Thursday, December 1, 2011

Linear stable models

I just heard from Alex Ihler, UC Irvine, that he participated in early Novemeber in Workshop called "Counting, Inference, and Optimization on Graphs" in Princeton University, NJ. Yongi Mao from Otawa University Gave a nice talk title "Normal Factor Graphs, Linear Algebra and Probablistic Modeling".

In my NIPS 2010 paper, I (and my advisor Carlos Guestrin) where the first to show how to compute inference in linear models involving heavy tailed stable distributions. This was the first closed form solution to this problem. The trick was to use duality and compute inference in the Fourier (characteristic function) domain. My work is heavily based on Mao's work, since he was the first to formulate this duality in a general linear model. Here are his related papers:
Y. Mao and F. R. Kschischang. On factor graphs and the Fourier transform. In IEEE Trans. Inform. Theory, volume 51, pages 1635–1649, August 2005.
Y. Mao, F. R. Kschischang, and B. J. Frey. Convolutional factor graphs as probabilistic models. In UAI ’04: Proceedings of the 20th conference on Uncertainty in artificial intelligence, pages 374–381, Arlington, Virginia, United States, 2004. AUAI Press.

It seems that Mao was quite frustrated that his work seemed merely theoretical at that time, while it was hard for him to find an application to his construction. So he was delighted to see that I have actually used his construction towards a very useful application. That is why he titles my work "a missed opportunity" because he is a bit upset that he did not think about it at the time... But anyway this is science - a small progress at each step..

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