We present a neural network regression method for relighting realworld scenes from a small number of images. The relighting in this work is formulated as the product of the scene's light transport matrix and new lighting vectors, with the light transport matrix reconstructed from the input images. Based on the observation that there should exist non-linear local coherence in the light transport matrix, our method approximates matrix segments using neural networks that model light transport as a non-linear function of light source position and pixel coordinates. Central to this approach is a proposed neural network design which incorporates various elements that facilitate modeling of light transport from a small image set. In contrast to most image based relighting techniques, this regression-based approach allows input images to be captured under arbitrary illumination conditions, including light sources moved freely by hand. We validate our method with light transport data of real scenes containing complex lighting effects, and demonstrate that fewer input images are required in comparison to related techniques.