Abstract: Gaussian fields (GF) have recently received considerable attention for dimension reduction and semi-supervised classification. This paper presents two contributions. First, we show how the GF framework can be used for regression tasks on high-dimensional data. We consider an active learning strategy based on entropy minimization and a maximum likelihood model selection method. Second, we show how a recent generalization of the Locally Linear Embedding algorithm for correspondence learning can also be cast into the GF framework, which obviates the need to choose a representation dimensionality.