method for training deep neural networks in a semi-supervised setting where only a small portion of training data is labeled. We introduce self-ensembling, where we form a consensus prediction of the unknown labels using the outputs of the network-in-training on different epochs, and most importantly, under different regularization and input augmentation conditions. This ensemble prediction can be expected to be a better predictor for the unknown labels than the output of the network at the most recent training epoch, and can thus be used as a target for training. Using our method, we set new records for two standard semi-supervised learning benchmarks, reducing the (non-augmented) classification error rate from 18.44 to 7.05 in SVHN with 500 labels and from 18.63 to 16.55 in CIFAR-10 with 4000 labels, and further to 5.12 and 12.16 by enabling the standard augmentations. We additionally obtain a clear improvement in CIFAR-100 classification accuracy by using random images from the Tiny Images dataset as unlabeled extra inputs during training. Finally, we demonstrate good tolerance to incorrect labels. We consider a framework for structured prediction based on search in the space of complete structured outputs. Given a structured input, an output is produced by running a time-bounded search procedure guided by a learned cost function, and then returning the least cost output uncovered during the search. This framework can be instantiated for a wide range of search spaces and search procedures, and easily incorporates arbitrary structured-prediction loss functions. In this paper, we make two main technical contributions. First, we describe a novel approach to automatically defining an effective search space over structured outputs, which is able to leverage the availability of powerful classification learning algorithms. In particular, we define the limited-discrepancy search space and relate the quality of that space to the quality of learned classifiers. We also define a sparse version of the search space to improve the effciency of our overall approach. Second, we give a generic cost function learning approach that is applicable to a wide range of search procedures. The key idea is to learn a cost function that attempts to mimic the behavior of conducting searches guided by the true loss function. Our experiments on six benchmark domains show that a small amount of search in limited discrepancy search space is often sufficient for significantly improving on state-of-the-art structured-prediction performance. We also demonstrate significant speed improvements for our approach using sparse search spaces with little or no loss in accuracy. This paper focuses on structured-output learning using deep neural networks for 3D human pose estimation from monocular images. Our network takes an image and 3D pose as inputs and outputs a score value, which is high when the image-pose pair matches and low otherwise. The network structure consists of a convolutional neural network for image feature extraction, followed by two sub-networks for transforming the image features and pose into a joint embedding. The score function is then the dot-product between the image and pose embeddings. The image-pose embedding and score function are jointly trained using a maximum-margin cost function. Our proposed framework can be interpreted as a special form of structured support vector machines where the joint feature space is discriminatively learned using deep neural networks. We test our framework on the Human3.6m dataset and obtain state-of-the-art results compared to other recent methods. Finally, we present visualizations of the image-pose embedding space, demonstrating the network has learned a high-level embedding of body-orientation and pose-configuration. Adaptive tracking-by-detection methods are widely used in computer vision for tracking arbitrary objects. Current approaches treat the tracking problem as a classification task and use online learning techniques to update the object model. However, for these updates to happen one needs to convert the estimated object position into a set of labelled training examples, and it is not clear how best to perform this intermediate step. Furthermore, the objective for the classifier (label prediction) is not explicitly coupled to the objective for the tracker (accurate estimation of object position). In this paper, we present a framework for adaptive visual object tracking based on structured output prediction. By explicitly allowing the output space to express the needs of the tracker, we are able to avoid the need for an intermediate classification step. Our method uses a kernelized structured output support vector machine (SVM), which is learned online to provide adaptive tracking. To allow for real-time application, we introduce a budgeting mechanism which prevents the unbounded growth in the number of support vectors which would otherwise occur during tracking. Experimentally, we show that our algorithm is able to outperform state-of-the-art trackers on various benchmark videos. Additionally, we show that we can easily incorporate additional features and kernels into our framework, which results in increased performance. We propose a simple, interpretable framework for solving a wide range of image reconstruction problems such as denoising and deconvolution. Given a corrupted input image, the model synthesizes a spatially varying linear filter which, when applied to the input image, reconstructs the desired output. The model parameters are learned using supervised or self-supervised training. We test this model on three tasks: non-uniform motion blur removal, lossy-compression artifact reduction and single image super resolution. We demonstrate that our model substantially outperforms state-of-the-art methods on all these tasks and is significantly faster than optimization-based approaches to deconvolution. Unlike models that directly predict output pixel values, the predicted filter flow is controllable and interpretable, which we demonstrate by visualizing the space of predicted filters for different tasks. This paper focuses on structured-output learning using deep neural networks for 3D human pose estimation from monocular images. Our network takes an image and 3D pose as inputs and outputs a score value, which is high when the image-pose pair matches and low otherwise. The network structure consists of a convolutional neural network for image feature extraction, followed by two sub-networks for transforming the image features and pose into a joint embedding. The score function is then the dot-product between the image and pose embeddings. The image-pose embedding and score function are jointly trained using a maximum-margin cost function. Our proposed framework can be interpreted as a special form of structured support vector machines where the joint feature space is discriminatively learned using deep neural networks. We also propose an efficient recurrent neural network for performing inference with the learned image-embedding. We test our framework on the Human3.6m dataset and obtain state-of-the-art results compared to other recent methods. Finally, we present visualizations of the image-pose embedding space, demonstrating the network has learned a high-level embedding of body-orientation and pose-configuration. We introduce structured prediction energy networks (SPENs), a flexible framework for structured prediction. A deep architecture is used to define an energy function of candidate labels, and then predictions are produced by using back-propagation to iteratively optimize the energy with respect to the labels. This deep architecture captures dependencies between labels that would lead to intractable graphical models, and performs structure learning by automatically learning discriminative features of the structured output. One natural application of our technique is multi-label classification, which traditionally has required strict prior assumptions about the interactions between labels to ensure tractable learning and prediction. We are able to apply SPENs to multi-label problems with substantially larger label sets than previous applications of structured prediction, while modeling high-order interactions using minimal structural assumptions. Overall, deep learning provides remarkable tools for learning features of the inputs to a prediction problem, and this work extends these techniques to learning features of structured outputs. Our experiments provide impressive performance on a variety of benchmark multi-label classification tasks, demonstrate that our technique can be used to provide interpretable structure learning, and illuminate fundamental trade-offs between feed-forward and iterative structured prediction. We study the problem of mapping an input image to a tied pair consisting of a vector of parameters and an image that is created using a graphical engine from the vector of parameters. The mapping's objective is to have the output image as similar as possible to the input image. During training, no supervision is given in the form of matching inputs and outputs. This learning problem extends two literature problems: unsupervised domain adaptation and cross domain transfer. We define a generalization bound that is based on discrepancy, and employ a GAN to implement a network solution that corresponds to this bound. Experimentally, our method is shown to solve the problem of automatically creating avatars. Convolutional Neural Network (CNN) image classifiers are traditionally designed to have sequential convolutional layers with a single output layer. This is based on the assumption that all target classes should be treated equally and exclusively. However, some classes can be more difficult to distinguish than others, and classes may be organized in a hierarchy of categories. At the same time, a CNN is designed to learn internal representations that abstract from the input data based on its hierarchical layered structure. So it is natural to ask if an inverse of this idea can be applied to learn a model that can predict over a classification hierarchy using multiple output layers in decreasing order of class abstraction. In this paper, we introduce a variant of the traditional CNN model named the Branch Convolutional Neural Network (B-CNN). A B-CNN model outputs multiple predictions ordered from coarse to fine along the concatenated convolutional layers corresponding to the hierarchical structure of the target classes, which can be regarded as a form of prior knowledge on the output. To learn with B-CNNs a novel training strategy, named the Branch Training strategy (BT-strategy), is introduced which balances the strictness of the prior with the freedom to adjust parameters on the output layers to minimize the loss. In this way we show that CNN based models can be forced to learn successively coarse to fine concepts in the internal layers at the output stage, and that hierarchical prior knowledge can be adopted to boost CNN models' classification performance. Our models are evaluated to show that the B-CNN extensions improve over the corresponding baseline CNN on the benchmark datasets MNIST, CIFAR-10 and CIFAR-100. Many real life prediction problems involve predicting a structured output. Multi-target regression is an instance of structured output prediction whose task is to predict for multiple target variables. Structured output algorithms are usually computationally and memory demanding, hence are not suited for dealing with massive amounts of data. Most of these algorithms can be categorized as local or global methods. Local methods produce individual models for each output component and combine them to produce the structured prediction. Global methods adapt traditional learning algorithms to predict the output structure as a whole. We propose the first rule-based algorithm for solving multi-target regression problems from data streams. The algorithm builds on the adaptive model rules framework. In contrast to the majority of the structured output predictors, this particular algorithm does not fall into the local and global categories. Instead, each rule specializes on related subsets of the output attributes. To evaluate the performance of the proposed algorithm, two other rule-based algorithms were developed, one using the local strategy and the other using the global strategy. These methods were compared considering their prediction error, memory usage, computational time, and model complexity. Experimental results on synthetic and real data show that the local-strategy algorithm usually obtains the lowest error. However, the proposed and the global-strategy algorithms use much less memory and run significantly much faster at the cost of a slightly increase in the error, which make them very attractive when computation resources are an important factor. Also, the models produced by the latter approaches are much easier to understand since considerably less rules are produced. Adaptive tracking-by-detection methods are widely used in computer vision for tracking arbitrary objects. Current approaches treat the tracking problem as a classification task and use online learning techniques to update the object model. However, for these updates to happen one needs to convert the estimated object position into a set of labelled training examples, and it is not clear how best to perform this intermediate step. Furthermore, the objective for the classifier (label prediction) is not explicitly coupled to the objective for the tracker (estimation of object position). In this paper, we present a framework for adaptive visual object tracking based on structured output prediction. By explicitly allowing the output space to express the needs of the tracker, we avoid the need for an intermediate classification step. Our method uses a kernelised structured output support vector machine (SVM), which is learned online to provide adaptive tracking. To allow our tracker to run at high frame rates, we (a) introduce a budgeting mechanism that prevents the unbounded growth in the number of support vectors that would otherwise occur during tracking, and (b) show how to implement tracking on the GPU. Experimentally, we show that our algorithm is able to outperform state-of-the-art trackers on various benchmark videos. Additionally, we show that we can easily incorporate additional features and kernels into our framework, which results in increased tracking performance. In recent years, distributed representations of inputs have led to performance gains in many applications by allowing statistical information to be shared across inputs. However, the predicted outputs (labels, and more generally structures) are still treated as discrete objects even though outputs are often not discrete units of meaning. In this paper, we present a new formulation for structured prediction where we represent individual labels in a structure as dense vectors and allow semantically similar labels to share parameters. We extend this representation to larger structures by defining compositionality using tensor products to give a natural generalization of standard structured prediction approaches. We define a learning objective for jointly learning the model parameters and the label vectors and propose an alternating minimization algorithm for learning. We show that our formulation outperforms structural SVM baselines in two tasks: multiclass document classification and part-of-speech tagging.