Semi-supervised regression with temporal image sequences

We consider a semi-supervised regression setting where we have temporal sequences of partially labeled data, under the assumption that the labels should vary slowly along a sequence, but that nearby points in input space may have drastically different labels. The setting is motivated by problems such as determining the time of the day or the level of air visibility given an image of a landscape, which is hard because the time or visibility label is related in a complex way with the pixel values. We propose a regression framework regularized with a graph Laplacian prior, where the graph is given by the sequential information. We show this outperforms graphs learned in an unsupervised way for detecting the rotation of MNIST digits and estimating the time of day an image is captured, and provides modest improvement in the challenging visibility problem.