The number and magnitude of process variation sources are increasing as we scale further into the nano regime. Today's most successful response surface methods limit us to low-order forms - linear, quadratic - to make the fitting tractable. Unfortunately, not all variational scenarios are well modeled with low-order surfaces. We show how to exploit latent variable regression ideas to support efficient extraction of arbitrarily nonlinear statistical response surfaces. An implementation of these ideas called SiLVR, applied to a range of analog and digital circuits, in technologies from 90 to 45nm, shows significant improvements in prediction, with errors reduced by up to 21X, with very reasonable runtime costs.