text: 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.
  @cite_19: This paper studies global ranking problem by learning to rank methods. Conventional learning to rank methods are usually designed for 'local ranking', in the sense that the ranking model is defined on a single object, for example, a document in information retrieval. For many applications, this is a very loose approximation. Relations always exist between objects and it is better to define the ranking model as a function on all the objects to be ranked (i.e., the relations are also included). This paper refers to the problem as global ranking and proposes employing a Continuous Conditional Random Fields (CRF) for conducting the learning task. The Continuous CRF model is defined as a conditional probability distribution over ranking scores of objects conditioned on the objects. It can naturally represent the content information of objects as well as the relation information between objects, necessary for global ranking. Taking two specific information retrieval tasks as examples, the paper shows how the Continuous CRF method can perform global ranking better than baselines.
  @cite_18: 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.
summary: 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.