Carnegie Mellon University
Machine Learning Dept.








Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed 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 heavy-tailed 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 non-Gaussian noise.


  • Inference with multivariate heavy-tails in linear models. D. Bickson and C. Guestrin. In Neural Information Processing Systems (NIPS) 2010, Vancouver, Canada, Dec. 2010. arxiv
    Heatmap showing LCM with alpha=1Heatmap showing LCM with alpha=2

    Source Code

    Linear-Stable Matlab Toolbox


  • D. Bickson would like to thank Andrea Pagnani (ISI) for inspiring the direction of this research.
  • To John P. Nolan (American University) for sharing parts of his excellent book about stable distribution online,
  • To Mark Veillette (Boston University) for sharing his stable distribution code online
  • To Jason K. Johnson (LANL) for assisting in the convergence analysis
  • To Sapan Bathia, Marc E. Fiuczynski (Princeton University) from the PlanetLab project for providing the PlanetFlow data.
  • This research was supported by Army Research Office MURI W911NF0710287.

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