Title: Modal Logic, Temporal Models and Neural Circuits:What Connects Them (NYU-CS-TR907) Authors: Samantha Kleinberg, Marco Antoniotti, Naren Ramakrishnan and Bud Mishra Abstract: Traditional methods for supervised learning involve treating the input data as a set of independent, identically distributed samples. However, in many situations, the samples are related in such a way that variables associated with one sample depend on other samples. We present a new form of relational graphical model that, in addition to capturing the dependence of the output on sample specific features, can also capture hidden relationships among samples through a non-parametric latent manifold. Learning in the proposed graphical model involves simultaneously learning the non-parametric latent manifold along with a non-relational parametric model. Efficient inference algorithms are introduced to accomplish this task. The method is applied to the prediction of house prices. A non-relational model predicts an ``intrinsic" price of the house which depends only on its individual characteristics, and a relational model estimates a hidden surface of ``desirability'' coefficients which links the price of a house to that of similar houses in the neighborhood.