Learning Degrees of Freedom/Shape Parameter for Student-t

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• Monday, March 05, 2012 4:09 PM

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  (Apologies for the earlier spam reply now deleted)

  We do have code in to learn shape of a gamma (which would give you dof), but it is not working correctly right now (it is still a work in progress). The best you can do is learn the rate of a gamma which relates to the variance of the student-t (considered as a Gaussian with uncertain precision). So in the code below, shape can only be a constant or observed, whereas rate can be a random variable.

  double[] xdata = new double[] {1, 2, 3};
  
  //var shape = Variable.GammaFromShapeAndRate(2, 2).Named("shape");
  var shape = 1.0;
  var rate = Variable.GammaFromShapeAndRate(2, 2).Named("rate");
  var tau = Variable.GammaFromShapeAndRate(shape, rate).Named("tau");
  var mean = 1.0;
  var n = new Range(xdata.Length).Named("n");
  var x = Variable.Array<double>(n).Named("x");
  x[n] = Variable.GaussianFromMeanAndPrecision(mean, tau).ForEach(n);
  x.ObservedValue = xdata;
  var engine = new InferenceEngine(new VariationalMessagePassing());
  Console.WriteLine("rate = {0}", engine.Infer(rate));

  John
  
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• Thursday, May 31, 2012 7:54 PM

   

   
  

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  John--

       Thanks for the clarification. The earlier response had indeed struck me as odd.

  Regards,

  Philip

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• Thursday, October 04, 2012 10:20 AM

   

   
  

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  Learning the shape of a gamma is now supported in version 2.5.  In the code posted by John Guiver, you can use the first (commented-out) definition of 'shape'.
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