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Displayed wPosterior in the Bayes Point Machine example
Question

I was analyzing the BPM machine example provided on the website and there's something I can't figure out about the wPosterior that's printed on screen in the console
We can now train our Bayes Point Machine by using expectation propagation to infer the posterior over w, InferenceEngine engine = new InferenceEngine(new ExpectationPropagation()); VectorGaussian wPosterior = engine.Infer<VectorGaussian>(w); Console.WriteLine("Dist over w=\n"+wPosterior); When this code is executed, the result is
Dist over w= VectorGaussian(0.06323 0.006453 1.408, 0.001157 0.0004818 0.01197 ) 0.0004818 0.0006099 0.006733 0.01197 0.006733 0.5215
I bolded the part I don't understand. First we have the vector gaussian as a 3x2 matrix between ()
Then two lines below strangely aligned. Where do those lines come from and why are they so strangely aligned? What do they represent?
Friday, June 29, 2012 7:01 PM
Answers

Hi Tramagust,
VectorGaussian is the prior for Vector. In this example it is given by a 3dimensional mean vector (0.06323, 0.006453, 1.408) and a 3x3 covariance matrix. The numbers are more properly aligned in the Bayes Point Machine example. You might want to look at the definition of Multivariate Gaussian.
Yordan
 Edited by Yordan ZaykovMicrosoft employee Sunday, July 1, 2012 8:43 AM
 Proposed as answer by Yordan ZaykovMicrosoft employee Sunday, July 1, 2012 8:45 AM
 Marked as answer by Tramagust Saturday, July 14, 2012 6:04 PM
Sunday, July 1, 2012 8:41 AM
All replies

Hi Tramagust,
VectorGaussian is the prior for Vector. In this example it is given by a 3dimensional mean vector (0.06323, 0.006453, 1.408) and a 3x3 covariance matrix. The numbers are more properly aligned in the Bayes Point Machine example. You might want to look at the definition of Multivariate Gaussian.
Yordan
 Edited by Yordan ZaykovMicrosoft employee Sunday, July 1, 2012 8:43 AM
 Proposed as answer by Yordan ZaykovMicrosoft employee Sunday, July 1, 2012 8:45 AM
 Marked as answer by Tramagust Saturday, July 14, 2012 6:04 PM
Sunday, July 1, 2012 8:41 AM 
This is from the BPM example. My problem was the way it was displayed. As I understand it from you the proper interpretation is
(0.06323 0.006453 1.408) is the mean vector
and
0.001157 0.0004818 0.01197
0.0004818 0.0006099 0.006733
0.01197 0.006733 0.5215
is the covariance matrix.
Monday, July 2, 2012 8:43 PM 
Correct.Monday, July 2, 2012 8:52 PM