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_4: Background Multiple imputation is becoming increasingly popular for handling missing data. However, it is often implemented without adequate consideration of whether it offers any advantage over complete case analysis for the research question of interest, or whether potential gains may be offset by bias from a poorly fitting imputation model, particularly as the amount of missing data increases.
  @cite_11: The predictive analysis of longitudinal social surveys is highly sensitive to the effects of missing data in temporal observations. Such high sensitivity to missing values raises the need for accurate data imputation, because without it a large fraction of collected data could not be used properly. Previous studies focused on the treatment of missing data in longitudinal social networks due to non-respondents and dealt with the problem largely by imputing missing links in isolation or analyzing the imputation effects on network statistics. We propose to account for changing network topology and interdependence between actors' links and attributes to construct a unified approach for imputation of links and attributes in longitudinal social surveys. The new method, based on an exponential random graph model, is evaluated experimentally for five scenarios of missing data models utilizing synthetic and real life datasets with 20 ---60 of nodes missing. The obtained results outperformed all alternatives, four of which were link imputation methods and two node attribute imputation methods. We further discuss the applicability and scalability of our approach to real life problems and compare our model with the latest advancements in the field. Our findings suggest that the proposed method can be used as a viable imputation tool in longitudinal studies.
summary: One of the standard ways of handling missing values is imputing values based on some predictive model, and then applying the analysis on a fully observed dataset. To exploit the graph structure, previous studies have proposed imputation of missing values based on the exponential random graph model @cite_11 . The limitation of such an approach is that it is slow, as it requires Gibbs sampling, and so it cannot handle large graphs. Imputation of missing values can also be accomplished using matrix (or tensor) factorization methods. These methods can impute missing values with high accuracy even when large percentages (up to 95 , imputation-based methods use only point estimates of the missing values, effectively ignoring the prediction uncertainty when learning with imputed values. Techniques known as Multiple Imputation (MI) try to correct for this drawback, by sampling from the posterior distribution of missing values. On the other hand, these techniques can be less effective when a larger fraction of data is missing @cite_4 , and can be computationally very demanding.