Gaussian Conditional Distribution

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venerdì 9 marzo 2012 09:52

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Hey Guys,

I'm new to working with Infer.net, and am struggling to perform a task which I believe should be quite easy! Maybe I'm tackling this in the wrong way so I'd value any input from readers of the forum.

I've completed all of the exercises/tutorials and have not come accross a solution so I thought I would post.

Essentially I am trying to learn a 2 dimensional Gaussian distribution. i've seen this accomplished in the Gaussian Mixtures example, so I know how to do this. The problem is, I would like to learn said 2d distribution, then condition upon one of the axes. So for example, should i have a gaussian on something like (Price,Amount), I would like to specify a price, and work out the posterior distribution on the amount.

I know one solution would be specify a linear combination of variables (learn a multiplicative factor along with an offset), but i don't want to learn a linear relationship between price and amount. I want to learn the 2 dimensional distribution.

Any ideas how to perfrom this, or where to start? At the moment I'm modelling this linearly as specified above, but want to progress from this.

All help appreciated!

Best,

Doug
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martedì 13 marzo 2012 09:52

Proprietario

Hi Doug

The following code gives an idea of how to do this. It is inefficient as it stands because it will compile (model compiler not C# compiler) each time, so you should put the two models in classes so that the training model, and the model for the conditionals are just compiled once. The code returns the conditional as a Vector Gaussian so you can use this code for more than two dimensions.

John

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

using MicrosoftResearch.Infer;
using MicrosoftResearch.Infer.Maths;
using MicrosoftResearch.Infer.Models;
using MicrosoftResearch.Infer.Distributions;

namespace ConditionalGaussian
{

	class Program
	{
		public static Tuple<VectorGaussian, Wishart> LearnGaussian(Vector[] obs)
		{
			int numData = obs.Length;
			int dim = obs[0].Count;
			Variable<Vector> mean = Variable.VectorGaussianFromMeanAndPrecision(
				Vector.Zero(dim),
				PositiveDefiniteMatrix.IdentityScaledBy(dim,10.0)).Named("mean");
			Variable<PositiveDefiniteMatrix> prec = Variable.WishartFromShapeAndScale(
				100.0, PositiveDefiniteMatrix.IdentityScaledBy(dim, 0.01));
			Range n = new Range(obs.Length).Named("n");
			VariableArray<Vector> data = Variable.Array<Vector>(n).Named("x");
			data[n] = Variable.VectorGaussianFromMeanAndPrecision(mean, prec).ForEach(n);
			data.ObservedValue = obs;

			var engine = new InferenceEngine(new VariationalMessagePassing());
			var meanPosterior = engine.Infer<VectorGaussian>(mean);
			var precPosterior = engine.Infer<Wishart>(prec);

			return new Tuple<VectorGaussian, Wishart>(meanPosterior, precPosterior);
		}

		public static VectorGaussian Conditional(Tuple<VectorGaussian, Wishart> priors, int observedIndex, double observedValue)
		{
			Variable<Vector> mean = Variable.Random(priors.Item1);
			Variable<PositiveDefiniteMatrix> prec = Variable.Random(priors.Item2);
			Variable<Vector> v = Variable.VectorGaussianFromMeanAndPrecision(mean, prec);
			// Initialise v to a proper distribution (to avoid improper messages)
			v.InitialiseTo(new VectorGaussian(priors.Item1.GetMean(), priors.Item2.GetMean()));
			Variable<double> observedV = Variable.GetItem(v, observedIndex);
			observedV.ObservedValue = observedValue;
			var engine = new InferenceEngine(new VariationalMessagePassing());
			var vPosterior = engine.Infer<VectorGaussian>(v);
			return vPosterior;
		}
		
		static void Main(string[] args)
		{
			Vector[] obs = new Vector[] {
				Vector.FromArray(1.0, -2.0),
				Vector.FromArray(1.5, 1.0),
				Vector.FromArray(2.0, -1.0),
				Vector.FromArray(0.5, 2.5),
				Vector.FromArray(0, -1)};
			var priors = LearnGaussian(obs);
			Console.WriteLine(priors.Item1);
			double val = -2.0;
			double inc = .5;
			for (int i = 0; i < 9; i++)
			{
				Console.WriteLine(Conditional(priors, 0, val));
				val += inc;
			}
		}
	}
}

Contrassegnato come risposta DougMc412 giovedì 15 marzo 2012 10:27

giovedì 15 marzo 2012 10:26

0

Hi John,

Great, many thanks for your comprehensive reply! FYI I tried several approaches, but the missing key for me was:

Variable<double> observedV = Variable.GetItem(v, observedIndex);
observedV.ObservedValue = observedValue;
var engine = new InferenceEngine(new VariationalMessagePassing());

I just didn't realise that you pull Variables from Variable<Vector> types. :-)

Thanks and best wishes,

Doug
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