Neural Computation
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Extending factor graphs so as to unify directed and undirected graphical models
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
On factor graphs and the Fourier transform
IEEE Transactions on Information Theory
A new approach to constructing CSS codes based on factor graphs
Information Sciences: an International Journal
Graphical Methods for Efficient Likelihood Inference in Gaussian Covariance Models
The Journal of Machine Learning Research
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Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred to as multiplicative factor graphs (MFGs). This paper shows that CFGs are natural models for probability functions when summation of independent latent random variables is involved. In particular, 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 Gaussian models and independent factor models as examples to demonstrate the use of CFGs. The requirement of a linear transformation between latent variables (with certain independence restriction) and the observed variables, to an extent, limits the modelling flexibility 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 represented by the CFG, the resulting function is represented by a MFG with identical structure. This Fourier transform duality allows inference problems on a CFG to be solved on the corresponding dual MFG.