Convolutional factor graphs as probabilistic models
Yongyi Mao, Frank R. Kschischang, Brendan J. Frey · 2004
Based on a recent development in the area of error control coding, we introduce the no-tion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical mod-els. In this context, the conventional fac-tor graphs are referred to as multiplicative factor graphs (MFGs). This paper shows that CFGs are natural models for probability functions when summation of independent la-tent random variables is involved. In par-ticular, CFGs capture a large class of linear models, where the linearity is in the sense that the observed variables are obtained as a linear transformation of the latent variables taking arbitrary distributions. We use Gaus-sian models and independent factor models as examples to demonstrate the use of CFGs. The requirement of a linear transformation between latent variables (with certain inde-pendence restriction) and the observed vari-ables, to an extent, limits the modelling flex-ibility of CFGs. This structural restriction however provides a powerful analytic tool to the framework of CFGs; that is, upon taking the Fourier transform of the function repre-sented by the CFG, the resulting function is represented by a MFG with identical struc-ture. This Fourier transform duality allows inference problems on a CFG to be solved on the corresponding dual MFG. 1