Nonlinear Markov Networks for Continuous Variables

Abstract

We address the problem oflearning structure in nonlinear Markov networks with continuous variables. This can be viewed as non-Gaussian multidi(cid:173) mensional density estimation exploiting certain conditional independencies in the variables. Markov networks are a graphical way of describing con(cid:173) ditional independencies well suited to model relationships which do not ex(cid:173) hibit a natural causal ordering. We use neural network structures to model the quantitative relationships between variables. The main focus in this pa(cid:173) per will be on learning the structure for the purpose of gaining insight into the underlying process. Using two data sets we show that interesting struc(cid:173) tures can be found using our approach. Inference will be briefly addressed.