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L2 norm for Variable<vector>
Question

Hi All,
I am new to infer.net and need some help.
I wrote and tried the following code :
Variable<double> A = Variable.GaussianFromMeanVariance(0,9)
Variable<double> B = Variable.GaussianFromMeanVariance(10,16)
Variable<double> d = Variable.GaussianFromMeanVariance(10,0.01)Variable.constrainTrue((d(BA)) < 0.01);
Variable.constrainTrue((d(BA)) > 0.01);InferenceEngine e = new InferenceEngine();
console.writeline(e.infer(A)+" "+e.infer(B)+" "+e.infer(d));
This worked satisfactorily for me.
However, I am having trouble moving to 2 dimensions using Multivariate Gaussian's with vector gaussians while
creating a constraint based on the L2 Norm. Here is the code I tried.double[] mean1 = {0,0};
double [,] covariance1 = new double[,] { {9,0} , {0,9}};
PositiveDefiniteMatrix matrix1 = new PositiveDefiniteMatrix(covariance1);
Variable<Vector> A = Variable.VectorGaussianFromMeanAndVariance(Vector.FromArray(mean1), matrix1);double[] mean2 = { 10, 10 };
double[,] covariance2 = new double[,] { { 16, 0 }, { 0, 16 } };
PositiveDefiniteMatrix matrix2 = new PositiveDefiniteMatrix(covariance2);
Variable<Vector> B = Variable.VectorGaussianFromMeanAndVariance(Vector.FromArray(mean2), matrix2);Variable<double> d = Variable.GaussianFromMeanAndVariance(10, 0.01);
%I want d^2  L2Norm(BA) < 0.01 and d^2  L2Norm(BA) > 0.01Variable.ConstrainTrue((d*d  (Variable<Vector>.innerProduct(BA,BA))) < 0.01);
Variable.constrainTrue((d*d (Variable<Vector>.innerProduct(BA,BA))) > 0.01);InferenceEngine e = new InferenceEngine();
console.writeline(e.infer(A)+" "+e.infer(B)+" "+e.infer(d));
We get the following error.No operator factor registered for 'Minus' with argument type MicrosoftResearch.Infer.Maths.Vector.What should I do?
Friday, December 9, 2011 9:42 AM
All replies

Infer.NET does not yet support vector subtraction, and it also does not support L2Norm. Even if you got around the subtraction issue, InnerProduct would not allow you to multiply a random vector with itself, or even multiply a random scalar with itself. This is a known limitation. To get around it, you would have to implement your own factor for L2Norm (or more specific to your problem, ConstrainL2NormBetween). However, this is nontrivial, which is why we haven't done it yet.Friday, December 9, 2011 10:10 AMOwner

Hi Minka,
Thanks for the reply. On a related note, how do we use Gaussian Mixtures instead of Gaussians?
For example is there a way we can do the following?
Variable<double> A = Variable.GaussianMixture(double[] weights,double[] means, double[] variances)
Variable<double> B = Variable.GaussianMixture(double[] weights,double[] means, double[] variances)
Variable<double> d = Variable.GaussianMixture(double[] weights,double[] means, double[] variances)
Variable.constrainTrue((d(BA)) < 0.01);
Variable.constrainTrue((d(BA)) > 0.01);InferenceEngine e = new InferenceEngine();
console.writeline(e.infer(A)+" "+e.infer(B)+" "+e.infer(d));
We have already the Gaussian Mixture example http://research.microsoft.com/enus/um/cambridge/projects/infernet/docs/Mixture%20of%20Gaussians%20tutorial.aspx .
But it was not clear how we could use this?Friday, December 9, 2011 11:45 AM 
In the Gaussian Mixture example, 'data' is distributed according to a Gaussian mixture. It happens to be observed in that example, but this isn't essential. To make this easier, you can write a function GaussianMixture(double[] weights,double[] means, double[] variances) that constructs a variable with the same definition as 'data' in the example, and then call this 3 times. In your case, 'data' would be a Variable<double> instead of a VariableArray<Vector>.Friday, December 9, 2011 11:53 AMOwner