
Heavytailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closedform in graphical models which involve such heavytailed distributions. In this work, we propose a novel simple linear graphical model for independent latent random variables, called linear characteristic model (LCM), defined in the characteristic function domain. Using stable distributions, a heavytailed family of distributions which is a generalization of Cauchy, L\'evy and Gaussian distributions, we show for the first time, how to compute both exact and approximate inference in such a linear multivariate graphical model. LCMs are not limited to stable distributions, in fact LCMs are always defined for any random variables (discrete, continuous or a mixture of both). We provide a realistic problem from the field of computer networks to demonstrate the applicability of our construction. Other potential application is iterative decoding of linear channels with nonGaussian noise. Papers
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