Analyzing data with latent spatial and/or temporal structure is a challenge for machine learning. In this paper, we propose a novel nonlinear model for studying data with latent dependence structure. It successfully combines the concepts of Markov random fields, transductive learning, and regression, making heavy use of the notion of joint feature maps. Our transductive conditional random field regression model is able to infer the latent states by combining limited labeled data of high precision with unlabeled data containing measurement uncertainty. In this manner, we can propagate accurate information and greatly reduce uncertainty. We demonstrate the usefulness of our novel framework on generated time series data with the known temporal structure and successfully validate it on synthetic as well as real-world offshore data with the spatial structure from the oil industry to predict rock porosities from acoustic impedance data.
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