Nonlinear Markov Networks for Continuous Variables

We address the problem of learning structure in nonlinear Markov networks with continuous variables. This can be viewed as non-Gaussian multidimensional density estimation exploiting certain conditional independencies in the variables. Markov networks are a graphical way of describing conditional independencies well suited to model relationships which do not exhibit a natural causal ordering. We use neural network structures to model the quantitative relationships between variables. The main focus in this paper will be on learning the structure for the purpose of gaining insight into the underlying process. Using two data sets we show that interesting structures can be found using our approach. Inference will be brie¤y addressed.

• Type: Conference
• Year: 1997
• Where: NIPS
• Authors: Reimar Hofmann, Volker Tresp
• Keywords: Conditional Independencies, Markov Networks, NIPS 1997, NIPS 2007, Nonlinear Markov Networks