/// <summary>
/// Compiles a model for the specified query variables and returns the generated inference algorithm.
/// </summary>
/// <param name="name">The name of the generated inference algorithm.</param>
/// <param name="generatedSourceFolder">The folder to drop the generated inference algorithm to.</param>
/// <param name="queryVariables">The query variables.</param>
private static void GetCompiledInferenceAlgorithm(string name, string generatedSourceFolder, params IVariable[] queryVariables)
{
const string modelNamespace = "Microsoft.ML.Probabilistic.Learners.BayesPointMachineClassifierInternal";
// Create the inference engine
var engine = new InferenceEngine
{
ModelNamespace = modelNamespace,
ModelName = name,
ShowProgress = false
};
engine.Compiler.AddComments = false; // avoid irrelevant code changes
engine.Compiler.FreeMemory = false;
engine.Compiler.GeneratedSourceFolder = generatedSourceFolder;
engine.Compiler.GenerateInMemory = true;
engine.Compiler.GivePriorityTo(typeof(GammaFromShapeAndRateOp_Laplace));
engine.Compiler.RecommendedQuality = QualityBand.Experimental; // bug
engine.Compiler.ReturnCopies = false;
engine.Compiler.ShowWarnings = true;
engine.Compiler.UseSerialSchedules = true;
engine.Compiler.WriteSourceFiles = true;
// Generate the inference algorithm
engine.GetCompiledInferenceAlgorithm(queryVariables);
}
public Gaussian[] IndexOfMaximumExplicit(Discrete y, out double logEvidence)
{
int N = y.Dimension;
var ev = Variable.Bernoulli(0.5).Named("ev");
var block = Variable.If(ev);
var x = Enumerable.Range(0, N).Select(o => Variable.GaussianFromMeanAndPrecision(0, 1)).ToArray();
var yVar = Variable <int> .Random(y).Named("y");
for (int index = 0; index < N; index++)
{
using (Variable.Case(yVar, index))
{
for (int i = 0; i < N; i++)
{
if (i != index)
{
Variable.ConstrainPositive(x[index] - x[i]);
}
}
}
}
block.CloseBlock();
var ie = new InferenceEngine();
//ie.NumberOfIterations = 2;
var toInfer = x.Select(o => (IVariable)o).ToList();
toInfer.Add(ev);
var ca = ie.GetCompiledInferenceAlgorithm(toInfer.ToArray());
ca.Execute(10);
logEvidence = ca.Marginal <Bernoulli>(ev.NameInGeneratedCode).LogOdds;
return(x.Select(o => ca.Marginal <Gaussian>(o.NameInGeneratedCode)).ToArray());
}
//[Fact]
internal void GaussianTimesBetaTest2()
{
Variable<bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
//Variable<double> x = Variable.GaussianFromMeanAndVariance(1.2, 3.4).Named("x");
//var x = Variable.Constant<double>(1.2).Named("x");
var s = Variable.Beta(5.6, 4.8).Named("s");
//var s = Variable.GaussianFromMeanAndPrecision(0, 1).Named("s");
Variable<double> y = 1.2*s;
y.Name = "y";
Variable.ConstrainEqualRandom(y, new Gaussian(2.7, 0.001));
block.CloseBlock();
InferenceEngine engine = new InferenceEngine(new VariationalMessagePassing());
var ca = engine.GetCompiledInferenceAlgorithm(evidence, s);
ca.Reset();
double oldLogEvidence = double.NegativeInfinity;
for (int i = 0; i < 1000; i++)
{
ca.Update(1);
double logEvidence1 = ca.Marginal<Bernoulli>(evidence.NameInGeneratedCode).LogOdds;
Console.WriteLine(logEvidence1);
if (i > 20 && System.Math.Abs(logEvidence1 - oldLogEvidence) < 0.01)
break;
oldLogEvidence = logEvidence1;
}
//Gaussian xActual = ca.Marginal<Gaussian>(x);
Beta sActual = ca.Marginal<Beta>(s.NameInGeneratedCode);
//Console.WriteLine("x = {0}", xActual);
Console.WriteLine("s = {0}", sActual);
}
public BayesPointMachine(int nFeatures, double noise)
{
// Training model
nTrain = Variable.Observed(default(int)).Named(nameof(nTrain));
Range trainItem = new Range(nTrain);
trainItem.Name = nameof(trainItem);
trainingLabels = Variable.Observed(default(bool[]), trainItem).Named(nameof(trainingLabels));
trainingItems = Variable.Observed(default(Vector[]), trainItem).Named(nameof(trainingItems));
weights = Variable.Random(new VectorGaussian(Vector.Zero(nFeatures), PositiveDefiniteMatrix.Identity(nFeatures))).Named(nameof(weights));
trainingLabels[trainItem] = Variable.IsPositive(Variable.GaussianFromMeanAndVariance(Variable.InnerProduct(weights, trainingItems[trainItem]), noise));
// Testing model
nTest = Variable.Observed(default(int)).Named(nameof(nTest));
Range testItem = new Range(nTest);
testItem.Name = nameof(testItem);
testItems = Variable.Observed(default(Vector[]), testItem).Named(nameof(testItems));
testLabels = Variable.Array <bool>(testItem).Named(nameof(testLabels));
engine = new InferenceEngine();
engine.ShowProgress = false;
engine.Compiler.WriteSourceFiles = false;
engine.NumberOfIterations = 5;
if (singleModel)
{
testLabels[testItem] = Variable.IsPositive(Variable.GaussianFromMeanAndVariance(Variable.InnerProduct(weights, testItems[testItem]), noise));
}
else
{
weightPosterior = Variable.Observed(default(VectorGaussian)).Named(nameof(weightPosterior));
Variable <Vector> testWeights = Variable <Vector> .Random(weightPosterior);
testLabels[testItem] = Variable.IsPositive(Variable.GaussianFromMeanAndVariance(Variable.InnerProduct(testWeights, testItems[testItem]), noise));
// Force compilation of the training model.
engine.GetCompiledInferenceAlgorithm(weights);
}
// Force compilation of the testing model.
// This also defines the variables to be inferred, obviating OptimizeForVariables.
// This requires observed variables to have values, but they can be null.
engine.GetCompiledInferenceAlgorithm(testLabels);
}
internal void FitNegativeBinomial()
{
// generate data from the model
double r = 2;
double p = 0.3;
int[] data = new int[] { 1, 4, 5, 14, 0, 3, 2, 18, 0, 1, 8, 1, 4, 3, 6, 4, 9, 5, 1, 10, 5, 9, 2, 3, 3, 9, 14, 3, 5, 12 };
int N = data.Length;
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
var rate = Variable.GammaFromShapeAndRate(1, 1).Named("rate");
//var shape = Variable.GammaFromShapeAndRate(1,1).Named("shape");
var shape = Variable.GammaFromShapeAndRate(1, 1).Named("shape");
var lambda = Variable.GammaFromShapeAndRate(shape, rate).Named("lambda");
Range Nrange = new Range(N);
var y = Variable.Array <int>(Nrange).Named("y");
y[Nrange] = Variable.Poisson(lambda).ForEach(Nrange);
y.ObservedValue = data;
block.CloseBlock();
InferenceEngine ie = new InferenceEngine(new VariationalMessagePassing());
ie.ShowFactorGraph = true;
var ca = ie.GetCompiledInferenceAlgorithm(evidence, rate, shape);
ca.Reset();
double oldLogEvidence = double.NegativeInfinity;
for (int i = 0; i < 1000; i++)
{
ca.Update(1);
double logEvidence1 = ca.Marginal <Bernoulli>(evidence.NameInGeneratedCode).LogOdds;
Console.WriteLine(logEvidence1);
if (i > 20 && System.Math.Abs(logEvidence1 - oldLogEvidence) < 0.01)
{
break;
}
oldLogEvidence = logEvidence1;
}
Gamma shapePost = ca.Marginal <Gamma>(shape.NameInGeneratedCode);
Gamma ratePost = ca.Marginal <Gamma>(rate.NameInGeneratedCode);
double mean, variance;
shapePost.GetMeanAndVariance(out mean, out variance);
Console.WriteLine("shape = " + mean + " +/- " + System.Math.Sqrt(variance) + " true= " + r);
ratePost.GetMeanAndVariance(out mean, out variance);
Console.WriteLine("rate = " + mean + " +/- " + System.Math.Sqrt(variance) + " true= " + p / (1 - p));
}
public void PoissonExpTest2()
{
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
Variable <double> x = Variable.GaussianFromMeanAndVariance(1.2, 3.4).Named("x");
Rand.Restart(12347);
int n = 10;
int N = 10;
int[] data = new int[N];
for (int i = 0; i < N; i++)
{
data[i] = Rand.Binomial(n, 1.0 / (double)n);
}
data = new int[] { 5, 6, 7 };
Range item = new Range(data.Length).Named("item");
VariableArray <double> ex = Variable.Array <double>(item).Named("ex");
ex[item] = Variable.Exp(x).ForEach(item);
VariableArray <int> y = Variable.Array <int>(item).Named("y");
y[item] = Variable.Poisson(ex[item]);
block.CloseBlock();
y.ObservedValue = data;
InferenceEngine ie = new InferenceEngine(new VariationalMessagePassing());
var ca = ie.GetCompiledInferenceAlgorithm(evidence, x);
double oldLogEvidence = double.NegativeInfinity;
for (int i = 0; i < 1000; i++)
{
ca.Update(1);
double logEvidence1 = ca.Marginal <Bernoulli>(evidence.NameInGeneratedCode).LogOdds;
Console.WriteLine(logEvidence1);
if (i > 20 && System.Math.Abs(logEvidence1 - oldLogEvidence) < 1e-10)
{
break;
}
oldLogEvidence = logEvidence1;
}
Gaussian xExpected = new Gaussian(1.755071011884509, 0.055154577283323);
Gaussian xActual = ca.Marginal <Gaussian>(x.NameInGeneratedCode);
Console.WriteLine("x = {0} should be {1}", xActual, xExpected);
Assert.True(xExpected.MaxDiff(xActual) < 1e-3);
}
/// <summary>
/// Compiles a model for the specified query variables and returns the generated inference algorithm.
/// </summary>
/// <param name="name">The name of the generated inference algorithm.</param>
/// <param name="generatedSourceFolder">The folder to drop the generated inference algorithm to.</param>
/// <param name="queryVariables">The query variables.</param>
private static void GetCompiledInferenceAlgorithm(string name, string generatedSourceFolder, params IVariable[] queryVariables)
{
// Create the inference engine
var engine = new InferenceEngine
{
ModelName = name,
ShowProgress = false
};
engine.Compiler.AddComments = true;
engine.Compiler.FreeMemory = false;
engine.Compiler.GeneratedSourceFolder = generatedSourceFolder;
engine.Compiler.GenerateInMemory = true;
engine.Compiler.GivePriorityTo(typeof(GammaFromShapeAndRateOp_Laplace));
engine.Compiler.RecommendedQuality = QualityBand.Experimental; // TFS bug 399
engine.Compiler.ReturnCopies = false;
engine.Compiler.ShowWarnings = true;
engine.Compiler.UseSerialSchedules = true;
engine.Compiler.WriteSourceFiles = true;
// Generate the inference algorithm
engine.GetCompiledInferenceAlgorithm(queryVariables);
}
public Gaussian[] IndexOfMaximumFactorCA(Discrete y, out double logEvidence)
{
int N = y.Dimension;
var n = new Range(N);
var ev = Variable.Bernoulli(0.5).Named("ev");
var block = Variable.If(ev);
var x = Variable.Array <double>(n).Named("x");
x[n] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(n);
var p = IndexOfMaximum(x);
Variable.ConstrainEqualRandom(p, y);
block.CloseBlock();
var ie = new InferenceEngine();
ie.ModelName = "IndexOfMaximumCA";
//ie.NumberOfIterations = 2;
var toinfer = new List <IVariable>();
toinfer.Add(x);
toinfer.Add(ev);
ie.OptimiseForVariables = toinfer;
var ca = ie.GetCompiledInferenceAlgorithm(x, ev);
ca.Reset();
Gaussian[] xPost = null;
logEvidence = 0;
for (int i = 0; i < 10; i++)
{
ca.Update(1);
logEvidence = ca.Marginal <Bernoulli>(ev.NameInGeneratedCode).LogOdds;
xPost = ca.Marginal <Gaussian[]>(x.NameInGeneratedCode);
}
return(xPost);
}
/// <summary>
/// Initializes a new instance of the <see cref="BinaryModel"/> class.
/// </summary>
/// <param name="trainModel">If set to <c>true</c> train model.</param>
/// <param name="showFactorGraph">If set to <c>true</c> show factor graph.</param>
/// <param name="debug">If set to <c>true</c> debug.</param>
public BinaryModel(bool trainModel, bool showFactorGraph = false, bool debug = false)
{
evidence = Variable.Bernoulli(0.5).Named("evidence");
using (Variable.If(evidence))
{
numberOfResidents = Variable.New<int>().Named("numberOfResidents").Attrib(new DoNotInfer());
numberOfFeatures = Variable.New<int>().Named("numberOfFeatures").Attrib(new DoNotInfer());
var resident = new Range(numberOfResidents).Named("resident");
var feature = new Range(numberOfFeatures).Named("feature");
numberOfExamples = Variable.Array<int>(resident).Named("numberOfExamples").Attrib(new DoNotInfer());
var example = new Range(numberOfExamples[resident]).Named("example").Attrib(new Sequential());
noisePrecision = Variable.New<double>().Named("noisePrecision").Attrib(new DoNotInfer());
weightPriorMeans = Variable.New<GaussianArray>().Named("weightPriorMeans").Attrib(new DoNotInfer());
weightPriorPrecisions = Variable.New<GammaArray>().Named("weightPriorPrecisions").Attrib(new DoNotInfer());
weightMeans = Variable.Array<double>(feature).Named("weightMeans");
weightPrecisions = Variable.Array<double>(feature).Named("weightPrecisions");
weightMeans.SetTo(Variable<double[]>.Random(weightPriorMeans));
weightPrecisions.SetTo(Variable<double[]>.Random(weightPriorPrecisions));
weights = Variable.Array(Variable.Array<double>(feature), resident).Named("weights");
featureValues = Variable.Array(Variable.Array(Variable.Array<double>(feature), example), resident).Named("featureValues").Attrib(new DoNotInfer());
// if (!useBias)
// {
// thresholdPriors = Variable.New<GaussianArray>().Named("thresholdPrior").Attrib(new DoNotInfer());
// thresholds = Variable.Array<double>(resident).Named("threshold");
// thresholds.SetTo(Variable<double[]>.Random(thresholdPriors));
// }
activities = Variable.Array(Variable.Array<bool>(example), resident).Named("activities");
// activities[resident][example].AddAttribute(new MarginalPrototype(new Bernoulli()));
using (Variable.ForEach(resident))
{
var products = Variable.Array(Variable.Array<double>(feature), example).Named("products");
var scores = Variable.Array<double>(example).Named("scores");
var scoresPlusNoise = Variable.Array<double>(example).Named("scoresPlusNoise");
weights[resident][feature] = Variable.GaussianFromMeanAndPrecision(weightMeans[feature], weightPrecisions[feature]);
using (Variable.ForEach(example))
{
using (Variable.ForEach(feature))
{
products[example][feature] = weights[resident][feature] * featureValues[resident][example][feature];
}
scores[example] = Variable.Sum(products[example]).Named("score");
scoresPlusNoise[example] = Variable.GaussianFromMeanAndPrecision(scores[example], noisePrecision).Named("scorePlusNoise");
// if (useBias)
{
activities[resident][example] = scoresPlusNoise[example] > 0;
}
// else
// {
// var diff = (scoresPlusNoise[example] - thresholds[resident]).Named("diff");
// activities[example][resident] = diff > 0;
// }
}
}
}
engine = new InferenceEngine
{
Algorithm = new ExpectationPropagation { DefaultNumberOfIterations = trainModel ? 10 : 1 },
ShowFactorGraph = showFactorGraph,
ShowProgress = false,
// BrowserMode = BrowserMode.Never, // debug ? BrowserMode.OnError : BrowserMode.Never,
ShowWarnings = debug
};
if (debug)
{
engine.Compiler.GenerateInMemory = false;
engine.Compiler.WriteSourceFiles = true;
engine.Compiler.IncludeDebugInformation = true;
engine.Compiler.CatchExceptions = true;
}
#if USE_PRECOMPILED_ALGORITHM
numberOfResidents.ObservedValue = default(int);
numberOfExamples.ObservedValue = default(int);
numberOfFeatures.ObservedValue = default(int);
noisePrecision.ObservedValue = default(double);
featureValues.ObservedValue = default(double[][][]);
weightPriorMeans.ObservedValue = default(DistributionStructArray<Gaussian, double>); // (DistributionStructArray<Gaussian, double>)Distribution<double>.Array(default(Gaussian[]));
weightPriorPrecisions.ObservedValue = default(DistributionStructArray<Gamma, double>); // (DistributionStructArray<Gamma, double>)Distribution<double>.Array(default(Gamma[]));
activities.ObservedValue = default(bool[][]);
if (trainModel)
{
activities.AddAttribute(new DoNotInfer());
algorithm = engine.GetCompiledInferenceAlgorithm(new IVariable[] { weights, weightMeans, weightPrecisions });
}
else
{
activities.AddAttribute(QueryTypes.Marginal);
algorithm = engine.GetCompiledInferenceAlgorithm(new IVariable[] { activities });
}
#endif
}
public int MulticlassRegression(Vector[] xObs, int[] yObs, int C, out VectorGaussian[] bPost, out Gaussian[] meanPost, out double lowerBound, object softmaxOperator,
bool trackLowerBound = false)
{
int N = xObs.Length;
int K = xObs[0].Count;
var c = new Range(C).Named("c");
var n = new Range(N).Named("n");
Variable <bool> ev = null;
IfBlock model = null;
if (trackLowerBound)
{
ev = Variable.Bernoulli(0.5).Named("evidence");
model = Variable.If(ev);
}
// model
var B = Variable.Array <Vector>(c).Named("coefficients");
B[c] = Variable.VectorGaussianFromMeanAndPrecision(Vector.Zero(K), PositiveDefiniteMatrix.Identity(K)).ForEach(c);
var m = Variable.Array <double>(c).Named("mean");
m[c] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(c);
Variable.ConstrainEqualRandom(B[C - 1], VectorGaussian.PointMass(Vector.Zero(K)));
Variable.ConstrainEqualRandom(m[C - 1], Gaussian.PointMass(0));
var x = Variable.Array <Vector>(n);
x.ObservedValue = xObs;
var yData = Variable.Array <int>(n);
yData.ObservedValue = yObs;
var g = Variable.Array(Variable.Array <double>(c), n);
g[n][c] = Variable.InnerProduct(B[c], x[n]) + m[c];
var p = Variable.Array <Vector>(n);
p[n] = Variable.Softmax(g[n]);
using (Variable.ForEach(n))
yData[n] = Variable.Discrete(p[n]);
if (trackLowerBound)
{
model.CloseBlock();
}
// inference
var ie = new InferenceEngine(new VariationalMessagePassing());
ie.Compiler.GivePriorityTo(softmaxOperator);
var ca = ie.GetCompiledInferenceAlgorithm(ev, B, m);
var start = DateTime.Now;
var initBound = double.NegativeInfinity;
int i = 0;
lowerBound = 0;
for (i = 1; i <= 50; i++)
{
ca.Update(1);
lowerBound = ca.Marginal <Bernoulli>(ev.NameInGeneratedCode).LogOdds;
Console.WriteLine(i + "," + lowerBound + "," + (DateTime.Now - start).TotalMilliseconds);
if (System.Math.Abs(initBound - lowerBound) < 1e-2)
{
break;
}
initBound = lowerBound;
start = DateTime.Now;
}
bPost = ca.Marginal <VectorGaussian[]>(B.NameInGeneratedCode);
meanPost = ca.Marginal <Gaussian[]>(m.NameInGeneratedCode);
return(i);
}
internal void BetaRegression()
{
int P = 8;
double[] b = new double[P];
for (int p = 0; p < P; p++)
{
b[p] = Rand.Beta(1, 1);
}
int N = 100;
double[][] X = new double[N][];
//Gaussian[][] softX = new Gaussian[N][];
double[] Y = new double[N];
for (int n = 0; n < N; n++)
{
X[n] = new double[P];
//softX[n] = new Gaussian[P];
Y[n] = 0;
for (int p = 0; p < P; p++)
{
X[n][p] = Rand.Normal();
//softX[n][p] = new Gaussian(X[n][p], 1e-4);
Y[n] += X[n][p] * b[p];
}
}
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
Range dim = new Range(P).Named("P");
Range item = new Range(N).Named("N");
VariableArray <double> w = Variable.Array <double>(dim).Named("w");
w[dim] = Variable.Beta(1, 1).ForEach(dim);
var x = Variable.Array(Variable.Array <double>(dim), item).Named("x");
var softXvar = Variable.Array(Variable.Array <double>(dim), item).Named("softx");
softXvar.ObservedValue = X;
x[item][dim] = Variable.GaussianFromMeanAndPrecision(softXvar[item][dim], 1e4);
var wx = Variable.Array(Variable.Array <double>(dim), item).Named("wx");
wx[item][dim] = x[item][dim] * w[dim];
var sum = Variable.Array <double>(item).Named("sum");
sum[item] = Variable.Sum(wx[item]);
var prec = Variable.GammaFromShapeAndRate(.1, .1).Named("Noise");
var y = Variable.Array <double>(item).Named("y");
y[item] = Variable.GaussianFromMeanAndPrecision(sum[item], prec);
block.CloseBlock();
y.ObservedValue = Y;
InferenceEngine engine = new InferenceEngine(new VariationalMessagePassing());
var ca = engine.GetCompiledInferenceAlgorithm(evidence, w);
ca.Reset();
double oldLogEvidence = double.NegativeInfinity;
for (int i = 0; i < 1000; i++)
{
ca.Update(1);
double logEvidence1 = ca.Marginal <Bernoulli>(evidence.NameInGeneratedCode).LogOdds;
Console.WriteLine(logEvidence1);
if (i > 20 && System.Math.Abs(logEvidence1 - oldLogEvidence) < 0.01)
{
break;
}
oldLogEvidence = logEvidence1;
}
DistributionArray <Beta> wInferred = ca.Marginal <DistributionArray <Beta> >(w.NameInGeneratedCode);
for (int p = 0; p < P; p++)
{
Console.WriteLine("w[{0}] = {1} +/- {2} should be {3}",
p, wInferred[p].GetMean(), System.Math.Sqrt(wInferred[p].GetVariance()), b[p]);
}
}
/// <summary>
/// Initializes a new instance of the <see cref="BinaryModel"/> class.
/// </summary>
/// <param name="trainModel">If set to <c>true</c> train model.</param>
/// <param name="showFactorGraph">If set to <c>true</c> show factor graph.</param>
/// <param name="debug">If set to <c>true</c> debug.</param>
public BinaryModel(bool trainModel, bool showFactorGraph = false, bool debug = false)
{
evidence = Variable.Bernoulli(0.5).Named("evidence");
using (Variable.If(evidence))
{
numberOfResidents = Variable.New <int>().Named("numberOfResidents").Attrib(new DoNotInfer());
numberOfFeatures = Variable.New <int>().Named("numberOfFeatures").Attrib(new DoNotInfer());
var resident = new Range(numberOfResidents).Named("resident");
var feature = new Range(numberOfFeatures).Named("feature");
numberOfExamples = Variable.Array <int>(resident).Named("numberOfExamples").Attrib(new DoNotInfer());
var example = new Range(numberOfExamples[resident]).Named("example").Attrib(new Sequential());
noisePrecision = Variable.New <double>().Named("noisePrecision").Attrib(new DoNotInfer());
weightPriorMeans = Variable.New <GaussianArray>().Named("weightPriorMeans").Attrib(new DoNotInfer());
weightPriorPrecisions = Variable.New <GammaArray>().Named("weightPriorPrecisions").Attrib(new DoNotInfer());
weightMeans = Variable.Array <double>(feature).Named("weightMeans");
weightPrecisions = Variable.Array <double>(feature).Named("weightPrecisions");
weightMeans.SetTo(Variable <double[]> .Random(weightPriorMeans));
weightPrecisions.SetTo(Variable <double[]> .Random(weightPriorPrecisions));
weights = Variable.Array(Variable.Array <double>(feature), resident).Named("weights");
featureValues = Variable.Array(Variable.Array(Variable.Array <double>(feature), example), resident).Named("featureValues").Attrib(new DoNotInfer());
// if (!useBias)
// {
// thresholdPriors = Variable.New<GaussianArray>().Named("thresholdPrior").Attrib(new DoNotInfer());
// thresholds = Variable.Array<double>(resident).Named("threshold");
// thresholds.SetTo(Variable<double[]>.Random(thresholdPriors));
// }
activities = Variable.Array(Variable.Array <bool>(example), resident).Named("activities");
// activities[resident][example].AddAttribute(new MarginalPrototype(new Bernoulli()));
using (Variable.ForEach(resident))
{
var products = Variable.Array(Variable.Array <double>(feature), example).Named("products");
var scores = Variable.Array <double>(example).Named("scores");
var scoresPlusNoise = Variable.Array <double>(example).Named("scoresPlusNoise");
weights[resident][feature] = Variable.GaussianFromMeanAndPrecision(weightMeans[feature], weightPrecisions[feature]);
using (Variable.ForEach(example))
{
using (Variable.ForEach(feature))
{
products[example][feature] = weights[resident][feature] * featureValues[resident][example][feature];
}
scores[example] = Variable.Sum(products[example]).Named("score");
scoresPlusNoise[example] = Variable.GaussianFromMeanAndPrecision(scores[example], noisePrecision).Named("scorePlusNoise");
// if (useBias)
{
activities[resident][example] = scoresPlusNoise[example] > 0;
}
// else
// {
// var diff = (scoresPlusNoise[example] - thresholds[resident]).Named("diff");
// activities[example][resident] = diff > 0;
// }
}
}
}
engine = new InferenceEngine
{
Algorithm = new ExpectationPropagation {
DefaultNumberOfIterations = trainModel ? 10 : 1
},
ShowFactorGraph = showFactorGraph,
ShowProgress = false,
// BrowserMode = BrowserMode.Never, // debug ? BrowserMode.OnError : BrowserMode.Never,
ShowWarnings = debug
};
if (debug)
{
engine.Compiler.GenerateInMemory = false;
engine.Compiler.WriteSourceFiles = true;
engine.Compiler.IncludeDebugInformation = true;
engine.Compiler.CatchExceptions = true;
}
#if USE_PRECOMPILED_ALGORITHM
numberOfResidents.ObservedValue = default(int);
numberOfExamples.ObservedValue = default(int);
numberOfFeatures.ObservedValue = default(int);
noisePrecision.ObservedValue = default(double);
featureValues.ObservedValue = default(double[][][]);
weightPriorMeans.ObservedValue = default(DistributionStructArray <Gaussian, double>); // (DistributionStructArray<Gaussian, double>)Distribution<double>.Array(default(Gaussian[]));
weightPriorPrecisions.ObservedValue = default(DistributionStructArray <Gamma, double>); // (DistributionStructArray<Gamma, double>)Distribution<double>.Array(default(Gamma[]));
activities.ObservedValue = default(bool[][]);
if (trainModel)
{
activities.AddAttribute(new DoNotInfer());
algorithm = engine.GetCompiledInferenceAlgorithm(new IVariable[] { weights, weightMeans, weightPrecisions });
}
else
{
activities.AddAttribute(QueryTypes.Marginal);
algorithm = engine.GetCompiledInferenceAlgorithm(new IVariable[] { activities });
}
#endif
}
/// <summary>
/// Primary definition of the GPRN model as an Infer.NET model.
/// </summary>
/// <param name="inputs">Covariates X</param>
/// <param name="data">Outputs Y</param>
/// <param name="Q">Number of latent functions</param>
/// <param name="missing">Which elements of Y are missing</param>
/// <param name="nodeFunctionNoise">Whether to include node noise</param>
/// <param name="constrainWpositive">Whether to constrain W to be positive [experimental]</param>
/// <param name="isotropicNoise">Whether to use isotropic observation noise</param>
/// <param name="meanFunctions">Whether to include a per output mean function</param>
/// <param name="initLoglengthscales">Initial values for the length scales of the kernels</param>
/// <param name="sw">An output file for logging</param>
public void GPRN_InferNET_model(Vector[] inputs,
double[,] data,
int Q,
bool grid = false,
bool[,] missing = null,
bool nodeFunctionNoise = false,
bool constrainWpositive = false,
bool isotropicNoise = true,
bool meanFunctions = false,
double[] initLoglengthscales = null,
StreamWriter sw = null)
{
var toInfer = new List <IVariable>();
SummationKernel kf_node = new SummationKernel(new SquaredExponential(0)) + new WhiteNoise(-3);
var K_node = Utils.GramMatrix(kf_node, inputs);
SummationKernel kf_weights = new SummationKernel(new SquaredExponential(1)) + new WhiteNoise(-3);
var K_weights = Utils.GramMatrix(kf_weights, inputs);
var D = Variable.Observed <int>(data.GetLength(0)).Named("D");
var d = new Range(D).Named("d");
var Qvar = Variable.Observed <int>(Q).Named("Q");
var q = new Range(Qvar).Named("q");
var N = Variable.Observed <int>(data.GetLength(1)).Named("N");
var n = new Range(N).Named("n");
if (missing == null)
{
missing = new bool[D.ObservedValue, N.ObservedValue]; // check this is all false
}
var ev = Variable.Bernoulli(.5).Named("ev");
var modelBlock = Variable.If(ev);
var nodeSignalPrecisions = Variable.Array <double>(q).Named("nodeSignalPrecisions");
// set this to 1 if not learning signal variance
var nodeSignalPrecisionsPrior = Variable.Observed(Enumerable.Range(0, Q).Select(_ => Gamma.FromShapeAndRate(.1, .1)).ToArray(), q).Named("nodeSignalPrecisionsPrior");
nodeSignalPrecisions[q] = Variable.Random <double, Gamma>(nodeSignalPrecisionsPrior[q]);
var nodeFunctions = Variable.Array <Vector>(q).Named("nodeFunctions");
var K_node_inverse = Variable.Observed(K_node.Inverse()).Named("K_node_inverse");
nodeFunctions[q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, nodeSignalPrecisions[q], K_node_inverse);
nodeFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
var nodeFunctionValues = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValues");
var nodeFunctionValuesPredictive = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesPredictive");
VariableArray <double> nodeNoisePrecisions = null;
if (nodeFunctionNoise)
{
var nodeFunctionValuesClean = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesClean");
nodeFunctionValuesClean[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
nodeNoisePrecisions = Variable.Array <double>(q).Named("nodeNoisePrecisions");
var nodeNoisePrecisionPrior = Variable.Observed(Enumerable.Range(0, Q).Select(_ => Gamma.FromShapeAndRate(.1, .01)).ToArray(), q).Named("nodeNoisePrecisionPrior");
nodeNoisePrecisions[q] = Variable.Random <double, Gamma>(nodeNoisePrecisionPrior[q]);
toInfer.Add(nodeNoisePrecisions);
nodeFunctionValues[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
nodeFunctionValuesPredictive[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
}
else
{
nodeFunctionValues[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
nodeFunctionValuesPredictive[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
}
var weightFunctions = Variable.Array <Vector>(d, q).Named("weightFunctions");
var K_weights_inverse = Variable.Observed(K_weights.Inverse()).Named("K_weights_inverse");
weightFunctions[d, q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, Variable.Constant <double>(1), K_weights_inverse).ForEach(d, q);
weightFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
var weightFunctionValues = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValues");
var weightFunctionValues2 = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValuesPredictive");
weightFunctionValues[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
if (constrainWpositive)
{
var weightFunctionValuesCopy = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValuesCopy");
weightFunctionValuesCopy[d, q][n] = Variable.GaussianFromMeanAndPrecision(weightFunctionValues[d, q][n], 100);
Variable.ConstrainPositive(weightFunctionValuesCopy[d, q][n]);
}
weightFunctionValues2[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
var observedData = Variable.Array <double>(d, n).Named("observedData");
var noisePrecisionPrior = Variable.Observed(Gamma.FromShapeAndRate(1, .1)).Named("noisePrecisionPrior");
Variable <double> noisePrecision = null;
VariableArray <double> noisePrecisionArray = null;
if (isotropicNoise)
{
noisePrecision = Variable.Random <double, Gamma>(noisePrecisionPrior).Named("noisePrecision");
toInfer.Add(noisePrecision);
}
else
{
noisePrecisionArray = Variable.Array <double>(d).Named("noisePrecision");
noisePrecisionArray[d] = Variable.Random <double, Gamma>(noisePrecisionPrior).ForEach(d);
toInfer.Add(noisePrecisionArray);
}
var isMissing = Variable.Array <bool>(d, n).Named("isMissing");
isMissing.ObservedValue = missing;
var noiseLessY = Variable.Array <double>(d, n).Named("noiseLessY");
VariableArray <VariableArray <double>, double[][]> meanFunctionValues = null;
if (meanFunctions)
{
GPFactor.settings = new Settings
{
solverMethod = Settings.SolverMethod.GradientDescent,
};
VariableArray <KernelFunction> kf = Variable.Array <KernelFunction>(d);
kf.ObservedValue = Enumerable.Range(0, D.ObservedValue).Select(
o => new SummationKernel(new SquaredExponential()) + new WhiteNoise(-3)).ToArray();
var mf = Variable.Array <Vector>(d).Named("meanFunctions");
mf[d] = Variable <Vector> .Factor <double, Vector[], int[], KernelFunction>(MyFactors.GP, 1.0 /*Variable.GammaFromShapeAndRate(1,1)*/, inputs, new int[] { 0 },
kf[d]);
mf.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
meanFunctionValues = Variable.Array(Variable.Array <double>(n), d).Named("meanFunctionValues");
meanFunctionValues[d] = Variable.ArrayFromVector(mf[d], n);
toInfer.Add(meanFunctionValues);
}
using (Variable.ForEach(n))
using (Variable.ForEach(d))
{
var temp = Variable.Array <double>(q).Named("temp");
temp[q] = weightFunctionValues[d, q][n] * nodeFunctionValues[q][n];
if (meanFunctions)
{
noiseLessY[d, n] = Variable.Sum(temp) + meanFunctionValues[d][n];
}
else
{
noiseLessY[d, n] = Variable.Sum(temp);
}
using (Variable.IfNot(isMissing[d, n]))
if (isotropicNoise)
{
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(noiseLessY[d, n], noisePrecision);
}
else
{
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(noiseLessY[d, n], noisePrecisionArray[d]);
}
using (Variable.If(isMissing[d, n]))
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(0, 1);
}
observedData.ObservedValue = data;
var nodeFunctionsInit = Enumerable.Range(0, Q).Select(i =>
VectorGaussian.FromMeanAndVariance(
VectorGaussian.Sample(Vector.Zero(N.ObservedValue), PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100)),
PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100))).ToArray(); // should put this manually in generated code
var distArray = Distribution <Vector> .Array(nodeFunctionsInit);
var nodeFunctionsInitVar = Variable.Observed(distArray).Named("nodeFunctionsInitVar");
nodeFunctions.InitialiseTo(nodeFunctionsInitVar);
modelBlock.CloseBlock();
toInfer.AddRange(new List <IVariable>()
{
ev, noiseLessY, nodeFunctionValues, nodeSignalPrecisions, nodeFunctionValuesPredictive, weightFunctionValues, weightFunctionValues2
});
var infer = new InferenceEngine(new VariationalMessagePassing());
infer.ModelName = "MeanFunction";
var ca = infer.GetCompiledInferenceAlgorithm(toInfer.ToArray());
var kernel = new SummationKernel(new SquaredExponential(initLoglengthscales[0]));
kernel += new WhiteNoise(-3);
ca.SetObservedValue(K_node_inverse.NameInGeneratedCode, Utils.GramMatrix(kernel, inputs).Inverse());
kernel = new SummationKernel(new SquaredExponential(initLoglengthscales[1]));
kernel += new WhiteNoise(-3);
ca.SetObservedValue(K_weights_inverse.NameInGeneratedCode, Utils.GramMatrix(kernel, inputs).Inverse());
ca.Reset();
double oldML = double.NegativeInfinity;
double ml = 0;
int it = 0;
for (; it < 100; it++)
{
ca.Update(1);
ml = ca.Marginal <Bernoulli>(ev.NameInGeneratedCode).LogOdds;
Console.WriteLine(ml);
if (Math.Abs(oldML - ml) < .1)
{
break;
}
oldML = ml;
}
Console.WriteLine("Finished after " + it);
}
/// <summary>
/// An implementation of GPRN specialised for one step look ahead multivariate volatility experiments
/// </summary>
/// <param name="inputs">Covariates X</param>
/// <param name="data">Outputs Y</param>
/// <returns>Predicted covariance for the next time point</returns>
public VectorGaussian GPRN_MultivariateVolatility(
Vector[] inputs,
double[,] data,
double[] nodeSignalPrecs,
double[] nodeNoisePrecs,
double obsNoisePrec,
ref VectorGaussian[] finit,
ref VectorGaussian[,] winit,
KernelFunction nodeKernel,
KernelFunction weightKernel)
{
var missing = new bool[data.GetLength(0), data.GetLength(1)];
for (int i = 0; i < data.GetLength(0); i++)
{
missing[i, data.GetLength(1) - 1] = true; // last data point is missing
}
int Q = nodeSignalPrecs.Length;
var toInfer = new List <IVariable>();
var K_node = Utils.GramMatrix(nodeKernel, inputs);
var K_weights = Utils.GramMatrix(weightKernel, inputs);
var D = Variable.Observed <int>(data.GetLength(0)).Named("D");
var d = new Range(D).Named("d");
var Qvar = Variable.Observed <int>(Q).Named("Q");
var q = new Range(Qvar).Named("q");
var N = Variable.Observed <int>(data.GetLength(1)).Named("N");
var n = new Range(N).Named("n");
var ev = Variable.Bernoulli(.5).Named("ev");
var modelBlock = Variable.If(ev);
var nodeSignalPrecisions = Variable.Array <double>(q).Named("nodeSignalPrecisions");
nodeSignalPrecisions.ObservedValue = nodeSignalPrecs;
var nodeFunctions = Variable.Array <Vector>(q).Named("nodeFunctions");
var K_node_inverse = Variable.Observed(K_node.Inverse()).Named("K_node_inverse");
nodeFunctions[q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, nodeSignalPrecisions[q], K_node_inverse);
nodeFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
var nodeFunctionValues = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValues");
var nodeFunctionValuesPredictive = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesPredictive");
var nodeFunctionValuesClean = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesClean");
nodeFunctionValuesClean[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
var nodeNoisePrecisions = Variable.Array <double>(q).Named("nodeNoisePrecisions");
nodeNoisePrecisions.ObservedValue = nodeNoisePrecs;
nodeFunctionValues[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
nodeFunctionValuesPredictive[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
var weightFunctions = Variable.Array <Vector>(d, q).Named("weightFunctions");
var K_weights_inverse = Variable.Observed(K_weights.Inverse()).Named("K_weights_inverse");
weightFunctions[d, q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, Variable.Constant <double>(1), K_weights_inverse).ForEach(d, q);
weightFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
var weightFunctionValues = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValues");
var weightFunctionValuesPredictive = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValuesPredictive");
weightFunctionValues[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
weightFunctionValuesPredictive[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
var observedData = Variable.Array <double>(d, n).Named("observedData");
var noisePrecision = Variable.Observed(obsNoisePrec).Named("noisePrecision");
var isMissing = Variable.Array <bool>(d, n).Named("isMissing");
isMissing.ObservedValue = missing;
var noiseLessY = Variable.Array <double>(d, n).Named("noiseLessY");
using (Variable.ForEach(n))
using (Variable.ForEach(d))
{
var temp = Variable.Array <double>(q).Named("temp");
temp[q] = weightFunctionValues[d, q][n] * nodeFunctionValues[q][n];
noiseLessY[d, n] = Variable.Sum(temp);
using (Variable.IfNot(isMissing[d, n]))
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(noiseLessY[d, n], noisePrecision);
using (Variable.If(isMissing[d, n]))
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(0, 1);
}
observedData.ObservedValue = data;
var nodeFunctionsInit = Enumerable.Range(0, Q).Select(i =>
VectorGaussian.FromMeanAndVariance(
VectorGaussian.Sample(Vector.Zero(N.ObservedValue), PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100)),
PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100))).ToArray(); // should put this manually in generated code
var distArray = Distribution <Vector> .Array(nodeFunctionsInit);
var nodeFunctionsInitVar = Variable.Observed(distArray).Named("nodeFunctionsInitVar");
nodeFunctions.InitialiseTo(nodeFunctionsInitVar);
var finitNew = finit.Select(i => Utils.extendByOneDimension(i, Gaussian.FromMeanAndVariance(0, 1))).ToArray();
nodeFunctions.InitialiseTo(Distribution <Vector> .Array(finitNew));
var winitNew = new VectorGaussian[data.GetLength(0), Q];
for (int i = 0; i < data.GetLength(0); i++)
{
for (int j = 0; j < Q; j++)
{
winitNew[i, j] = Utils.extendByOneDimension(winit[i, j], Gaussian.FromMeanAndVariance(0, 1));
}
}
weightFunctions.InitialiseTo(Distribution <Vector> .Array(winitNew));
modelBlock.CloseBlock();
toInfer.AddRange(new List <IVariable>()
{
ev, noiseLessY, nodeFunctions, weightFunctions, nodeFunctionValuesPredictive, weightFunctionValues, weightFunctionValuesPredictive /* is this redundant? */
});
var ie = new InferenceEngine(new VariationalMessagePassing());
var ca = ie.GetCompiledInferenceAlgorithm(toInfer.ToArray());
ca.SetObservedValue(K_node_inverse.NameInGeneratedCode, Utils.GramMatrix(nodeKernel, inputs).Inverse());
ca.SetObservedValue(K_weights_inverse.NameInGeneratedCode, Utils.GramMatrix(weightKernel, inputs).Inverse());
ca.Reset();
double oldML = double.NegativeInfinity;
double ml = 0;
int it = 0;
for (; it < 30; it++)
{
ca.Update(1);
ml = ca.Marginal <Bernoulli>(ev.NameInGeneratedCode).LogOdds;
Console.WriteLine(ml);
if (Math.Abs(oldML - ml) < .1)
{
break;
}
oldML = ml;
}
var f = ca.Marginal <Gaussian[][]>("nodeFunctionValuesPredictive");
var W = ca.Marginal <Gaussian[, ][]>("weightFunctionValuesPredictive");
finit = ca.Marginal <VectorGaussian[]>(nodeFunctions.NameInGeneratedCode);
winit = ca.Marginal <VectorGaussian[, ]>(weightFunctions.NameInGeneratedCode);
return(Utils.CorrelatedPredictionsHelper(f, W, Gamma.PointMass(obsNoisePrec), Q, data.GetLength(0), data.GetLength(1) - 1));
}
/// <summary>
/// Infer.NET definition of the Semi Parametric Latent Factor Model of
/// Teh, Y., Seeger, M., and Jordan, M. (AISTATS 2005).
/// </summary>
/// <param name="inputs">Covariates X</param>
/// <param name="data">Outputs Y</param>
/// <param name="Q">Number of latent functions</param>
/// <param name="missing">Which elements of Y are missing</param>
/// <param name="nodeFunctionNoise">Whether to include node noise</param>
public void SPLFM(
Vector[] inputs,
double[,] data,
int Q,
bool[,] missing = null,
bool nodeFunctionNoise = false)
{
var toInfer = new List <IVariable>();
SummationKernel kf_node = new SummationKernel(new SquaredExponential(0));
var K_node = Utils.GramMatrix(kf_node, inputs);
var D = Variable.Observed <int>(data.GetLength(0)).Named("D");
var d = new Range(D).Named("d");
var Qvar = Variable.Observed <int>(Q).Named("Q");
var q = new Range(Qvar).Named("q");
var N = Variable.Observed <int>(data.GetLength(1)).Named("N");
var n = new Range(N).Named("n");
if (missing == null)
{
missing = new bool[D.ObservedValue, N.ObservedValue]; // check this is all false
}
var ev = Variable.Bernoulli(.5).Named("ev");
var modelBlock = Variable.If(ev);
var nodeSignalPrecisions = Variable.Array <double>(q).Named("nodeSignalPrecisions");
// set this to 1 if not learning signal variance
var nodeSignalPrecisionsPrior = Variable.Observed(Enumerable.Range(0, Q).Select(_ => Gamma.FromShapeAndRate(.1, .1)).ToArray(), q).Named("nodeSignalPrecisionsPrior");
nodeSignalPrecisions[q] = Variable.Random <double, Gamma>(nodeSignalPrecisionsPrior[q]);
var nodeFunctions = Variable.Array <Vector>(q).Named("nodeFunctions");
var K_node_inverse = Variable.Observed(K_node.Inverse()).Named("K_node_inverse");
nodeFunctions[q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, nodeSignalPrecisions[q], K_node_inverse);
nodeFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
var nodeFunctionValues = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValues");
var nodeFunctionValuesPredictive = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesPredictive");
VariableArray <double> nodeNoisePrecisions = null;
if (nodeFunctionNoise)
{
var nodeFunctionValuesClean = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesClean");
nodeFunctionValuesClean[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
nodeNoisePrecisions = Variable.Array <double>(q).Named("nodeNoisePrecisions");
var nodeNoisePrecisionPrior = Variable.Observed(Enumerable.Range(0, Q).Select(_ => Gamma.FromShapeAndRate(.1, .01)).ToArray(), q).Named("nodeNoisePrecisionPrior");
nodeNoisePrecisions[q] = Variable.Random <double, Gamma>(nodeNoisePrecisionPrior[q]);
toInfer.Add(nodeNoisePrecisions);
nodeFunctionValues[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
nodeFunctionValuesPredictive[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
}
else
{
nodeFunctionValues[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
nodeFunctionValuesPredictive[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
}
var weights = Variable.Array <double>(d, q).Named("weights");
weights[d, q] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(d, q);
var observedData = Variable.Array <double>(d, n).Named("observedData");
var noisePrecisionPrior = Variable.Observed(Gamma.FromShapeAndRate(1, .1)).Named("noisePrecisionPrior");
var noisePrecision = Variable.Random <double, Gamma>(noisePrecisionPrior).Named("noisePrecision");
var isMissing = Variable.Array <bool>(d, n).Named("isMissing");
isMissing.ObservedValue = missing;
var noiseLessY = Variable.Array <double>(d, n).Named("noiseLessY");
using (Variable.ForEach(n))
using (Variable.ForEach(d))
{
var temp = Variable.Array <double>(q).Named("temp");
temp[q] = weights[d, q] * nodeFunctionValues[q][n];
noiseLessY[d, n] = Variable.Sum(temp);
using (Variable.IfNot(isMissing[d, n]))
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(noiseLessY[d, n], noisePrecision);
using (Variable.If(isMissing[d, n]))
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(0, 1);
}
observedData.ObservedValue = data;
var nodeFunctionsInit = Enumerable.Range(0, Q).Select(i =>
VectorGaussian.FromMeanAndVariance(
VectorGaussian.Sample(Vector.Zero(N.ObservedValue), PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100)),
PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100))).ToArray(); // should put this manually in generated code
var distArray = Distribution <Vector> .Array(nodeFunctionsInit);
var nodeFunctionsInitVar = Variable.Observed(distArray).Named("nodeFunctionsInitVar");
nodeFunctions.InitialiseTo(nodeFunctionsInitVar);
modelBlock.CloseBlock();
toInfer.AddRange(new List <IVariable>()
{
ev, noiseLessY, noisePrecision, nodeFunctionValues, nodeSignalPrecisions, nodeFunctionValuesPredictive, weights
});
var ie = new InferenceEngine(new VariationalMessagePassing());
ie.ModelName = "SPLFM";
var ca = ie.GetCompiledInferenceAlgorithm(toInfer.ToArray());
ca.Execute(100);
var fvals = ca.Marginal <Gaussian[][]>(nodeFunctionValues.NameInGeneratedCode)[0]; // [q][n]
var x = inputs.Select(i => i[0]).ToArray();
var mplWrapper = new MatplotlibWrapper();
mplWrapper.AddArray("x", x);
mplWrapper.AddArray("y", fvals.Select(i => i.GetMean()).ToArray());
mplWrapper.AddArray("s", fvals.Select(i => Math.Sqrt(i.GetVariance())).ToArray());
mplWrapper.Plot(new string[] {
"fill_between(x,y-s,y+s,color=\"gray\")",
"ylabel(\"node (fitted)\")"
});
}