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.