Controlling how inference is performed

You can get fine-grained control of how inference is performed by getting hold of a compiled algorithm object. The following code shows, for the simple Gaussian example, how to do this. The starting point is to call GetCompiledInferenceAlgorithm on an InferenceEngine, passing in the complete set of variables that you want the compiled algorithm to be able to infer. 
// Set the inference algorithm
InferenceEngine engine = new InferenceEngine(new VariationalMessagePassing());
// Get the compiled inference algorithm
var ca = engine.GetCompiledInferenceAlgorithm(mean, precision);
Once you have a reference to the compiled algorithm, you can explicitly control the initialisation and updates of the algorithm. This allows, for example, implementation of a custom convergence criterion by monitoring the level of change in certain marginals of interest.  The IGeneratedAlgorithm object that you get is the same that you would get if you precompiled your inference algorithm.

The following code snippets illustrate all the ways in which you can use the compiled algorithm object:

Reset

This method sets all internal state to its initialised values.  It is useful when you want to force the algorithm to restart its convergence.

ca.Reset();

Update

The Update method performs a specified number of algorithm updates, starting from the current message state.  Each update is an entire single pass through the schedule which updates all forward and backward messages.  If the scheduler has determined that iteration is not necessary for inference, then this does nothing after the first iteration (unless observed values change).

// Run through the schedule 10 times
ca.Update(10);

Execute

The execute method provides a short-cut for performing a reset followed by a series of updates. The following code snippet sets the number of iterations to 10 and gives equivalent results to ca.Reset() followed by ca.Update(10).   However, Execute tries to minimize the amount of computation based on the existing message state.  For example, if Execute(10) was just called and no observed values were changed, then calling Execute(10) again does nothing.  Similarly, if Execute(9) was just called, then Execute(10) will do one additional update.

// Execute 10 iterations of the algorithm
ca.Execute(10);

Setting observed values

When using a compiled algorithm directly, you must use the SetObservedValue(variableName, value) method to ensure that the compiled algorithm is aware of the latest value of an observed variable.  You can also retrieve these values back using GetObservedValue(variableName).  To get the name of a variable in the generated code, use the NameInGeneratedCode property.  The compiled algorithm is automatically filled in with any observed values that were in place at the point when GetCompiledInferenceAlgorithm was called, so you only need to update the compiled algorithm when an observed value changes after that point.

Getting marginals

When using a compiled algorithm directly, you use the Marginal(variableName) method to retrieve marginal distributions (see below for an example).  This can be done at any time, for example, so that the change in the marginal distribution during inference can be monitored to check for convergence.  Unlike engine.Infer, this method does not cause inference to run; it simply returns whatever has already been computed by the compiled algorithm. 

Example

The following example illustrates these mechanisms by extending the simple Gaussian example in several ways. The purpose of this example is to perform inference using the same model for two different data sets, whilst avoiding compilation of the model between the two calls.

Firstly, the observed data changes for each call of the algorithm. We still create data as a variable array which is observed; however we defer setting what those observed values are until we are ready to call the algorithm; Note that we do need to set an initial dummy value to let the algorithm know that data is observed (in the code below it is just given a null value).

Because the length of data is now variable, we introduce a dataCount variable to indicate its length. Again, we will set the observed value of this variable when we are ready to call the inference, but we initialise it with a dummy value of 0.

The call to GetCompiledInferenceAlgorithm compiles the model and returns a IGeneratedAlgorithm object which can be then used to perform inference any number of times. The values for data and dataCount are changed in the body of the for loop, by calling SetObservedValue. The inference is then performed by calling the Execute method.

// The model
Variable<double> mean = Variable.GaussianFromMeanAndVariance(0, 100);
Variable<double> precision = Variable.GammaFromShapeAndScale(1, 1);
Variable<int> dataCount = Variable.Observed(0);
Range item = new Range(dataCount);
VariableArray<double> data = Variable.Observed<double>(null, item).Named("data");
data[item] =
Variable.GaussianFromMeanAndPrecision(mean, precision).ForEach(item);

// The data
double[][] dataSets = new double[][]
{
   
new double[] { 11, 5, 8, 9 },
   
new double[] { -1, -3, 2, 3, -5 }
};

// Set the inference algorithm
InferenceEngine engine = new InferenceEngine(new VariationalMessagePassing());

// Get the compiled inference algorithm
var ca = engine.GetCompiledInferenceAlgorithm(mean, precision);

// Run the inference on each data set
for (int j = 0; j < dataSets.Length; j++)
{
 
// Set the data and the size of the range
 
ca.SetObservedValue(dataCount.NameInGeneratedCode, dataSets[j].Length);
  ca.SetObservedValue(data.NameInGeneratedCode, dataSets[j]);
 
 
// Execute the inference, running 10 iterations
 
ca.Execute(10);

 
// Retrieve the posterior distributions
 
Gaussian marginalMean = ca.Marginal<Gaussian>(mean.NameInGeneratedCode);
 
Gamma marginalPrecision = ca.Marginal<Gamma>(precision.NameInGeneratedCode);
 
Console.WriteLine("mean=" + marginalMean);
 
Console.WriteLine("prec=" + marginalPrecision);
}

The output from the inference is:

mean=Gaussian(8.165, 1.026)
prec=Gamma(3, 0.08038)
mean=Gaussian(-0.7877, 1.532)
prec=Gamma(3.5, 0.03672)

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