  We introduce the truncated Gaussian graphical model (TGGM) as a novel
framework for designing statistical models for nonlinear learning. A TGGM is a
Gaussian graphical model (GGM) with a subset of variables truncated to be
nonnegative. The truncated variables are assumed latent and integrated out to
induce a marginal model. We show that the variables in the marginal model are
non-Gaussian distributed and their expected relations are nonlinear. We use
expectation-maximization to break the inference of the nonlinear model into a
sequence of TGGM inference problems, each of which is efficiently solved by
using the properties and numerical methods of multivariate Gaussian
distributions. We use the TGGM to design models for nonlinear regression and
classification, with the performances of these models demonstrated on extensive
benchmark datasets and compared to state-of-the-art competing results.
