Logistic transform of a multivariate normal

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  I want to try out an extension of the StudentSkills tutorial but I am having trouble coding up what I want. I want to add a multivariate normal distribution (of dimension equal to number of skills) for each student (so something like theta[student][skill]) and make the hasSkillVar[student][skill] be a logistic function of theta[student][skill].

  In the StudentSkills tutorial we have (leaving out irrelevant snippets)

  VariableArray<double> slipVar, guessVar, pSkillVar;
  VariableArray<VariableArray<bool>, bool[][]> hasSkillVar;
  
  Range student = new Range(num_students);
  Range question = new Range(num_items);
  Range skill = new Range(num_skills);
  
  pSkillVar = Variable.Array<double>(skill).Named("pSkill");
  pSkillVar[skill] = Variable.Beta(1, 1).ForEach(skill);
  
  hasSkillVar[student][skill] = Variable.Bernoulli(pSkillVar[skill]).ForEach(student);

  
  

  I want to do something like this but its not right:

  VariableArray<Vector> abilityVar;
  abilityVar = Variable.Array<Vector>(student).Named("ability");
  abilityVar[student] = Variable.VectorGaussianFromMeanAndPrecision(
                  Vector.Zero(num_skills), PositiveDefiniteMatrix.Identity(num_skills)).ForEach(student);
  
  
  using (Variable.ForEach(student))
  {
    using (Variable.ForEach(skill))
    {
      hasSkillVar[student][skill] = Variable.Bernoulli(Variable.Logistic(Variable.GetItem(abilityVar[student], skill)));
    }
  }

  
  

  skill is a range not an int. 

  
  

  • Edited by cyentist Friday, September 8, 2017 4:58 PM

  Friday, September 8, 2017 4:51 PM