We present LTLS, a technique for multiclass and multilabel prediction that can perform training and inference in logarithmic time and space. LTLS embeds large classification problems into simple structured prediction problems and relies on efficient dynamic programming algorithms for inference. We train LTLS with stochastic gradient descent on a number of multiclass and multilabel datasets and show that despite its small memory footprint it is often competitive with existing approaches.
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even when an arbitrary number of hidden layers are present. In this paper, we generalize this result to a much broader set of learning problems: all those where inference consists of summing a function over a semiring. This includes satisfiability, constraint satisfaction, optimization, integration, and others. In any semiring, for summation to be tractable it suffices that the factors of every product have disjoint scopes. This unifies and extends many previous results in the literature. Enforcing this condition at learning time thus ensures that the learned models are tractable. We illustrate the power and generality of this approach by applying it to a new type of structured prediction problem: learning a nonconvex function that can be globally optimized in polynomial time. We show empirically that this greatly outperforms the standard approach of learning without regard to the cost of optimization.
Conditional Random Field (CRF) and recurrent neural models have achieved success in structured prediction. More recently, there is a marriage of CRF and recurrent neural models, so that we can gain from both non-linear dense features and globally normalized CRF objective. These recurrent neural CRF models mainly focus on encode node features in CRF undirected graphs. However, edge features prove important to CRF in structured prediction. In this work, we introduce a new recurrent neural CRF model, which learns non-linear edge features, and thus makes non-linear features encoded completely. We compare our model with different neural models in well-known structured prediction tasks. Experiments show that our model outperforms state-of-the-art methods in NP chunking, shallow parsing, Chinese word segmentation and POS tagging.
Automatic segmentation of retinal blood vessels from fundus images plays an important role in the computer aided diagnosis of retinal diseases. The task of blood vessel segmentation is challenging due to the extreme variations in morphology of the vessels against noisy background. In this paper, we formulate the segmentation task as a multi-label inference task and utilize the implicit advantages of the combination of convolutional neural networks and structured prediction. Our proposed convolutional neural network based model achieves strong performance and significantly outperforms the state-of-the-art for automatic retinal blood vessel segmentation on DRIVE dataset with 95.33% accuracy and 0.974 AUC score.
Given an image, we would like to learn to detect objects belonging to particular object categories. Common object detection methods train on large annotated datasets which are annotated in terms of bounding boxes that contain the object of interest. Previous works on object detection model the problem as a structured regression problem which ranks the correct bounding boxes more than the background ones. In this paper we develop algorithms which actively obtain annotations from human annotators for a small set of images, instead of all images, thereby reducing the annotation effort. Towards this goal, we make the following contributions: 1. We develop a principled version space based active learning method that solves for object detection as a structured prediction problem in a weakly supervised setting 2. We also propose two variants of the margin sampling strategy 3. We analyse the results on standard object detection benchmarks that show that with only 20% of the data we can obtain more than 95% of the localization accuracy of full supervision. Our methods outperform random sampling and the classical uncertainty-based active learning algorithms like entropy
In this work we propose a structured prediction technique that combines the virtues of Gaussian Conditional Random Fields (G-CRF) with Deep Learning: (a) our structured prediction task has a unique global optimum that is obtained exactly from the solution of a linear system (b) the gradients of our model parameters are analytically computed using closed form expressions, in contrast to the memory-demanding contemporary deep structured prediction approaches that rely on back-propagation-through-time, (c) our pairwise terms do not have to be simple hand-crafted expressions, as in the line of works building on the DenseCRF, but can rather be `discovered' from data through deep architectures, and (d) out system can trained in an end-to-end manner. Building on standard tools from numerical analysis we develop very efficient algorithms for inference and learning, as well as a customized technique adapted to the semantic segmentation task. This efficiency allows us to explore more sophisticated architectures for structured prediction in deep learning: we introduce multi-resolution architectures to couple information across scales in a joint optimization framework, yielding systematic improvements. We demonstrate the utility of our approach on the challenging VOC PASCAL 2012 image segmentation benchmark, showing substantial improvements over strong baselines. We make all of our code and experiments available at {https://github.com/siddharthachandra/gcrf}
Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational inference algorithms, soft- or hard-constrained inference using Lagrangian relaxation or linear programming, collective graphical models, and forms of semi-supervised learning such as posterior regularization. We present a method to discriminatively learn broad families of inference objectives, capturing powerful non-local statistics of the latent variables, while maintaining tractable and provably fast inference using non-Euclidean projected gradient descent with a distance-generating function given by the Bethe entropy. We demonstrate the performance and flexibility of our method by (1) extracting structured citations from research papers by learning soft global constraints, (2) achieving state-of-the-art results on a widely-used handwriting recognition task using a novel learned non-convex inference procedure, and (3) providing a fast and highly scalable algorithm for the challenging problem of inference in a collective graphical model applied to bird migration.
This paper focuses on the challenging problem of 3D pose estimation of a diverse spectrum of articulated objects from single depth images. A novel structured prediction approach is considered, where 3D poses are represented as skeletal models that naturally operate on manifolds. Given an input depth image, the problem of predicting the most proper articulation of underlying skeletal model is thus formulated as sequentially searching for the optimal skeletal configuration. This is subsequently addressed by convolutional neural nets trained end-to-end to render sequential prediction of the joint locations as regressing a set of tangent vectors of the underlying manifolds. Our approach is examined on various articulated objects including human hand, mouse, and fish benchmark datasets. Empirically it is shown to deliver highly competitive performance with respect to the state-of-the-arts, while operating in real-time (over 30 FPS).
We present a general theoretical analysis of structured prediction with a series of new results. We give new data-dependent margin guarantees for structured prediction for a very wide family of loss functions and a general family of hypotheses, with an arbitrary factor graph decomposition. These are the tightest margin bounds known for both standard multi-class and general structured prediction problems. Our guarantees are expressed in terms of a data-dependent complexity measure, factor graph complexity, which we show can be estimated from data and bounded in terms of familiar quantities. We further extend our theory by leveraging the principle of Voted Risk Minimization (VRM) and show that learning is possible even with complex factor graphs. We present new learning bounds for this advanced setting, which we use to design two new algorithms, Voted Conditional Random Field (VCRF) and Voted Structured Boosting (StructBoost). These algorithms can make use of complex features and factor graphs and yet benefit from favorable learning guarantees. We also report the results of experiments with VCRF on several datasets to validate our theory.
Semantic sparsity is a common challenge in structured visual classification problems; when the output space is complex, the vast majority of the possible predictions are rarely, if ever, seen in the training set. This paper studies semantic sparsity in situation recognition, the task of producing structured summaries of what is happening in images, including activities, objects and the roles objects play within the activity. For this problem, we find empirically that most object-role combinations are rare, and current state-of-the-art models significantly underperform in this sparse data regime. We avoid many such errors by (1) introducing a novel tensor composition function that learns to share examples across role-noun combinations and (2) semantically augmenting our training data with automatically gathered examples of rarely observed outputs using web data. When integrated within a complete CRF-based structured prediction model, the tensor-based approach outperforms existing state of the art by a relative improvement of 2.11% and 4.40% on top-5 verb and noun-role accuracy, respectively. Adding 5 million images with our semantic augmentation techniques gives further relative improvements of 6.23% and 9.57% on top-5 verb and noun-role accuracy.
Pixel wise image labeling is an interesting and challenging problem with great significance in the computer vision community. In order for a dense labeling algorithm to be able to achieve accurate and precise results, it has to consider the dependencies that exist in the joint space of both the input and the output variables. An implicit approach for modeling those dependencies is by training a deep neural network that, given as input an initial estimate of the output labels and the input image, it will be able to predict a new refined estimate for the labels. In this context, our work is concerned with what is the optimal architecture for performing the label improvement task. We argue that the prior approaches of either directly predicting new label estimates or predicting residual corrections w.r.t. the initial labels with feed-forward deep network architectures are sub-optimal. Instead, we propose a generic architecture that decomposes the label improvement task to three steps: 1) detecting the initial label estimates that are incorrect, 2) replacing the incorrect labels with new ones, and finally 3) refining the renewed labels by predicting residual corrections w.r.t. them. Furthermore, we explore and compare various other alternative architectures that consist of the aforementioned Detection, Replace, and Refine components. We extensively evaluate the examined architectures in the challenging task of dense disparity estimation (stereo matching) and we report both quantitative and qualitative results on three different datasets. Finally, our dense disparity estimation network that implements the proposed generic architecture, achieves state-of-the-art results in the KITTI 2015 test surpassing prior approaches by a significant margin.
Existing models based on artificial neural networks (ANNs) for sentence classification often do not incorporate the context in which sentences appear, and classify sentences individually. However, traditional sentence classification approaches have been shown to greatly benefit from jointly classifying subsequent sentences, such as with conditional random fields. In this work, we present an ANN architecture that combines the effectiveness of typical ANN models to classify sentences in isolation, with the strength of structured prediction. Our model achieves state-of-the-art results on two different datasets for sequential sentence classification in medical abstracts.
A key problem in structured output prediction is direct optimization of the task reward function that matters for test evaluation. This paper presents a simple and computationally efficient approach to incorporate task reward into a maximum likelihood framework. By establishing a link between the log-likelihood and expected reward objectives, we show that an optimal regularized expected reward is achieved when the conditional distribution of the outputs given the inputs is proportional to their exponentiated scaled rewards. Accordingly, we present a framework to smooth the predictive probability of the outputs using their corresponding rewards. We optimize the conditional log-probability of augmented outputs that are sampled proportionally to their exponentiated scaled rewards. Experiments on neural sequence to sequence models for speech recognition and machine translation show notable improvements over a maximum likelihood baseline by using reward augmented maximum likelihood (RAML), where the rewards are defined as the negative edit distance between the outputs and the ground truth labels.
We propose a deep learning model for identifying structure within experiment narratives in scientific literature. We take a sequence labeling approach to this problem, and label clauses within experiment narratives to identify the different parts of the experiment. Our dataset consists of paragraphs taken from open access PubMed papers labeled with rhetorical information as a result of our pilot annotation. Our model is a Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM) cells that labels clauses. The clause representations are computed by combining word representations using a novel attention mechanism that involves a separate RNN. We compare this model against LSTMs where the input layer has simple or no attention and a feature rich CRF model. Furthermore, we describe how our work could be useful for information extraction from scientific literature.
We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of output labels, we first estimate the conditional risk function by solving a (possibly infinite) collection of regularized least squares problems. A prediction is made by solving an inference problem that minimizes the estimated conditional risk function over the output space. We show that this approach enables, in some cases, efficient training and inference without explicitly introducing a convex surrogate for the original loss function, even when it is discontinuous. Empirical evaluations on real-world and synthetic data sets demonstrate the effectiveness of our method in adapting to a variety of loss functions.
Restricted Boltzmann machines~(RBMs) and conditional RBMs~(CRBMs) are popular models for a wide range of applications. In previous work, learning on such models has been dominated by contrastive divergence~(CD) and its variants. Belief propagation~(BP) algorithms are believed to be slow for structured prediction on conditional RBMs~(e.g., Mnih et al. [2011]), and not as good as CD when applied in learning~(e.g., Larochelle et al. [2012]). In this work, we present a matrix-based implementation of belief propagation algorithms on CRBMs, which is easily scalable to tens of thousands of visible and hidden units. We demonstrate that, in both maximum likelihood and max-margin learning, training conditional RBMs with BP as the inference routine can provide significantly better results than current state-of-the-art CD methods on structured prediction problems. We also include practical guidelines on training CRBMs with BP, and some insights on the interaction of learning and inference algorithms for CRBMs.
We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby partially answering a 30 year-old conjecture. We also survey other convergence results and highlight gaps in the theoretical underpinnings of FW-style algorithms. Motivating applications without known efficient alternatives are explored through structured prediction with combinatorial penalties as well as games over matching polytopes involving an exponential number of constraints.
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propagated by the chain rule through the graph are low variance unbiased estimators of the gradients of the expected loss. While many continuous random variables have such reparameterizations, discrete random variables lack useful reparameterizations due to the discontinuous nature of discrete states. In this work we introduce Concrete random variables---continuous relaxations of discrete random variables. The Concrete distribution is a new family of distributions with closed form densities and a simple reparameterization. Whenever a discrete stochastic node of a computation graph can be refactored into a one-hot bit representation that is treated continuously, Concrete stochastic nodes can be used with automatic differentiation to produce low-variance biased gradients of objectives (including objectives that depend on the log-probability of latent stochastic nodes) on the corresponding discrete graph. We demonstrate the effectiveness of Concrete relaxations on density estimation and structured prediction tasks using neural networks.
We present an integral framework for training sketch simplification networks that convert challenging rough sketches into clean line drawings. Our approach augments a simplification network with a discriminator network, training both networks jointly so that the discriminator network discerns whether a line drawing is a real training data or the output of the simplification network, which in turn tries to fool it. This approach has two major advantages. First, because the discriminator network learns the structure in line drawings, it encourages the output sketches of the simplification network to be more similar in appearance to the training sketches. Second, we can also train the simplification network with additional unsupervised data, using the discriminator network as a substitute teacher. Thus, by adding only rough sketches without simplified line drawings, or only line drawings without the original rough sketches, we can improve the quality of the sketch simplification. We show how our framework can be used to train models that significantly outperform the state of the art in the sketch simplification task, despite using the same architecture for inference. We additionally present an approach to optimize for a single image, which improves accuracy at the cost of additional computation time. Finally, we show that, using the same framework, it is possible to train the network to perform the inverse problem, i.e., convert simple line sketches into pencil drawings, which is not possible using the standard mean squared error loss. We validate our framework with two user tests, where our approach is preferred to the state of the art in sketch simplification 92.3% of the time and obtains 1.2 more points on a scale of 1 to 5.
Social networking on mobile devices has become a commonplace of everyday life. In addition, photo capturing process has become trivial due to the advances in mobile imaging. Hence people capture a lot of photos everyday and they want them to be visually-attractive. This has given rise to automated, one-touch enhancement tools. However, the inability of those tools to provide personalized and content-adaptive enhancement has paved way for machine-learned methods to do the same. The existing typical machine-learned methods heuristically (e.g. kNN-search) predict the enhancement parameters for a new image by relating the image to a set of similar training images. These heuristic methods need constant interaction with the training images which makes the parameter prediction sub-optimal and computationally expensive at test time which is undesired. This paper presents a novel approach to predicting the enhancement parameters given a new image using only its features, without using any training images. We propose to model the interaction between the image features and its corresponding enhancement parameters using the matrix factorization (MF) principles. We also propose a way to integrate the image features in the MF formulation. We show that our approach outperforms heuristic approaches as well as recent approaches in MF and structured prediction on synthetic as well as real-world data of image enhancement.