Sum factor in VMP RRS feed

  • Question

  • I am wondering what is beneath the summation factor when it comes to the VMP engine? Can it be seen as a determestic function - delta(output - sum_(inputs)) ? Is it only supposed to be used with independent Gaussian variables? 

    The reason why I ask is that in Winn's tutorial on VMP it is shown that it is not possible to use a summation of Gaussian variables as a parent for the variance for another Gaussian. Now, in gaussian belief propagation sum of independent gaussians is a common thing. And when I took a look at the sources for the sum factor, it seems that for VMP the same update rules are used as those generally used in GBP. How do these things correspond to each other? 

    Thank you!

    Friday, April 5, 2013 5:58 PM


  • VMP requires the approximate marginals to be conjugate with respect to the attached factors.  Thus the summation factor can only be used with variables whose marginal is being approximated as Gaussian.  The variables do not need to be independent (although in VMP their posterior will be approximated as independent).  For the same reason, the variance of a Gaussian cannot be a variable whose marginal is being approximated as Gaussian, since this is not conjugate.
    • Marked as answer by psycharo Wednesday, April 10, 2013 7:55 PM
    Friday, April 5, 2013 9:58 PM