Conditional probabilistic graphical models provide a powerful framework for structured regression in spatio-temporal datasets with complex correlation patterns. However, in real-life applications a large fraction of observations is often missing, which can severely limit the representational power of these models. In this paper we propose a Marginalized Gaussian Conditional Random Fields (m-GCRF) structured regression model for dealing with missing labels in partially observed temporal attributed graphs. This method is aimed at learning with both labeled and unlabeled parts and effectively predicting future values in a graph. The method is even capable of learning from nodes for which the response variable is never observed in history, which poses problems for many state-of-the-art models that can handle missing data. The proposed model is characterized for various missingness mechanisms on 500 synthetic graphs. The benefits of the new method are also demonstrated on a challenging application for predicting precipitation based on partial observations of climate variables in a temporal graph that spans the entire continental US. We also show that the method can be useful for optimizing the costs of data collection in climate applications via active reduction of the number of weather stations to consider. In experiments on these real-world and synthetic datasets we show that the proposed model is consistently more accurate than alternative semi-supervised structured models, as well as models that either use imputation to deal with missing values or simply ignore them altogether.
There also exist variants of the conditional graphical CRF models for regression (e.g. the CCRF @cite_19 , or GCRF @cite_18 models). However, these structured regression models are not designed to cope with unlabeled data, other than ignoring the portion of data with missing labels.
@cite_19 @cite_18
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Conditional random fields (CRF) are widely used for predicting output variables that have some internal structure. Most of the CRF research has been done on structured classification where the outputs are discrete. In this study we propose a CRF probabilistic model for structured regression that uses multiple non-structured predictors as its features. We construct features as squared prediction errors and show that this results in a Gaussian predictor. Learning becomes a convex optimization problem leading to a global solution for a set of parameters. Inference can be conveniently conducted through matrix computation. Experimental results on the remote sensing problem of estimating Aerosol Optical Depth (AOD) provide strong evidence that the proposed CRF model successfully exploits the inherent spatio-temporal properties of AOD data. The experiments revealed that CRF are more accurate than the baseline neural network and domain-based predictors. Hierarchical conditional random fields have been successfully applied to object segmentation. One reason is their ability to incorporate contextual information at different scales. However, these models do not allow multiple labels to be assigned to a single node. At higher scales in the image, this yields an oversimplified model, since multiple classes can be reasonable expected to appear within one region. This simplified model especially limits the impact that observations at larger scales may have on the CRF model. Neglecting the information at larger scales is undesirable since class-label estimates based on these scales are more reliable than at smaller, noisier scales. To address this problem, we propose a new potential, called harmony potential, which can encode any possible combination of class labels. We propose an effective sampling strategy that renders tractable the underlying optimization problem. Results show that our approach obtains state-of-the-art results on two challenging datasets: Pascal VOC 2009 and MSRC-21. Conditional Random Fields (CRFs) are an effective tool for a variety of different data segmentation and labeling tasks including visual scene interpretation, which seeks to partition images into their constituent semantic-level regions and assign appropriate class labels to each region. For accurate labeling it is important to capture the global context of the image as well as local information. We introduce a CRF based scene labeling model that incorporates both local features and features aggregated over the whole image or large sections of it. Secondly, traditional CRF learning requires fully labeled datasets which can be costly and troublesome to produce. We introduce a method for learning CRFs from datasets with many unlabeled nodes by marginalizing out the unknown labels so that the log-likelihood of the known ones can be maximized by gradient ascent. Loopy Belief Propagation is used to approximate the marginals needed for the gradient and log-likelihood calculations and the Bethe free-energy approximation to the log-likelihood is monitored to control the step size. Our experimental results show that effective models can be learned from fragmentary labelings and that incorporating top-down aggregate features significantly improves the segmentations. The resulting segmentations are compared to the state-of-the-art on three different image datasets. Conditional Random Fields (CRFs) are widely known to scale poorly, particularly for tasks with large numbers of states or with richly connected graphical structures. This is a consequence of inference having a time complexity which is at best quadratic in the number of states. This paper describes a novel parameterisation of the CRF which ties the majority of clique potentials, while allowing individual potentials for a subset of the labellings. This has two beneficial effects: the parameter space of the model (and thus the propensity to over-fit) is reduced, and the time complexity of training and decoding becomes sub-quadratic. On a standard natural language task, we reduce CRF training time four-fold, with no loss in accuracy. We also show how inference can be performed efficiently in richly connected graphs, in which current methods are intractable. Conditional random fields (, 2001) are quite effective at sequence labeling tasks like shallow parsing (Sha and Pereira, 2003) and named-entity extraction (McCallum and Li, 2003). CRFs are log-linear, allowing the incorporation of arbitrary features into the model. To train on unlabeled data, we require unsupervised estimation methods for log-linear models; few exist. We describe a novel approach, contrastive estimation. We show that the new technique can be intuitively understood as exploiting implicit negative evidence and is computationally efficient. Applied to a sequence labeling problem---POS tagging given a tagging dictionary and unlabeled text---contrastive estimation outperforms EM (with the same feature set), is more robust to degradations of the dictionary, and can largely recover by modeling additional features. We describe a probabilistic approach to content selection for meeting summarization. We use skipchain Conditional Random Fields (CRF) to model non-local pragmatic dependencies between paired utterances such as Question-Answer that typically appear together in summaries, and show that these models outperform linear-chain CRFs and Bayesian models in the task. We also discuss different approaches for ranking all utterances in a sequence using CRFs. Our best performing system achieves 91.3 of human performance when evaluated with the Pyramid evaluation metric, which represents a 3.9 absolute increase compared to our most competitive non-sequential classifier. Until recently, the lack of ground truth data has hindered the application of discriminative structured prediction techniques to the stereo problem. In this paper we use ground truth data sets that we have recently constructed to explore different model structures and parameter learning techniques. To estimate parameters in Markov random fields (MRFs) via maximum likelihood one usually needs to perform approximate probabilistic inference. Conditional random fields (CRFs) are discriminative versions of traditional MRFs. We explore a number of novel CRF model structures including a CRF for stereo matching with an explicit occlusion model. CRFs require expensive inference steps for each iteration of optimization and inference is particularly slow when there are many discrete states. We explore belief propagation, variational message passing and graph cuts as inference methods during learning and compare with learning via pseudolikelihood. To accelerate approximate inference we have developed a new method called sparse variational message passing which can reduce inference time by an order of magnitude with negligible loss in quality. Learning using sparse variational message passing improves upon previous approaches using graph cuts and allows efficient learning over large data sets when energy functions violate the constraints imposed by graph cuts. This paper describes a parsing model that combines the exact dynamic programming of CRF parsing with the rich nonlinear featurization of neural net approaches. Our model is structurally a CRF that factors over anchored rule productions, but instead of linear potential functions based on sparse features, we use nonlinear potentials computed via a feedforward neural network. Because potentials are still local to anchored rules, structured inference (CKY) is unchanged from the sparse case. Computing gradients during learning involves backpropagating an error signal formed from standard CRF sufficient statistics (expected rule counts). Using only dense features, our neural CRF already exceeds a strong baseline CRF model (, 2014). In combination with sparse features, our system1 achieves 91.1 F1 on section 23 of the Penn Treebank, and more generally outperforms the best prior single parser results on a range of languages. Conditional random fields (CRFs) are popular discriminative models for computer vision and have been successfully applied in the domain of image restoration, especially to image denoising. For image deblurring, however, discriminative approaches have been mostly lacking. We posit two reasons for this: First, the blur kernel is often only known at test time, requiring any discriminative approach to cope with considerable variability. Second, given this variability it is quite difficult to construct suitable features for discriminative prediction. To address these challenges we first show a connection between common half-quadratic inference for generative image priors and Gaussian CRFs. Based on this analysis, we then propose a cascade model for image restoration that consists of a Gaussian CRF at each stage. Each stage of our cascade is semi-parametric, i.e., it depends on the instance-specific parameters of the restoration problem, such as the blur kernel. We train our model by loss minimization with synthetically generated training data. Our experiments show that when applied to non-blind image deblurring, the proposed approach is efficient and yields state-of-the-art restoration quality on images corrupted with synthetic and real blur. Moreover, we demonstrate its suitability for image denoising, where we achieve competitive results for grayscale and color images. In this paper, we present a Conditional Random Field (CRF) model to deal with the problem of segmenting handwritten historical document images into different regions. We consider page segmentation as a pixel-labeling problem, i.e., each pixel is assigned to one of a set of labels. Features are learned from pixel intensity values with stacked convolutional autoencoders in an unsupervised manner. The features are used for the purpose of initial classification with a multilayer perceptron. Then a CRF model is introduced for modeling the local and contextual information jointly in order to improve the segmentation. For the purpose of decreasing the time complexity, we perform labeling at superpixel level. In the CRF model, graph nodes are represented by superpixels. The label of each pixel is determined by the label of the superpixel to which it belongs. Experiments on three public datasets demonstrate that, compared to previous methods, the proposed method achieves more accurate segmentation results and is much faster. Identifying expansion forms for acronyms is beneficial to many natural language processing and information retrieval tasks. In this work, we study the problem of finding expansions in texts for given acronym queries by modeling the problem as a sequence labeling task. However, it is challenging for traditional sequence labeling models like Conditional Random Fields (CRF) due to the complexity of the input sentences and the substructure of the categories. In this paper, we propose a Latent-state Neural Conditional Random Fields model (LNCRF) to deal with the challenges. On one hand, we extend CRF by coupling it with nonlinear hidden layers to learn multi-granularity hierarchical representations of the input data under the framework of Conditional Random Fields. On the other hand, we introduce latent variables to capture the fine granular information from the intrinsic substructures within the structured output labels implicitly. The experimental results on real data show that our model achieves the best performance against the state-of-the-art baselines. Recently, models based on conditional random fields (CRF) have produced promising results on labeling sequential data in several scientific fields. However, in the vision task of continuous action recognition, the observations of visual features have dimensions as high as hundreds or even thousands. This might pose severe difficulties on parameter estimation and even degrade the performance. To bridge the gap between the high dimensional observations and the random fields, we propose a novel model that replace the observation layer of a traditional random fields model with a latent pose estimator. In training stage, the human pose is not observed in the action data, and the latent pose estimator is learned under the supervision of the labeled action data, instead of image-to-pose data. The advantage of this model is twofold. First, it learns to convert the high dimensional observations into more compact and informative representations. Second, it enables transfer learning to fully utilize the existing knowledge and data on image-to-pose relationship. The parameters of the latent pose estimator and the random fields are jointly optimized through a gradient ascent algorithm. Our approach is tested on HumanEva [1] --- a publicly available dataset. The experiments show that our approach can improve recognition accuracy over standard CRF model and its variations. The performance can be further significantly improved by using additional image-to-pose data for training. Our experiments also show that the model trained on HumanEva can generalize to different environment and human subjects. In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when long-range dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linear-chain conditional random fields (CRFs) in which each time slice contains a set of state variables and edges---a distributed state representation as in dynamic Bayesian networks (DBNs)---and parameters are tied across slices. Since exact inference can be intractable in such models, we perform approximate inference using several schedules for belief propagation, including tree-based reparameterization (TRP). On a natural-language chunking task, we show that a DCRF performs better than a series of linear-chain CRFs, achieving comparable performance using only half the training data. Conditional Random Fields (CRFs) provide a powerful instrument for labeling sequences. So far, however, CRFs have only been considered for labeling sequences over flat alphabets. In this paper, we describe TildeCRF, the first method for training CRFs on logical sequences, i.e., sequences over an alphabet of logical atoms. TildeCRF's key idea is to use relational regression trees in 's gradient tree boosting approach. Thus, the CRF potential functions are represented as weighted sums of relational regression trees. Experiments show a significant improvement over established results achieved with hidden Markov models and Fisher kernels for logical sequences. In this work we introduce a structured prediction model that endows the Deep Gaussian Conditional Random Field (G-CRF) with a densely connected graph structure. We keep memory and computational complexity under control by expressing the pairwise interactions as inner products of low-dimensional, learnable embeddings. The G-CRF system matrix is therefore low-rank, allowing us to solve the resulting system in a few milliseconds on the GPU by using conjugate gradient. As in G-CRF, inference is exact, the unary and pairwise terms are jointly trained end-to-end by using analytic expressions for the gradients, while we also develop even faster, Potts-type variants of our embeddings. We show that the learned embeddings capture pixel-to-pixel affinities in a task-specific manner, while our approach achieves state of the art results on three challenging benchmarks, namely semantic segmentation, human part segmentation, and saliency estimation. Our implementation is fully GPU based, built on top of the Caffe library, and is available at https: github.com siddharthachandra gcrf-v2.0. We propose a novel and principled hybrid CNN+CRF model for stereo estimation. Our model allows to exploit the advantages of both, convolutional neural networks (CNNs) and conditional random fields (CRFs) in an unified approach. The CNNs compute expressive features for matching and distinctive color edges, which in turn are used to compute the unary and binary costs of the CRF. For inference, we apply a recently proposed highly parallel dual block descent algorithm which only needs a small fixed number of iterations to compute a high-quality approximate minimizer. As the main contribution of the paper, we propose a theoretically sound method based on the structured output support vector machine (SSVM) to train the hybrid CNN+CRF model on large-scale data end-to-end. Our trained models perform very well despite the fact that we are using shallow CNNs and do not apply any kind of post-processing to the final output of the CRF. We evaluate our combined models on challenging stereo benchmarks such as Middlebury 2014 and Kitti 2015 and also investigate the performance of each individual component. An increasing number of computer vision and pattern recognition problems require structured regression techniques. Problems like human pose estimation, unsegmented action recognition, emotion prediction and facial landmark detection have temporal or spatial output dependencies that regular regression techniques do not capture. In this paper we present continuous conditional neural fields (CCNF) – a novel structured regression model that can learn non-linear input-output dependencies, and model temporal and spatial output relationships of varying length sequences. We propose two instances of our CCNF framework: Chain-CCNF for time series modelling, and Grid-CCNF for spatial relationship modelling. We evaluate our model on five public datasets spanning three different regression problems: facial landmark detection in the wild, emotion prediction in music and facial action unit recognition. Our CCNF model demonstrates state-of-the-art performance on all of the datasets used. Large amounts of available training data and increasing computing power have led to the recent success of deep convolutional neural networks (CNN) on a large number of applications. In this paper, we propose an effective semantic pixel labelling using CNN features, hand-crafted features and Conditional Random Fields (CRFs). Both CNN and hand-crafted features are applied to dense image patches to produce per-pixel class probabilities. The CRF infers a labelling that smooths regions while respecting the edges present in the imagery. The method is applied to the ISPRS 2D semantic labelling challenge dataset with competitive classification accuracy. In this paper, we propose to incorporate convolutional neural networks with a multi-context attention mechanism into an end-to-end framework for human pose estimation. We adopt stacked hourglass networks to generate attention maps from features at multiple resolutions with various semantics. The Conditional Random Field (CRF) is utilized to model the correlations among neighboring regions in the attention map. We further combine the holistic attention model, which focuses on the global consistency of the full human body, and the body part attention model, which focuses on detailed descriptions for different body parts. Hence our model has the ability to focus on different granularity from local salient regions to global semantic consistent spaces. Additionally, we design novel Hourglass Residual Units (HRUs) to increase the receptive field of the network. These units are extensions of residual units with a side branch incorporating filters with larger receptive field, hence features with various scales are learned and combined within the HRUs. The effectiveness of the proposed multi-context attention mechanism and the hourglass residual units is evaluated on two widely used human pose estimation benchmarks. Our approach outperforms all existing methods on both benchmarks over all the body parts. Code has been made publicly available. Most state-of-the-art techniques for multi-class image segmentation and labeling use conditional random fields defined over pixels or image regions. While region-level models often feature dense pairwise connectivity, pixel-level models are considerably larger and have only permitted sparse graph structures. In this paper, we consider fully connected CRF models defined on the complete set of pixels in an image. The resulting graphs have billions of edges, making traditional inference algorithms impractical. Our main contribution is a highly efficient approximate inference algorithm for fully connected CRF models in which the pairwise edge potentials are defined by a linear combination of Gaussian kernels. Our experiments demonstrate that dense connectivity at the pixel level substantially improves segmentation and labeling accuracy.