private static void AngleScaleTest()
{
Variable<double> angle = Variable.GaussianFromMeanAndVariance(Math.PI / 6, 0.4 * 0.4);
Variable<double> scaleX = Variable.GaussianFromMeanAndVariance(1.5, 2 * 2);
Variable<double> scaleY = Variable.GaussianFromMeanAndVariance(1.5, 2 * 2);
Variable<PositiveDefiniteMatrix> prec = Variable<PositiveDefiniteMatrix>.Factor(ShapeFactors.MatrixFromAngleScale, scaleX, scaleY, angle);
Vector trueMean = Vector.Zero(2);
Range pointRange = new Range(5000);
VariableArray<Vector> points = Variable.Array<Vector>(pointRange);
points[pointRange] = Variable.VectorGaussianFromMeanAndPrecision(trueMean, prec).ForEach(pointRange);
PositiveDefiniteMatrix truePrec = ShapeFactors.MatrixFromAngleScale(2.0, 3.0, Math.PI / 5);
Vector[] observedPoints = Util.ArrayInit(pointRange.SizeAsInt, i => VectorGaussian.Sample(trueMean, truePrec));
points.ObservedValue = observedPoints;
prec.AddAttribute(new PointEstimate());
prec.AddAttribute(new MarginalPrototype(new Wishart(2)));
InferenceEngine engine = new InferenceEngine();
engine.Compiler.RequiredQuality = engine.Compiler.RecommendedQuality = QualityBand.Unknown;
Console.WriteLine(engine.Infer(angle));
Console.WriteLine(engine.Infer(scaleX));
Console.WriteLine(engine.Infer(scaleY));
}
static void Main(string[] args)
{
// data
ArrayList trainingData = readData(@"C:\Users\Jeremy\Documents\Visual Studio 2010\Projects\InferSandbox\train.txt");
// Create target y
VariableArray<double> y = Variable.Observed((double[])(trainingData[trainingData.Count-1])).Named("y");
Variable<Vector> w = Variable.Random(new VectorGaussian(Vector.Zero(trainingData.Count),
PositiveDefiniteMatrix.Identity(trainingData.Count))).Named("w");
trainingData.RemoveAt(trainingData.Count - 1);
BayesPointMachine(trainingData, w, y);
InferenceEngine engine = new InferenceEngine();
if (!(engine.Algorithm is GibbsSampling))
{
VectorGaussian wPosterior = engine.Infer<VectorGaussian>(w);
Console.WriteLine("Dist over w=\n" + wPosterior);
ArrayList testData = readData(@"C:\Users\Jeremy\Documents\Visual Studio 2010\Projects\InferSandbox\test.txt");
VariableArray<double> ytest = Variable.Array<double>(new Range(((double[])(testData[0])).Length)).Named("ytest");
BayesPointMachine(testData, Variable.Random(wPosterior).Named("w"), ytest);
Console.WriteLine("output=\n" + engine.Infer(ytest));
}
else Console.WriteLine("This model has a non-conjugate factor, and therefore cannot use Gibbs sampling");
}
//public int[] Classification(Vector[] features, int[] labels)
//{
//}
public double[] Regression(Vector[] features, double[] values)
{
var wMeans = Variable.Vector(Vector.Zero(features[0].Count).ToArray());
var wPrecision = Variable.WishartFromShapeAndRate(100, PositiveDefiniteMatrix.IdentityScaledBy(features[0].Count, 0.01));
var w = Variable.VectorGaussianFromMeanAndPrecision(wMeans, wPrecision).Named("w");
var numItems = Variable.New<int>().Named("numItems");
var i = new Range(numItems).Named("i");
i.AddAttribute(new Sequential());
var noisePrecision = Variable.New<double>().Named("noisePrecision");
var x = Variable.Array<Vector>(i).Named("x");
var y = Variable.Array<double>(i).Named("y");
using (Variable.ForEach(i))
{
y[i] = Variable.GaussianFromMeanAndPrecision(Variable.InnerProduct(w, x[i]), noisePrecision);
}
numItems.ObservedValue = features.Length;
x.ObservedValue = features;
y.ObservedValue = values;
var engine = new InferenceEngine();
engine.Compiler.UseSerialSchedules = true;
engine.ShowProgress = false;
var wPosterior = engine.Infer<VectorGaussian>(w);
y.ClearObservedValue();
w.ObservedValue = wPosterior.GetMean();
var inferredValues = engine.Infer<IList<Gaussian>>(y);
return inferredValues.Select(v => v.GetMean()).ToArray();
}
public void Run()
{
// data
double[] incomes = { 63, 16, 28, 55, 22, 20 };
double[] ages = { 38, 23, 40, 27, 18, 40 };
bool[] willBuy = { true, false, true, true, false, false };
// Create target y
VariableArray<bool> y = Variable.Observed(willBuy).Named("y");
Variable<Vector> w = Variable.Random(new VectorGaussian(Vector.Zero(3),
PositiveDefiniteMatrix.Identity(3))).Named("w");
BayesPointMachine(incomes, ages, w, y);
InferenceEngine engine = new InferenceEngine();
if (!(engine.Algorithm is GibbsSampling))
{
VectorGaussian wPosterior = engine.Infer<VectorGaussian>(w);
Console.WriteLine("Dist over w=\n"+wPosterior);
double[] incomesTest = { 58, 18, 22 };
double[] agesTest = { 36, 24, 37 };
VariableArray<bool> ytest = Variable.Array<bool>(new Range(agesTest.Length)).Named("ytest");
BayesPointMachine(incomesTest, agesTest, Variable.Random(wPosterior).Named("w"), ytest);
Console.WriteLine("output=\n" + engine.Infer(ytest));
}
else Console.WriteLine("This model has a non-conjugate factor, and therefore cannot use Gibbs sampling");
}
public InferenceResult<Cluster[]> Infer(Vector[] observedData, int clusters)
{
var dimensions = observedData.First().Count;
var evidence = Variable.Bernoulli(0.5).Named("evidence");
var evidenceBlock = Variable.If(evidence);
var clustersRange = new Range(clusters).Named("clustersRange");
var meansPrior = Variable.Array<Vector>(clustersRange).Named("meansPrior");
meansPrior[clustersRange] = Variable
.VectorGaussianFromMeanAndPrecision(
Vector.Zero(dimensions),
PositiveDefiniteMatrix.IdentityScaledBy(dimensions, 0.01))
.ForEach(clustersRange);
var precisionsPrior = Variable.Array<PositiveDefiniteMatrix>(clustersRange).Named("precisionsPrior");
precisionsPrior[clustersRange] = Variable.WishartFromShapeAndRate(100, PositiveDefiniteMatrix.IdentityScaledBy(dimensions, 0.01))
.ForEach(clustersRange);
var initialWeights = Enumerable.Range(0, clusters).Select(_ => 1.0).ToArray();
var mixtureWeightsPrior = Variable.Dirichlet(clustersRange, initialWeights).Named("mixtureWeightsPrior");
var dataRange = new Range(observedData.Length).Named("dataRange");
var data = Variable.Array<Vector>(dataRange).Named("data");
var latentIndex = Variable.Array<int>(dataRange).Named("latentIndex");
using (Variable.ForEach(dataRange))
{
latentIndex[dataRange] = Variable.Discrete(mixtureWeightsPrior);
using (Variable.Switch(latentIndex[dataRange]))
{
data[dataRange] = Variable.VectorGaussianFromMeanAndPrecision(meansPrior[latentIndex[dataRange]], precisionsPrior[latentIndex[dataRange]]);
}
}
var zinit = new Discrete[dataRange.SizeAsInt];
for (int i = 0; i < zinit.Length; i++)
zinit[i] = Discrete.PointMass(Rand.Int(clustersRange.SizeAsInt), clustersRange.SizeAsInt);
latentIndex.InitialiseTo(Distribution<int>.Array(zinit));
evidenceBlock.CloseBlock();
data.ObservedValue = observedData;
var ie = new InferenceEngine(new VariationalMessagePassing());
ie.ShowProgress = false;
var mixtureWeightsPosterior = ie.Infer(mixtureWeightsPrior);
var meansPosterior = ie.Infer<VectorGaussian[]>(meansPrior);
var precisionsPosterior = ie.Infer<Wishart[]>(precisionsPrior);
var bEvidence = ie.Infer<Bernoulli>(evidence);
var result = new List<Cluster>();
for (var i = 0; i < clusters; i++)
{
result.Add(new Cluster(meansPosterior[i].GetMean(), precisionsPosterior[i].GetMean().Inverse()));
}
return new InferenceResult<Cluster[]>(bEvidence, result.ToArray());
}
// Sample data from a DINA/NIDA model and then use Infer.NET to recover the parameters.
public void Run()
{
InferenceEngine engine = new InferenceEngine();
if (!(engine.Algorithm is ExpectationPropagation))
{
Console.WriteLine("This example only runs with Expectation Propagation");
return;
}
bool useDina = true;
Beta slipPrior = new Beta(1, 10);
Beta guessPrior = new Beta(1, 10);
Rand.Restart(0);
int nStudents = 100;
int nQuestions = 20;
int nSkills = 3;
int[][] skillsRequired = new int[nQuestions][];
for (int q = 0; q < nQuestions; q++) {
// each question requires a random set of skills
int[] skills = Rand.Perm(nSkills);
int n = Rand.Int(nSkills)+1;
skillsRequired[q] = Util.ArrayInit(n, i => skills[i]);
Console.WriteLine("skillsRequired[{0}] = {1}", q, Util.CollectionToString(skillsRequired[q]));
}
double[] pSkill, slip, guess;
bool[][] hasSkill;
VariableArray<double> slipVar, guessVar, pSkillVar;
VariableArray<VariableArray<bool>,bool[][]> hasSkillVar;
if (useDina) {
bool[][] responses = DinaSample(nStudents, nSkills, skillsRequired, slipPrior, guessPrior, out pSkill, out slip, out guess, out hasSkill);
DinaModel(responses, nSkills, skillsRequired, slipPrior, guessPrior, out pSkillVar, out slipVar, out guessVar, out hasSkillVar);
} else {
bool[][] responses = NidaSample(nStudents, nSkills, skillsRequired, slipPrior, guessPrior, out pSkill, out slip, out guess, out hasSkill);
NidaModel(responses, nSkills, skillsRequired, slipPrior, guessPrior, out pSkillVar, out slipVar, out guessVar, out hasSkillVar);
}
engine.NumberOfIterations = 10;
Bernoulli[][] hasSkillPost = engine.Infer<Bernoulli[][]>(hasSkillVar);
int numErrors = 0;
for (int i = 0; i < nStudents; i++) {
for (int s = 0; s < nSkills; s++) {
if (hasSkill[i][s] != (hasSkillPost[i][s].LogOdds > 0)) numErrors++;
}
}
Console.WriteLine("{0:0}% of skills recovered correctly", 100.0 - 100.0*numErrors/(nStudents*nSkills));
Beta[] pSkillPost = engine.Infer<Beta[]>(pSkillVar);
Beta[] slipPost = engine.Infer<Beta[]>(slipVar);
Beta[] guessPost = engine.Infer<Beta[]>(guessVar);
for (int s = 0; s < nSkills; s++) {
Console.WriteLine("pSkill[{0}] = {1} (sampled from {2})", s, pSkillPost[s], pSkill[s].ToString("g4"));
}
for (int i = 0; i < Math.Min(3,slipPost.Length); i++) {
Console.WriteLine("slip[{0}] = {1} (sampled from {2})", i, slipPost[i], slip[i].ToString("g4"));
}
for (int i = 0; i < Math.Min(3,guessPost.Length); i++) {
Console.WriteLine("guess[{0}] = {1} (sampled from {2})", i, guessPost[i], guess[i].ToString("g4"));
}
}
public void Run()
{
// Define a range for the number of mixture components
Range k = new Range(2).Named("k");
// Mixture component means
VariableArray<Vector> means = Variable.Array<Vector>(k).Named("means");
means[k] = Variable.VectorGaussianFromMeanAndPrecision(
Vector.FromArray(0.0,0.0),
PositiveDefiniteMatrix.IdentityScaledBy(2,0.01)).ForEach(k);
// Mixture component precisions
VariableArray<PositiveDefiniteMatrix> precs = Variable.Array<PositiveDefiniteMatrix>(k).Named("precs");
precs[k] = Variable.WishartFromShapeAndScale(100.0, PositiveDefiniteMatrix.IdentityScaledBy(2,0.01)).ForEach(k);
// Mixture weights
Variable<Vector> weights = Variable.Dirichlet(k, new double[] { 1, 1 }).Named("weights");
// Create a variable array which will hold the data
Range n = new Range(300).Named("n");
VariableArray<Vector> data = Variable.Array<Vector>(n).Named("x");
// Create latent indicator variable for each data point
VariableArray<int> z = Variable.Array<int>(n).Named("z");
// The mixture of Gaussians model
using (Variable.ForEach(n)) {
z[n] = Variable.Discrete(weights);
using (Variable.Switch(z[n])) {
data[n] = Variable.VectorGaussianFromMeanAndPrecision(means[z[n]], precs[z[n]]);
}
}
// Attach some generated data
data.ObservedValue = GenerateData(n.SizeAsInt);
// Initialise messages randomly so as to break symmetry
Discrete[] zinit = new Discrete[n.SizeAsInt];
for (int i = 0; i < zinit.Length; i++)
zinit[i] = Discrete.PointMass(Rand.Int(k.SizeAsInt), k.SizeAsInt);
z.InitialiseTo(Distribution<int>.Array(zinit));
// The inference
InferenceEngine ie = new InferenceEngine();
if (!(ie.Algorithm is ExpectationPropagation))
{
Console.WriteLine("Dist over pi=" + ie.Infer(weights));
Console.WriteLine("Dist over means=\n" + ie.Infer(means));
Console.WriteLine("Dist over precs=\n" + ie.Infer(precs));
}
else
Console.WriteLine("This example is not supported by Expectation Propagation");
}
public override void Run()
{
var rangeMin = -10;
var interval = 0.1;
var observationSize = 100;
var aActual = 0.2;
var bActual = 2.3;
var rand = new System.Random();
var actuals = Enumerable.Range(rangeMin, observationSize)
.Select(i => i * interval)
.Select(i => Tuple.Create((double) i, bActual * i + aActual))
.ToArray();
var samples = actuals.Select(tuple => Tuple.Create(tuple.Item1, tuple.Item2 + ((rand.NextDouble() - 0.5) * 10))).ToArray();
var series = new List<LabelledSeries<Tuple<double, double>>>();
series.Add(new LabelledSeries<Tuple<double, double>>(string.Format("Actual a+bx a={0} b={1}", aActual, bActual), actuals));
var aPrior = Variable.GaussianFromMeanAndPrecision(0, 0.01).Named("aPrior");
var bPrior = Variable.GaussianFromMeanAndPrecision(0, 0.01).Named("bPrior");
var noisePrior = Variable.GammaFromShapeAndScale(1, 5).Named("noisePrior");
var obsRange = new Range(samples.Length);
var xArray = Variable.Array<double>(obsRange);
var exprArray = Variable.Array<double>(obsRange);
using (Variable.ForEach(obsRange))
{
exprArray[obsRange] = Variable.GaussianFromMeanAndPrecision(aPrior + xArray[obsRange] * bPrior, noisePrior);
}
xArray.ObservedValue = samples.Select(t => (double)t.Item1).ToArray();
exprArray.ObservedValue = samples.Select(t => t.Item2).ToArray();
var engine = new InferenceEngine();
var aPosterior = engine.Infer<Gaussian>(aPrior);
var bPosterior = engine.Infer<Gaussian>(bPrior);
var noisePosterior = engine.Infer<Gamma>(noisePrior);
var aInferred = aPosterior.GetMean();
var bInferred = bPosterior.GetMean();
var inferred = Enumerable.Range(rangeMin, observationSize)
.Select(i => i * interval)
.Select(i => Tuple.Create((double)i, bInferred * i + aInferred))
.ToArray();
series.Add(new LabelledSeries<Tuple<double, double>>(string.Format("Inferred a+bx a={0} b={1}", Math.Round(aInferred, 4), Math.Round(bInferred, 4)), inferred));
series.Add(new LabelledSeries<Tuple<double, double>>(string.Format("Data", aActual, bActual), samples) { IsScatter = true });
this.Series = series.ToArray();
}
public void Run()
{
Rand.Restart(12347);
// The model
int N = RatsHeightData.GetLength(0);
int T = RatsHeightData.GetLength(1);
Range r = new Range(N).Named("N");
Range w = new Range(T).Named("T");
Variable<double> alphaC = Variable.GaussianFromMeanAndPrecision(0.0, 1e-4).Named("alphaC");
Variable<double> alphaTau = Variable.GammaFromShapeAndRate(1e-3, 1e-3).Named("alphaTau");
VariableArray<double> alpha = Variable.Array<double>(r).Named("alpha");
alpha[r] = Variable.GaussianFromMeanAndPrecision(alphaC, alphaTau).ForEach(r);
Variable<double> betaC = Variable.GaussianFromMeanAndPrecision(0.0, 1e-4).Named("betaC");
Variable<double> betaTau = Variable.GammaFromShapeAndRate(1e-3, 1e-3).Named("betaTau");
VariableArray<double> beta = Variable.Array<double>(r).Named("beta");
beta[r] = Variable.GaussianFromMeanAndPrecision(betaC, betaTau).ForEach(r);
Variable<double> tauC = Variable.GammaFromShapeAndRate(1e-3, 1e-3).Named("tauC");
VariableArray<double> x = Variable.Observed<double>(RatsXData, w).Named("x");
Variable<double> xbar = Variable.Sum(x)/T;
VariableArray2D<double> y = Variable.Observed<double>(RatsHeightData, r, w).Named("y");
y[r, w] = Variable.GaussianFromMeanAndPrecision(alpha[r] + (beta[r] * (x[w]-xbar)), tauC);
Variable<double> alpha0 = (alphaC - betaC * xbar).Named("alpha0");
// Initialise with the mean of the prior (needed for Gibbs to converge quickly)
alphaC.InitialiseTo(Gaussian.PointMass(0.0));
tauC.InitialiseTo(Gamma.PointMass(1.0));
alphaTau.InitialiseTo(Gamma.PointMass(1.0));
betaTau.InitialiseTo(Gamma.PointMass(1.0));
// Inference engine
InferenceEngine ie = new InferenceEngine();
if (!(ie.Algorithm is ExpectationPropagation))
{
Gaussian betaCMarg = ie.Infer<Gaussian>(betaC);
Gaussian alpha0Marg = ie.Infer<Gaussian>(alpha0);
Gamma tauCMarg = ie.Infer<Gamma>(tauC);
// Inference
Console.WriteLine("alpha0 = {0}[sd={1}]", alpha0Marg, Math.Sqrt(alpha0Marg.GetVariance()).ToString("g4"));
Console.WriteLine("betaC = {0}[sd={1}]", betaCMarg, Math.Sqrt(betaCMarg.GetVariance()).ToString("g4"));
Console.WriteLine("tauC = {0}", tauCMarg);
}
else
Console.WriteLine("This example does not run with Expectation Propagation");
}
public void Run()
{
Variable<bool> firstCoin = Variable.Bernoulli(0.5).Named("firstCoin");
Variable<bool> secondCoin = Variable.Bernoulli(0.5).Named("secondCoin");
Variable<bool> bothHeads = (firstCoin & secondCoin).Named("bothHeads");
InferenceEngine ie = new InferenceEngine();
if (!(ie.Algorithm is VariationalMessagePassing))
{
Console.WriteLine("Probability both coins are heads: "+ie.Infer(bothHeads));
bothHeads.ObservedValue=false;
Console.WriteLine("Probability distribution over firstCoin: " + ie.Infer(firstCoin));
}
else
Console.WriteLine("This example does not run with Variational Message Passing");
}
public override void Run()
{
var prices = GetPrices("SPY").Select(t => t.Item2).ToArray();
var inputs = prices.Take(prices.Length - 1).ToArray();
var inputVectors = inputs.Select(i => Vector.FromArray(new[] { i })).ToArray();
var outputs = prices.Skip(1).ToArray();
// Set up the GP prior, which will be filled in later
var prior = Variable.New<SparseGP>().Named("prior");
// The sparse GP variable - a distribution over functions
var f = Variable<IFunction>.Random(prior).Named("f");
// The locations to evaluate the function
var x = Variable.Observed(inputVectors).Named("x");
var j = x.Range.Named("j");
var y = Variable.Observed(outputs, j).Named("y");
y[j] = Variable.GaussianFromMeanAndVariance(Variable.FunctionEvaluate(f, x[j]), 0.1);
var kf = new SquaredExponential(-0.5);
// The basis
var rand = new Random(Environment.TickCount);
var basis = Enumerable.Range(1, 10).Select(i => Vector.FromArray(new double[1] {i*10})).ToArray();
//var basis = new Vector[] {
// Vector.FromArray(new double[1] {80}),
// Vector.FromArray(new double[1] {90}),
// Vector.FromArray(new double[1] {100})
//};
var gp = new GaussianProcess(new ConstantFunction(0), kf);
prior.ObservedValue = new SparseGP(new SparseGPFixed(gp, basis));
var engine = new InferenceEngine(new ExpectationPropagation());
var sgp = engine.Infer<SparseGP>(f);
var means = sgp.Mean(inputVectors).ToArray();
var stdDevs = inputVectors.Select(iv => Math.Sqrt(sgp.Variance(iv))).ToArray();
this.Series = new[]
{
new LabelledSeries<Tuple<double,double>>(
"input",
Enumerable.Range(0,inputs.Length)
.Select(i=> Tuple.Create((double)i, inputs[i]))),
new LabelledSeries<Tuple<double,double>>(
"infered mean",
Enumerable.Range(0,inputs.Length)
.Select(i=> Tuple.Create((double)i, means[i]))),
new LabelledSeries<Tuple<double,double>>(
"infered stddev",
Enumerable.Range(0,inputs.Length)
.Select(i=> Tuple.Create((double)i, stdDevs[i]))),
};
}
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 void RunCyclingTime1()
{
//[1] The model
Variable<double> averageTime = Variable.GaussianFromMeanAndPrecision(15, 0.01);
Variable<double> trafficNoise = Variable.GammaFromShapeAndScale(2.0, 0.5);
Variable<double> travelTimeMonday = Variable.GaussianFromMeanAndPrecision(averageTime, trafficNoise);
Variable<double> travelTimeTuesday = Variable.GaussianFromMeanAndPrecision(averageTime, trafficNoise);
Variable<double> travelTimeWednesday = Variable.GaussianFromMeanAndPrecision(averageTime, trafficNoise);
//[2] Train the model
travelTimeMonday.ObservedValue = 13;
travelTimeTuesday.ObservedValue = 17;
travelTimeWednesday.ObservedValue = 16;
InferenceEngine engine = new InferenceEngine();
Gaussian averageTimePosterior = engine.Infer<Gaussian>(averageTime);
Gamma trafficNoisePosterior = engine.Infer<Gamma>(trafficNoise);
Console.WriteLine("averageTimePosterior: " + averageTimePosterior);
Console.WriteLine("trafficNoisePosterior: " + trafficNoisePosterior);
//[3] Add a prediction variable and retrain the model
Variable<double> tomorrowsTime = Variable.GaussianFromMeanAndPrecision(
averageTime,
trafficNoise);
Gaussian tomorrowsTimeDist = engine.Infer<Gaussian>(tomorrowsTime);
double tomorrowsMean = tomorrowsTimeDist.GetMean();
double tomorrowsStdDev = Math.Sqrt(tomorrowsTimeDist.GetVariance());
// Write out the results.
Console.WriteLine("Tomorrows predicted time: {0:f2} plus or minus {1:f2}", tomorrowsMean, tomorrowsStdDev);
// You can also ask other questions of the model
double probTripTakesLongerThan18Minutes = engine.Infer<Bernoulli>(tomorrowsTime < 18.0).GetProbTrue();
Console.WriteLine(
"Probability that the trip takes less than 18 min: {0:f2}",
probTripTakesLongerThan18Minutes);
}
public void Run()
{
// Sample data from standard Gaussian
double[] data = new double[100];
for (int i = 0; i < data.Length; i++) data[i] = Rand.Normal(0, 1);
// Create mean and precision random variables
Variable<double> mean = Variable.GaussianFromMeanAndVariance(0, 100).Named("mean");
Variable<double> precision = Variable.GammaFromShapeAndScale(1, 1).Named("precision");
for (int i = 0; i < data.Length; i++)
{
Variable<double> x= Variable.GaussianFromMeanAndPrecision(mean, precision).Named("x"+i);
x.ObservedValue=data[i];
}
InferenceEngine engine = new InferenceEngine();
// Retrieve the posterior distributions
Console.WriteLine("mean=" + engine.Infer(mean));
Console.WriteLine("prec=" + engine.Infer(precision));
}
public void Run()
{
for (double thresh = 0; thresh <= 1; thresh += 0.1)
{
Variable<double> x = Variable.GaussianFromMeanAndVariance(0, 1).Named("x");
Variable.ConstrainTrue(x > thresh);
InferenceEngine engine = new InferenceEngine();
if (engine.Algorithm is ExpectationPropagation)
Console.WriteLine("Dist over x given thresh of " + thresh + "=" + engine.Infer(x));
else
Console.WriteLine("This example only runs with Expectation Propagation");
}
}
public void Run()
{
// Data from clinical trial
VariableArray<bool> controlGroup =
Variable.Observed(new bool[] { false, false, true, false, false }).Named("controlGroup");
VariableArray<bool> treatedGroup =
Variable.Observed(new bool[] { true, false, true, true, true }).Named("treatedGroup");
Range i = controlGroup.Range.Named("i"); Range j = treatedGroup.Range.Named("j");
// Prior on being effective treatment
Variable<bool> isEffective = Variable.Bernoulli(0.5).Named("isEffective");
Variable<double> probIfTreated, probIfControl;
using (Variable.If(isEffective))
{
// Model if treatment is effective
probIfControl = Variable.Beta(1, 1).Named("probIfControl");
controlGroup[i] = Variable.Bernoulli(probIfControl).ForEach(i);
probIfTreated = Variable.Beta(1, 1).Named("probIfTreated");
treatedGroup[j] = Variable.Bernoulli(probIfTreated).ForEach(j);
}
using (Variable.IfNot(isEffective))
{
// Model if treatment is not effective
Variable<double> probAll = Variable.Beta(1, 1).Named("probAll");
controlGroup[i] = Variable.Bernoulli(probAll).ForEach(i);
treatedGroup[j] = Variable.Bernoulli(probAll).ForEach(j);
}
InferenceEngine ie = new InferenceEngine();
if (!(ie.Algorithm is GibbsSampling))
{
Console.WriteLine("Probability treatment has an effect = " + ie.Infer(isEffective));
Console.WriteLine("Probability of good outcome if given treatment = "
+ (float)ie.Infer<Beta>(probIfTreated).GetMean());
Console.WriteLine("Probability of good outcome if control = "
+ (float)ie.Infer<Beta>(probIfControl).GetMean());
}
else
Console.WriteLine("This model is not supported by Gibbs sampling.");
}
public override void Run()
{
var inputs = new[]
{
JoinArrays(GetColorAttributeArray(Color.Blue), GetShapeAttributeArray(Shapes.Rectangle), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Red), GetShapeAttributeArray(Shapes.Rectangle), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Blue), GetShapeAttributeArray(Shapes.Star), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Blue), GetShapeAttributeArray(Shapes.Ring), new double[] { 15 }),
JoinArrays(GetColorAttributeArray(Color.Green), GetShapeAttributeArray(Shapes.Circle), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Yellow), GetShapeAttributeArray(Shapes.Circle), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Yellow), GetShapeAttributeArray(Shapes.Circle), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Blue), GetShapeAttributeArray(Shapes.Rectangle), new double[] { 15 }),
JoinArrays(GetColorAttributeArray(Color.Yellow), GetShapeAttributeArray(Shapes.Star), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Red), GetShapeAttributeArray(Shapes.Arrow), new double[] { 10 }),
JoinArrays(GetColorAttributeArray(Color.Green), GetShapeAttributeArray(Shapes.Trapezium), new double[] { 15 }),
JoinArrays(GetColorAttributeArray(Color.Green), GetShapeAttributeArray(Shapes.Diamond), new double[] { 15 }),
JoinArrays(GetColorAttributeArray(Color.Yellow), GetShapeAttributeArray(Shapes.Triangle), new double[] { 15 }),
JoinArrays(GetColorAttributeArray(Color.Red), GetShapeAttributeArray(Shapes.Ring), new double[] { 15 }),
JoinArrays(GetColorAttributeArray(Color.Yellow), GetShapeAttributeArray(Shapes.Circle), new double[] { 15 }),
JoinArrays(GetColorAttributeArray(Color.Red), GetShapeAttributeArray(Shapes.Ellipse), new double[] { 15 }),
};
var outputs = new bool[] { true, true, true, true, true, true, true, true, false, false, false, false, false, false, false, false };
var j = new Range(inputs.Length);
var noise = Variable.GammaFromMeanAndVariance(1, 1);
var X = Variable.Observed(inputs.Select(i => Vector.FromArray(i)).ToArray(), j).Named("X");
var Y = Variable.Observed(outputs, j).Named("Y");
var weights = Variable.VectorGaussianFromMeanAndPrecision(Vector.Zero(inputs.First().Length), PositiveDefiniteMatrix.Identity(inputs.First().Length))
.Named("weights");
Y[j] = Variable.GaussianFromMeanAndPrecision(Variable.InnerProduct(X[j], weights), noise) > 0;
var engine = new InferenceEngine();
var posteriorWeightsDist = engine.Infer<VectorGaussian>(weights);
var posteriorNoiseDist = engine.Infer<Gamma>(noise);
weights = Variable.Random(posteriorWeightsDist);
var testCase = JoinArrays(GetColorAttributeArray(Color.Red), GetShapeAttributeArray(Shapes.Trapezium), new double[] { 15 });
var testClassification = engine.Infer<Bernoulli>(Variable.InnerProduct(Vector.FromArray(testCase), weights) > 0);
}
//Addition by Guy Templeton, get log evidence from learned mixing coeff.
public double GetLogEvidence()
{
Variable<bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
Range classes = new Range(numOfClasses);
IfBlock block = Variable.If(evidence);
VectorGaussian[] wObserved = trainModel.wPrior.ObservedValue;
VectorGaussian[] empty = Util.ArrayInit(numOfClasses, c => (c == 0) ?
VectorGaussian.PointMass(Vector.Zero(numOfFeatures)) :
VectorGaussian.FromMeanAndPrecision(Vector.Zero(numOfFeatures), PositiveDefiniteMatrix.Identity(numOfFeatures)));
block.CloseBlock();
InferenceEngine engine = new InferenceEngine();
return engine.Infer<Bernoulli>(evidence).LogOdds;
}
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;
}
public override void Run()
{
var sourceMean = 11.4;
var sourcePrecision = 0.01;
var source = Gaussian.FromMeanAndPrecision(sourceMean, sourcePrecision);
var series = new List<LabelledSeries<Tuple<double, double>>>();
series.Add(new LabelledSeries<Tuple<double, double>>(string.Format("Actual mean {0} precision {1}", source.GetMean(), source.Precision), Enumerable.Range(-30, 80).Select(x => Tuple.Create((double)x, Math.Exp(source.GetLogProb(x))))));
// Prior distributions
var meanPriorDistr = Gaussian.FromMeanAndPrecision(0, 0.01);
var precisionPriorDistr = Gamma.FromMeanAndVariance(2, 5);
var meanPrior = Variable.Random(meanPriorDistr).Named("mean");
var precPrior = Variable.Random(precisionPriorDistr).Named("precision");
var tv = Variable.New<int>();
var tr = new Range(tv).Named("tr");
var engine = new InferenceEngine();
var xv = Variable.GaussianFromMeanAndPrecision(meanPrior, precPrior).Named("xv");
var xs = Variable.Array<double>(tr).Named("xs");
xs[tr] = xv.ForEach(tr);
var maxSampleSize = 250;
var sampleData = Enumerable.Range(0, maxSampleSize + 1).Select(_ => source.Sample()).ToArray();
for (var i = 50; i <= maxSampleSize; i += 50)
{
tv.ObservedValue = i;
xs.ObservedValue = sampleData.Take(i).ToArray();
var meanPost = engine.Infer<Gaussian>(meanPrior);
var precPost = engine.Infer<Gamma>(precPrior);
var estimateDist = Gaussian.FromMeanAndPrecision(meanPost.GetMean(), precPost.GetMean());
series.Add(new LabelledSeries<Tuple<double, double>>(string.Format("Implied mean {0} precision {1} with {2} samples", Math.Round(estimateDist.GetMean(), 4), Math.Round(estimateDist.Precision, 4), i), Enumerable.Range(-30, 80).Select(x => Tuple.Create((double)x, Math.Exp(estimateDist.GetLogProb(x))))));
}
this.Series = series.ToArray();
}
public VectorGaussian BatchRegression(Vector[] xdata, double[] ydata)
{
int ndim = xdata[0].Count;
Range row = new Range(xdata.Length);
VariableArray <Vector> x = Variable.Observed(xdata, row).Named("x");
// Set a prior on the weights and sample from it
Variable <Vector> w = Variable.VectorGaussianFromMeanAndPrecision(Vector.Constant(ndim, 0.0), PositiveDefiniteMatrix.Identity(ndim)).Named("w");
// Multiply to determine obeservations
VariableArray <double> y = Variable.Array <double>(row);
y[row] = Variable.GaussianFromMeanAndVariance(Variable.InnerProduct(x[row], w), 1.0);
y.ObservedValue = ydata;
InferenceEngine engine = new InferenceEngine();
VectorGaussian postW = engine.Infer <VectorGaussian>(w);
return(postW);
}
public void ConstrainEqualManyToOneTest()
{
double bPrior = 0.1;
double cPrior = 0.2;
var c = Variable.Bernoulli(cPrior).Named("c");
Range i = new Range(2).Named("i");
var bools = Variable.Array <bool>(i).Named("bools");
using (Variable.ForEach(i))
{
bools[i] = Variable.Bernoulli(bPrior);
Variable.ConstrainEqual(bools[i], c);
}
bools.ObservedValue = new bool[] { true, true };
InferenceEngine engine = new InferenceEngine();
Bernoulli cActual = engine.Infer <Bernoulli>(c);
Bernoulli cExpected = new Bernoulli(1);
Console.WriteLine("c = {0} should be {1}", cActual, cExpected);
Assert.True(cExpected.MaxDiff(cActual) < 1e-10);
}
public void BinomialMarginalPrototype2()
{
Variable <int> n = Variable.New <int>().Named("n");
//Variable<int> x = Variable.Binomial(n, 0.1);
n.ObservedValue = 4;
var x = Variable.New <int>();
var b = Variable.Observed(false);
using (Variable.If(b))
{
x.SetTo(Variable.DiscreteUniform(n + 1));
}
using (Variable.IfNot(b))
{
x.SetTo(Variable.Binomial(n, 0.1));
}
InferenceEngine ie = new InferenceEngine();
Console.WriteLine(ie.Infer(x));
}
public void CaseExampleEnum()
{
Variable <Coin> c = Variable.EnumDiscrete <Coin>(new double[] { 0.5, 0.5 });
Variable <double> x = Variable.New <double>();
Variable <int> cint = Variable.EnumToInt(c);
using (Variable.Case(cint, 0))
{
x.SetTo(Variable.GaussianFromMeanAndVariance(1, 1));
}
using (Variable.Case(cint, 1))
{
x.SetTo(Variable.GaussianFromMeanAndVariance(2, 1));
}
InferenceEngine engine = new InferenceEngine();
Gaussian expected = new Gaussian(1.5, 1.25);
Gaussian actual = engine.Infer <Gaussian>(x);
Console.WriteLine("x = {0} (should be {1})", actual, expected);
Assert.True(expected.MaxDiff(actual) < 1e-10);
}
static void Main(string[] args)
{
// the winner and loser in each of 6 games
var winnerData = new[] { 0, 0, 0, 1, 3, 4 };
var loserData = new[] { 1, 3, 4, 2, 1, 2 };
// Define the statistical model as a probabilistic program
var game = new Range(winnerData.Length);
var player = new Range(winnerData.Concat(loserData).Max() + 1);
var playerSkills = Variable.Array <double>(player);
playerSkills[player] = Variable.GaussianFromMeanAndVariance(6, 9).ForEach(player);
var winners = Variable.Array <int>(game);
var losers = Variable.Array <int>(game);
using (Variable.ForEach(game))
{
// the player performance is noisy version of their skill
var winnerPerformance = Variable.GaussianFromMeanAndVariance(playerSkills[winners[game]], 1.0);
var loserPerformance = Variable.GaussianFromMeanAndVariance(playerSkills[losers[game]], 1.0);
// The winner performed better in this game
Variable.ConstrainTrue(winnerPerformance > loserPerformance);
}
// attach data to model
winners.ObservedValue = winnerData;
losers.ObservedValue = loserData;
// runing inference
var inferenceEngine = new InferenceEngine();
var inferredSkills = inferenceEngine.Infer <Gaussian[]>(playerSkills);
// the inferred skills are uncertain, which is captured in their variance
var orderedPlayerSkills = inferredSkills
.Select((s, i) => new { Player = i, Skill = s })
.OrderByDescending(ps => ps.Skill.GetMean());
foreach (var playerSkill in orderedPlayerSkills)
{
Console.WriteLine($"Player {playerSkill.Player} skill: {playerSkill.Skill}");
}
}
public void TruncatedGaussianEntersGate2()
{
var x = Variable.GaussianFromMeanAndPrecision(0, 1).Named("x");
var xCopy = Variable.Copy(x);
xCopy.AddAttribute(new MarginalPrototype(new TruncatedGaussian()));
var l = Variable.Bernoulli(0.9).Named("l");
using (Variable.If(l))
{
var True = Variable.IsPositive(xCopy).Named("VarTrue");
True.ObservedValue = true;
}
using (Variable.IfNot(l))
{
var False = Variable.IsPositive(xCopy).Named("VarFalse");
False.ObservedValue = false;
}
var ie = new InferenceEngine(new VariationalMessagePassing());
Console.WriteLine(ie.Infer(x));
}
public static void Run()
{
var questionVsSkills = LoadQuestionsVsSkills();
var questiosVsUsers = LoadQuestionsVsUsers();
var indexes = GetIndexes(questionVsSkills);
var skills = new Range(7);
var skillsVars = Variable.Array <bool>(skills).Named("skillsVars");
skillsVars[skills] = Variable.Bernoulli(0.5).ForEach(skills);
var questions = new Range(48);
var correctAnswers = Variable.Array <bool>(questions);
var indices = ConvertIndexes(indexes, questions);
using (Variable.ForEach(questions))
{
var results = Variable.Subarray <bool>(skillsVars, indices[questions]);
var hasAllRelevantSkills = Variable.AllTrue(results);
using (Variable.If(hasAllRelevantSkills))
correctAnswers[questions].SetTo(Variable.Bernoulli(0.9));
using (Variable.IfNot(hasAllRelevantSkills))
correctAnswers[questions].SetTo(Variable.Bernoulli(Variable.Beta(3, 7)));
}
var engine = new InferenceEngine();
engine.ShowProgress = false;
foreach (var userAnswers in questiosVsUsers)
{
correctAnswers.ObservedValue = userAnswers;
dynamic result = engine.Infer(skillsVars);
foreach (var item in result)
{
Console.Write(item.ToString().Substring(9));
}
Console.WriteLine();
}
}
public void RunToConvergence(double tolerance = 1e-4)
{
engine.Compiler.ReturnCopies = true;
//engine.ShowProgress = true;
Diffable oldPost = null;
for (int i = 1; i < 1000; i++)
{
engine.NumberOfIterations = i;
Diffable newPost = engine.Infer <Diffable>(difficulty);
if (oldPost != null)
{
double activity = newPost.MaxDiff(oldPost);
//Console.WriteLine(activity);
if (activity < tolerance)
{
break;
}
}
oldPost = newPost;
}
}
public void MP_Switch()
{
var T_val_range = new Range(2);
Range T_cat_range = new Range(2);
var T_cat_val_p = Variable.Array <Vector>(T_cat_range).Named("T_cat_val_p");
using (Variable.ForEach(T_cat_range))
{
T_cat_val_p[T_cat_range] = Variable.DirichletUniform(T_val_range);
}
var v3 = Variable.DiscreteUniform(T_cat_range);
var v1 = Variable.New <Vector>();
using (Variable.Switch(v3))
{
v1.SetTo(Variable.Copy(T_cat_val_p[v3]));
}
InferenceEngine engine = new InferenceEngine();
Console.WriteLine(engine.Infer(v1));
}
private static void Experiment_1()
{
// PM erstellen
Variable <bool> ersteMünzeWurf = Variable.Bernoulli(0.5);
Variable <bool> zweiteMünzeWurf = Variable.Bernoulli(0.5);
Variable <bool> beideMünzenWurf = ersteMünzeWurf & zweiteMünzeWurf;
// Inferenz-Engine (IE) erstellen
InferenceEngine engine = new InferenceEngine();
#if SHOW_MODEL
engine.ShowFactorGraph = true; // PM visualisieren
#endif
// Inferenz ausführen
Bernoulli ergebnis = engine.Infer <Bernoulli>(beideMünzenWurf);
double beideMünzenZeigenKöpfe = ergebnis.GetProbTrue();
Console.WriteLine("Die Wahrscheinlichkeit - beide Münzen " +
"zeigen Köpfe: {0}", beideMünzenZeigenKöpfe);
}
public void ConstrainEqualCycleTest()
{
double xPrior = 0.1;
double yPrior = 0.2;
double zPrior = 0.3;
double wPrior = 0.4;
var x = Variable.Bernoulli(xPrior).Named("x");
var y = Variable.Bernoulli(yPrior).Named("y");
var z = Variable.Bernoulli(zPrior).Named("z");
var w = Variable.Bernoulli(wPrior).Named("w");
Variable.ConstrainEqual(x, y);
Variable.ConstrainEqual(y, z);
Variable.ConstrainEqual(x, z);
Variable.ConstrainEqual(z, w);
w.ObservedValue = true;
InferenceEngine engine = new InferenceEngine();
Bernoulli xActual = engine.Infer <Bernoulli>(x);
Bernoulli xExpected = new Bernoulli(1);
Console.WriteLine("x = {0} should be {1}", xActual, xExpected);
}
internal void LogisticIrtProductExpTest()
{
int numStudents = 20;
Range student = new Range(numStudents).Named("students");
var ability = Variable.Array <double>(student).Named("ability");
ability[student] = Variable.GaussianFromMeanAndPrecision(0, 1e-6).ForEach(student);
int numQuestions = 4;
Range question = new Range(numQuestions).Named("questions");
var difficulty = Variable.Array <double>(question).Named("difficulty");
difficulty[question] = Variable.GaussianFromMeanAndPrecision(0, 1e-6).ForEach(question);
var logDisc = Variable.Array <double>(question).Named("logDisc");
logDisc[question] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(question);
var response = Variable.Array <bool>(student, question).Named("response");
var minus = Variable.Array <double>(student, question).Named("minus");
minus[student, question] = (ability[student] - difficulty[question]);
var product = Variable.Array <double>(student, question).Named("product");
product[student, question] = Variable.ProductExp(minus[student, question], logDisc[question]);
response[student, question] = Variable.BernoulliFromLogOdds(product[student, question]);
bool[,] data = new bool[numStudents, numQuestions];
for (int i = 0; i < numStudents; i++)
{
for (int j = 0; j < numQuestions; j++)
{
data[i, j] = (i > j);
}
}
response.ObservedValue = data;
InferenceEngine engine = new InferenceEngine();
engine.ShowFactorGraph = true;
engine.Algorithm = new VariationalMessagePassing();
Console.WriteLine(engine.Infer(logDisc));
}
public void ConstantPropagationTest2()
{
var a = Variable.Bernoulli(0.5).Named("a");
var b = Variable.Bernoulli(0.5).Named("b");
var c = Variable.Bernoulli(0.5).Named("c");
var d = Variable.Bernoulli(0.5).Named("d");
using (Variable.If(c))
{
Variable.ConstrainTrue(d);
}
Variable.ConstrainEqual(b, c);
using (Variable.IfNot(a))
{
Variable.ConstrainTrue(b);
}
Variable.ConstrainTrue(a);
InferenceEngine engine = new InferenceEngine();
Bernoulli dActual = engine.Infer <Bernoulli>(d);
Bernoulli dExpected = new Bernoulli(2.0 / 3);
Assert.Equal(dActual, dExpected);
}
private static void Experiment_3()
{
// Wahrscheinlichkeit von 6 Würfelaugen ist 1 zu 6 = 1/6 ca 0,17
double erfolgWurfel = 0.17;
// PM erstellen
Variable <bool> ersterWürfelWurf = Variable.Bernoulli(erfolgWurfel);
Variable <bool> zweiterWürfelWurf = Variable.Bernoulli(erfolgWurfel);
Variable <bool> dritterWürfelWurf = Variable.Bernoulli(erfolgWurfel);
Variable <bool> alleWürfelWurf = ersterWürfelWurf & zweiterWürfelWurf & dritterWürfelWurf;
// Inferenz-Engine (IE) erstellen
InferenceEngine engine = new InferenceEngine();
#if SHOW_MODEL
engine.ShowFactorGraph = true; // PM visualisieren
#endif
// Inferenz ausführen - alle Würfel zeigen 6 Augen
Bernoulli ergebnis1 = engine.Infer <Bernoulli>(alleWürfelWurf);
double alleWürfelZeigenSechs = ergebnis1.GetProbTrue();
Console.WriteLine("Die Wahrscheinlichkeit, dass alle Würfel \"6\" zeigen, ist: {0}", alleWürfelZeigenSechs);
}
public void BernoulliFromLogOddsUnivariate()
{
Rand.Restart(12347);
Variable<double> x = Variable.GaussianFromMeanAndVariance(0, 1).Named("x");
Variable<bool> s = Variable.BernoulliFromLogOdds(x).Named("s");
s.ObservedValue = true;
InferenceEngine ie = new InferenceEngine(new VariationalMessagePassing());
ie.Compiler.GivePriorityTo(typeof (LogisticOp));
ie.Compiler.GivePriorityTo(typeof (BernoulliFromLogOddsOp));
Gaussian xActual = ie.Infer<Gaussian>(x);
Console.WriteLine("x = {0}", xActual);
double m, v;
xActual.GetMeanAndVariance(out m, out v);
double matlabM = 0.413126805979683;
double matlabV = 0.828868291887001;
Gaussian xExpected = new Gaussian(matlabM, matlabV);
double relErr = System.Math.Abs((m - matlabM)/ matlabM);
Console.WriteLine("Posterior mean is {0} should be {1} (relErr = {2})", m, matlabM, relErr);
Assert.True(relErr < 1e-6);
relErr = System.Math.Abs((v - matlabV)/ matlabV);
Console.WriteLine("Posterior variance is {0} should be {1} (relErr = {2})", v, matlabV, relErr);
Assert.True(relErr < 1e-6);
}
public void SimpleGatedModelTest1()
{
const double SelectorProbabilityTrue = 0.3;
Variable <string> str = Variable.New <string>().Named("str");
Variable <bool> selector = Variable.Bernoulli(SelectorProbabilityTrue).Named("selector");
using (Variable.If(selector))
{
str.SetTo("a");
}
using (Variable.IfNot(selector))
{
str.SetTo("b");
}
var engine = new InferenceEngine();
var strPosterior = engine.Infer <StringDistribution>(str);
StringInferenceTestUtilities.TestProbability(strPosterior, SelectorProbabilityTrue, "a");
StringInferenceTestUtilities.TestProbability(strPosterior, 1 - SelectorProbabilityTrue, "b");
}
public void SemanticWebTest2()
{
var prop0Dist = StringDistribution.OneOf("Anthony Blair", "Tony Blair");
var prop1Dist = StringDistribution.OneOf("6 May 1953", "May 6, 1953");
var prop0 = Variable.Random(prop0Dist);
var prop1 = Variable.Random(prop1Dist);
var template = Variable.Random(StringDistribution.Any());
var text = Variable.StringFormat(template, prop0, prop1);
var engine = new InferenceEngine();
engine.Compiler.RecommendedQuality = QualityBand.Experimental;
engine.NumberOfIterations = 1;
var textDist = engine.Infer <StringDistribution>(text);
Console.WriteLine("textDist={0}", textDist);
Assert.False(double.IsNegativeInfinity(textDist.GetLogProb("6 May 1953 is the date of birth of Tony Blair.")));
Assert.False(double.IsNegativeInfinity(textDist.GetLogProb("6 May 1953 is the date of birth of Anthony Blair.")));
Assert.False(double.IsNegativeInfinity(textDist.GetLogProb("Mr. Tony Blair was born on May 6, 1953.")));
}
public static void TruncatedGaussian(double mean, double variance)
{
//Conditional Random Variable
Variable <double> threshold = Variable.New <double>().Named("threshold");
Variable <double> x = Variable.GaussianFromMeanAndVariance(0, 1).Named("x");
Variable.ConstrainTrue(x > threshold);
InferenceEngine engine = new InferenceEngine();
if (engine.Algorithm is ExpectationPropagation)
{
for (double thresh = 0; thresh <= 1; thresh += 0.1)
{
threshold.ObservedValue = thresh;
//moment-matched Gaussian distribution.
Console.WriteLine($"Dist over x given thresh of {thresh}= {engine.Infer(x)}");
}
}
else
{
Console.WriteLine("This example only runs with Expectation Propagation");
}
}
public void SimpleGatedModelTest2()
{
const double SelectorProbabilityTrue = 0.3;
Variable <string> str = Variable.Random(StringDistribution.OneOf("a", "b", "c")).Named("str");
Variable <bool> selector = Variable.Bernoulli(SelectorProbabilityTrue).Named("selector");
using (Variable.If(selector))
{
Variable.ConstrainEqual(str, "a");
}
using (Variable.IfNot(selector))
{
Variable.ConstrainEqual(str, "b");
}
var engine = new InferenceEngine();
var strPosterior = engine.Infer <StringDistribution>(str);
StringInferenceTestUtilities.TestProbability(strPosterior, SelectorProbabilityTrue, "a");
StringInferenceTestUtilities.TestProbability(strPosterior, 1 - SelectorProbabilityTrue, "b");
}
public void ConstrainEqualGateExitTest4()
{
double bPrior = 0.1;
var b = Variable.Bernoulli(bPrior).Named("b");
var x = Variable.New <bool>().Named("x");
using (Variable.If(b))
{
x.SetTo(Variable.Bernoulli(0.2));
}
using (Variable.IfNot(b))
{
x.SetTo(Variable.Bernoulli(0.3));
}
Variable.ConstrainEqual(x, true);
InferenceEngine engine = new InferenceEngine();
Bernoulli xActual = engine.Infer <Bernoulli>(x);
double evExpected = bPrior * 0.2 + (1 - bPrior);
Bernoulli xExpected = new Bernoulli(1);
Console.WriteLine("x = {0} should be {1}", xActual, xExpected);
Assert.True(xExpected.MaxDiff(xActual) < 1e-10);
}
static void Main(string[] args)
{
Variable <double> X = Variable.GaussianFromMeanAndVariance(12.5, 5 * 5);
Variable <double> Y = Variable.GaussianFromMeanAndVariance(15, 5 * 5);
Variable <bool> Ywins = (Y > X);
//Ywins.ObservedValue = true;
var engine = new InferenceEngine();
engine.Algorithm = new ExpectationPropagation();
//Gaussian XperfPosterior = engine.Infer<Gaussian>(X);
//Gaussian YperfPosterior = engine.Infer<Gaussian>(Y);
var YwinsPosterior = engine.Infer <Bernoulli>(Ywins);
//Console.WriteLine(Xperf);
//Console.WriteLine(Yperf);
Console.WriteLine(YwinsPosterior);
}
static void Main(string[] args)
{
var winnerData = new [] { 0, 0, 0, 1, 3, 4 };
var loserData = new [] { 1, 3, 4, 2, 1, 2 };
var game = new Range(winnerData.Length);
var player = new Range(winnerData.Concat(loserData).Max() + 1);
var playerSkills = Variable.Array <double>(player);
playerSkills[player] = Variable.GaussianFromMeanAndVariance(6, 9).ForEach(player);
var winners = Variable.Array <int>(game);
var losers = Variable.Array <int>(game);
using (Variable.ForEach(game))
{
var winnerPerformance = Variable.GaussianFromMeanAndVariance(playerSkills[winners[game]], 1.0);
var loserPerformance = Variable.GaussianFromMeanAndVariance(playerSkills[losers[game]], 1.0);
Variable.ConstrainTrue(winnerPerformance > loserPerformance);
}
winners.ObservedValue = winnerData;
losers.ObservedValue = loserData;
var inferenceEngine = new InferenceEngine();
var inferredSkills = inferenceEngine.Infer <Gaussian[]>(playerSkills);
var orderedPlayerSkills = inferredSkills
.Select((x, i) => new { Player = i, Skill = x })
.OrderByDescending(x => x.Skill.GetMean());
foreach (var playerSkill in orderedPlayerSkills)
{
Console.WriteLine($"Player {playerSkill.Player} skill: {playerSkill.Skill}");
}
}
public static void Test()
{
var inputs = Enumerable.Range(0, 50).Select(i => Vector.Constant(1, i)).ToArray();
var data = inputs.Select(j => Math.Cos(2 * j[0] / 10.0)).ToArray();
var n = new Range(data.Length);
//var kf = new SummationKernel(new ARD(new double[]{ 0 }, 0))+new WhiteNoise();
var kf = new SummationKernel(new SquaredExponential()) + new WhiteNoise();
var y = Variable <Vector> .Factor <double, Vector[], int[], KernelFunction>(MyFactors.GP, 1.0 /*Variable.GammaFromShapeAndRate(1,1)*/, inputs, new int[] { 0, 1 },
kf);
GPFactor.settings = new Settings
{
solverMethod = Settings.SolverMethod.GradientDescent,
};
y.AddAttribute(new MarginalPrototype(new VectorGaussian(n.SizeAsInt)));
var y2 = Variable.ArrayFromVector(y, n);
y2.ObservedValue = data;
var ypredictive = Variable.ArrayFromVector(y, n);
var ie = new InferenceEngine(new VariationalMessagePassing());
var post = ie.Infer <Gaussian[]>(ypredictive);
var mplWrapper = new MatplotlibWrapper();
mplWrapper.AddArray("x", inputs.Select(j => j[0]).ToArray());
mplWrapper.AddArray("y", data);
var f = post.Select(i => i.GetMean()).ToArray();
var e = post.Select(i => Math.Sqrt(i.GetVariance())).ToArray();
mplWrapper.AddArray("f", f);
mplWrapper.AddArray("e", e);
mplWrapper.Plot(new string[] {
"fill_between(x,f-e,f+e,color=\"gray\")",
"scatter(x,y)"
});
}
public void ConstrainEqualCaseArrayTest()
{
Range i = new Range(4).Named("i");
VariableArray <double> x = Variable.Array <double>(i).Named("x");
VariableArray <int> c = Variable.Array <int>(i).Named("c");
using (Variable.ForEach(i))
{
c[i] = Variable.Discrete(new double[] { 0.5, 0.5 });
using (Variable.Case(c[i], 0))
{
x[i] = Variable.GaussianFromMeanAndVariance(1, 1);
}
using (Variable.Case(c[i], 1))
{
x[i] = Variable.GaussianFromMeanAndVariance(2, 1);
}
}
VariableArray <double> data = Variable.Observed(new double[] { 0.9, 1.1, 1.9, 2.1 }, i).Named("data");
Variable.ConstrainEqual(x[i], data[i]);
InferenceEngine engine = new InferenceEngine(new VariationalMessagePassing());
Discrete[] cExpectedArray = new Discrete[]
{
new Discrete(0.6457, 0.3543),
new Discrete(0.5987, 0.4013), new Discrete(0.4013, 0.5987),
new Discrete(0.3543, 0.6457)
};
IDistribution <int[]> cExpected = Distribution <int> .Array(cExpectedArray);
object cActual = engine.Infer(c);
Console.WriteLine(StringUtil.JoinColumns("c = ", cActual, " should be ", cExpected));
Assert.True(cExpected.MaxDiff(cActual) < 1e-4);
}
public void GatedModelObservedOutputTest2()
{
Variable <bool> selector = Variable.Bernoulli(0.5);
Variable <string> substr = Variable.New <string>();
using (Variable.If(selector))
{
Variable <string> str = Variable.Random(StringDistribution.OneOf("dbc", "abcd", "abcc"));
substr.SetTo(Variable.Substring(str, 1, 2));
}
using (Variable.IfNot(selector))
{
Variable <string> str = Variable.StringLower();
substr.SetTo(Variable.Substring(str, 0, 2));
}
substr.ObservedValue = "bc";
var engine = new InferenceEngine();
var selectorPosterior = engine.Infer <Bernoulli>(selector);
Assert.Equal(1.0 / (1.0 + (1.0 / (26 * 26))), selectorPosterior.GetProbTrue(), LogProbEps);
}
public void ImpossibleBranchTest2()
{
Variable <string> subStr = Variable.New <string>().Named("subStr");
Variable <int> selector = Variable.DiscreteUniform(2).Named("selector");
using (Variable.Case(selector, 0))
{
var str = Variable.StringUniform();
subStr.SetTo(Variable.Substring(str, 2, 2));
}
using (Variable.Case(selector, 1))
{
var str = Variable.StringUniform();
subStr.SetTo(Variable.Substring(str, 2, 3));
}
subStr.ObservedValue = "ab";
var engine = new InferenceEngine();
var selectorPosterior = engine.Infer <Discrete>(selector);
Assert.Equal(1.0, selectorPosterior[0]);
}
public void GatedModelUncertainOutputTest()
{
Variable <bool> selector = Variable.Bernoulli(0.5);
Variable <string> substr = Variable.New <string>();
using (Variable.If(selector))
{
Variable <string> str = Variable.Random(StringDistribution.OneOf("bcad", "bacd", "bca"));
substr.SetTo(Variable.Substring(str, 0, 2));
}
using (Variable.IfNot(selector))
{
Variable <string> str = Variable.Random(StringDistribution.OneOf("dbc", "abdd", "a"));
substr.SetTo(Variable.Substring(str, 1, 2));
}
Variable.ConstrainEqualRandom(substr, StringDistribution.OneOf("bc", "ba"));
var engine = new InferenceEngine();
var selectorPosterior = engine.Infer <Bernoulli>(selector);
Assert.Equal(2.0 / 3.0, selectorPosterior.GetProbTrue(), LogProbEps);
}
//Testing online learning :)
// [Fact]
internal void OnlineGaussian()
{
// make ddata
double psi;
int T = 1;
double[] data = CreateData("Parabola", T, out psi);
Console.WriteLine("psi = {0}", psi);
for (int i = 0; i < T; i++)
{
Console.Write(" " + data[i]);
}
Console.WriteLine();
InferenceEngine ie = new InferenceEngine();
ie.ShowFactorGraph = true;
Variable <double> m;
Variable <Gaussian> mprior = Variable.Observed(new Gaussian(data[0], 10 + psi));
// m = Variable.GaussianFromMeanAndVariance(Variable.Random<double, Gaussian>(mprior), psi).Named("m");
m = Variable.Random <double, Gaussian>(mprior).Named("m");
Variable <Gaussian> xObsDist = Variable.Observed(new Gaussian(data[0], 1));
Variable.ConstrainEqualRandom <double, Gaussian>(m, xObsDist);
for (int t = 0; t < T; t++)
{
xObsDist.ObservedValue = new Gaussian(data[t], 1);
Gaussian mpost = ie.Infer <Gaussian>(m);
double mpost_mean, mpost_var;
mpost.GetMeanAndVariance(out mpost_mean, out mpost_var);
mprior.ObservedValue = new Gaussian(mpost_mean, mpost_var + psi);
// mprior.Value = ie.Infer<Gaussian>(m);
Console.WriteLine(mpost);
}
}
public void LocalArrayMarginalPrototypeTest()
{
var TA_size = Variable.New <int>().Named("TA_size");
var TA_range = new Range(TA_size).Named("TA_range");
var TB_size = Variable.New <int>().Named("TB_size");
var TB_range = new Range(TB_size).Named("TB_range");
var TB_B = Variable.Array <int>(TB_range).Named("TB_B");
TB_B.SetValueRange(TA_range);
using (Variable.ForEach(TB_range))
{
var TA_range_clone = TA_range.Clone();
var array = Variable.Array <double>(TA_range_clone).Named("array");
using (Variable.ForEach(TA_range_clone))
{
array[TA_range_clone].SetTo(Variable.Constant(1.0));
}
var vector = Variable.Vector(array).Named("vector");
TB_B[TB_range].SetTo(Variable.Discrete(TA_range, vector));
}
var indices = Variable.Array <int>(new Range(2).Named("indices_range")).Named("indices");
indices.ObservedValue = new int[] { 0, 1 };
var TB_B_Subarray = Variable.Subarray(TB_B, indices).Named("TB_B_Subarray");
TB_B_Subarray.ObservedValue = new int[] { 0, 1 };
TA_size.ObservedValue = 3;
TB_size.ObservedValue = 3;
InferenceEngine engine = new InferenceEngine();
engine.OptimiseForVariables = new IVariable[] { TB_B };
Console.WriteLine("Z=" + engine.Infer(TB_B));
}
/// <summary>
/// Infers the posteriors of BCC using the attached data and priors.
/// </summary>
/// <param name="taskIndices">The matrix of the task indices (columns) of each worker (rows).</param>
/// <param name="workerLabels">The matrix of the labels (columns) of each worker (rows).</param>
/// <param name="priors">The priors of the BCC parameters.</param>
/// <returns></returns>
public virtual BCCPosteriors Infer(int[][] taskIndices, int[][] workerLabels, BCCPosteriors priors)
{
int workerCount = workerLabels.Length;
SetPriors(workerCount, priors);
AttachData(taskIndices, workerLabels, null);
var result = new BCCPosteriors();
Engine.NumberOfIterations = NumberOfIterations;
result.Evidence = Engine.Infer <Bernoulli>(Evidence);
result.BackgroundLabelProb = Engine.Infer <Dirichlet>(BackgroundLabelProb);
result.WorkerConfusionMatrix = Engine.Infer <Dirichlet[][]>(WorkerConfusionMatrix);
result.TrueLabel = Engine.Infer <Discrete[]>(TrueLabel);
result.TrueLabelConstraint = Engine.Infer <Discrete[]>(TrueLabel, QueryTypes.MarginalDividedByPrior);
// Prediction mode is indicated by none of the workers having a label.
// We can just look at the first one
if (workerLabels[0] == null)
{
result.WorkerPrediction = Engine.Infer <Discrete[][]>(WorkerLabel);
}
return(result);
}
public void Run()
{
InferenceEngine engine = new InferenceEngine();
if (!(engine.Algorithm is ExpectationPropagation))
{
Console.WriteLine("This example only runs with Expectation Propagation");
return;
}
Rand.Restart(0);
int nQuestions = 100;
int nSubjects = 40;
int nChoices = 4;
Gaussian abilityPrior = new Gaussian(0, 1);
Gaussian difficultyPrior = new Gaussian(0, 1);
Gamma discriminationPrior = Gamma.FromShapeAndScale(5, 1);
double[] trueAbility, trueDifficulty, trueDiscrimination;
int[] trueTrueAnswer;
int[][] data = Sample(nSubjects, nQuestions, nChoices, abilityPrior, difficultyPrior, discriminationPrior,
out trueAbility, out trueDifficulty, out trueDiscrimination, out trueTrueAnswer);
Range question = new Range(nQuestions).Named("question");
Range subject = new Range(nSubjects).Named("subject");
Range choice = new Range(nChoices).Named("choice");
var response = Variable.Array(Variable.Array<int>(question), subject).Named("response");
response.ObservedValue = data;
var ability = Variable.Array<double>(subject).Named("ability");
ability[subject] = Variable.Random(abilityPrior).ForEach(subject);
var difficulty = Variable.Array<double>(question).Named("difficulty");
difficulty[question] = Variable.Random(difficultyPrior).ForEach(question);
var discrimination = Variable.Array<double>(question).Named("discrimination");
discrimination[question] = Variable.Random(discriminationPrior).ForEach(question);
var trueAnswer = Variable.Array<int>(question).Named("trueAnswer");
trueAnswer[question] = Variable.DiscreteUniform(nChoices).ForEach(question);
using (Variable.ForEach(subject)) {
using (Variable.ForEach(question)) {
var advantage = (ability[subject] - difficulty[question]).Named("advantage");
var advantageNoisy = Variable.GaussianFromMeanAndPrecision(advantage, discrimination[question]).Named("advantageNoisy");
var correct = (advantageNoisy > 0).Named("correct");
using (Variable.If(correct))
response[subject][question] = trueAnswer[question];
using (Variable.IfNot(correct))
response[subject][question] = Variable.DiscreteUniform(nChoices);
}
}
engine.NumberOfIterations = 5;
subject.AddAttribute(new Sequential()); // needed to get stable convergence
engine.Compiler.UseSerialSchedules = true;
if (false) {
// set this to do majority voting
ability.ObservedValue = Util.ArrayInit(nSubjects, i => 0.0);
difficulty.ObservedValue = Util.ArrayInit(nQuestions, i => 0.0);
discrimination.ObservedValue = Util.ArrayInit(nQuestions, i => 1.0);
}
var trueAnswerPosterior = engine.Infer<IList<Discrete>>(trueAnswer);
int numCorrect = 0;
for (int q = 0; q < nQuestions; q++) {
int bestGuess = trueAnswerPosterior[q].GetMode();
if (bestGuess == trueTrueAnswer[q]) numCorrect++;
}
double pctCorrect = 100.0*numCorrect/nQuestions;
Console.WriteLine("{0}% TrueAnswers correct", pctCorrect.ToString("f0"));
var difficultyPosterior = engine.Infer<IList<Gaussian>>(difficulty);
for (int q = 0; q < Math.Min(nQuestions, 4); q++) {
Console.WriteLine("difficulty[{0}] = {1} (sampled from {2})", q, difficultyPosterior[q], trueDifficulty[q].ToString("g2"));
}
var discriminationPosterior = engine.Infer<IList<Gamma>>(discrimination);
for (int q = 0; q < Math.Min(nQuestions, 4); q++) {
Console.WriteLine("discrimination[{0}] = {1} (sampled from {2})", q, discriminationPosterior[q], trueDiscrimination[q].ToString("g2"));
}
var abilityPosterior = engine.Infer<IList<Gaussian>>(ability);
for (int s = 0; s < Math.Min(nSubjects, 4); s++) {
Console.WriteLine("ability[{0}] = {1} (sampled from {2})", s, abilityPosterior[s], trueAbility[s].ToString("g2"));
}
}
public LabelArray CompleteMasks(bool[][,] shapeMasks, bool[][,] availableMaskPixels)
{
Debug.Assert(this.initialized);
Debug.Assert(!this.working);
Debug.Assert(shapeMasks.Length == availableMaskPixels.Length);
Debug.Assert(shapeMasks.All(mask => mask.GetLength(0) == this.gridWidth.ObservedValue && mask.GetLength(1) == this.gridHeight.ObservedValue));
Debug.Assert(availableMaskPixels.All(mask => mask.GetLength(0) == this.gridWidth.ObservedValue && mask.GetLength(1) == this.gridHeight.ObservedValue));
this.working = true;
this.observationCount.ObservedValue = shapeMasks.Length;
this.InitializePerObservation();
for (int i = 0; i < shapeMasks.Length; ++i)
{
for (int x = 0; x < this.gridWidth.ObservedValue; ++x)
{
for (int y = 0; y < this.gridHeight.ObservedValue; ++y)
{
if (availableMaskPixels[i][x, y])
{
this.noisyLabelsConstraint.ObservedValue[i][x, y] = Bernoulli.PointMass(shapeMasks[i][x, y]);
}
}
}
}
var engine = new InferenceEngine();
engine.Compiler.RequiredQuality = QualityBand.Unknown;
engine.Compiler.RecommendedQuality = QualityBand.Unknown;
//engine.Compiler.UseParallelForLoops = true;
engine.OptimiseForVariables = new IVariable[]
{
this.labels,
};
for (int iteration = this.IterationsBetweenCallbacks; iteration <= this.MaskCompletionIterationCount; iteration += this.IterationsBetweenCallbacks)
{
engine.NumberOfIterations = iteration;
LabelArray completedLabels = engine.Infer<LabelArray>(this.labels);
if (this.MaskCompletionProgress != null)
{
this.MaskCompletionProgress(this, new MaskCompletionProgressEventArgs(iteration, completedLabels));
}
}
engine.NumberOfIterations = this.MaskCompletionIterationCount;
var result = engine.Infer<LabelArray>(this.labels);
this.working = false;
return result;
}
public void Run()
{
// This example requires EP
InferenceEngine engine = new InferenceEngine();
if (!(engine.Algorithm is ExpectationPropagation)) {
Console.WriteLine("This example only runs with Expectation Propagation");
return;
}
// Define counts
int numUsers = 50;
int numItems = 10;
int numTraits = 2;
Variable<int> numObservations = Variable.Observed(100).Named("numObservations");
int numLevels = 2;
// Define ranges
Range user = new Range(numUsers).Named("user");
Range item = new Range(numItems).Named("item");
Range trait = new Range(numTraits).Named("trait");
Range observation = new Range(numObservations).Named("observation");
Range level = new Range(numLevels).Named("level");
// Define latent variables
var userTraits = Variable.Array(Variable.Array<double>(trait), user).Named("userTraits");
var itemTraits = Variable.Array(Variable.Array<double>(trait), item).Named("itemTraits");
var userBias = Variable.Array<double>(user).Named("userBias");
var itemBias = Variable.Array<double>(item).Named("itemBias");
var userThresholds = Variable.Array(Variable.Array<double>(level), user).Named("userThresholds");
// Define priors
var userTraitsPrior = Variable.Array(Variable.Array<Gaussian>(trait), user).Named("userTraitsPrior");
var itemTraitsPrior = Variable.Array(Variable.Array<Gaussian>(trait), item).Named("itemTraitsPrior");
var userBiasPrior = Variable.Array<Gaussian>(user).Named("userBiasPrior");
var itemBiasPrior = Variable.Array<Gaussian>(item).Named("itemBiasPrior");
var userThresholdsPrior = Variable.Array(Variable.Array<Gaussian>(level), user).Named("userThresholdsPrior");
// Define latent variables statistically
userTraits[user][trait] = Variable<double>.Random(userTraitsPrior[user][trait]);
itemTraits[item][trait] = Variable<double>.Random(itemTraitsPrior[item][trait]);
userBias[user] = Variable<double>.Random(userBiasPrior[user]);
itemBias[item] = Variable<double>.Random(itemBiasPrior[item]);
userThresholds[user][level] = Variable<double>.Random(userThresholdsPrior[user][level]);
// Initialise priors
Gaussian traitPrior = Gaussian.FromMeanAndVariance(0.0, 1.0);
Gaussian biasPrior = Gaussian.FromMeanAndVariance(0.0, 1.0);
userTraitsPrior.ObservedValue = Util.ArrayInit(numUsers, u => Util.ArrayInit(numTraits, t => traitPrior));
itemTraitsPrior.ObservedValue = Util.ArrayInit(numItems, i => Util.ArrayInit(numTraits, t => traitPrior));
userBiasPrior.ObservedValue = Util.ArrayInit(numUsers, u => biasPrior);
itemBiasPrior.ObservedValue = Util.ArrayInit(numItems, i => biasPrior);
userThresholdsPrior.ObservedValue = Util.ArrayInit(numUsers, u =>
Util.ArrayInit(numLevels, l => Gaussian.FromMeanAndVariance(l - numLevels / 2.0 + 0.5, 1.0)));
// Break symmetry and remove ambiguity in the traits
for (int i = 0; i < numTraits; i++) {
// Assume that numTraits < numItems
for (int j = 0; j < numTraits; j++) {
itemTraitsPrior.ObservedValue[i][j] = Gaussian.PointMass(0);
}
itemTraitsPrior.ObservedValue[i][i] = Gaussian.PointMass(1);
}
// Declare training data variables
var userData = Variable.Array<int>(observation).Named("userData");
var itemData = Variable.Array<int>(observation).Named("itemData");
var ratingData = Variable.Array(Variable.Array<bool>(level), observation).Named("ratingData");
// Set model noises explicitly
Variable<double> affinityNoiseVariance = Variable.Observed(0.1).Named("affinityNoiseVariance");
Variable<double> thresholdsNoiseVariance = Variable.Observed(0.1).Named("thresholdsNoiseVariance");
// Model
using (Variable.ForEach(observation)) {
VariableArray<double> products = Variable.Array<double>(trait).Named("products");
products[trait] = userTraits[userData[observation]][trait] * itemTraits[itemData[observation]][trait];
Variable<double> bias = (userBias[userData[observation]] + itemBias[itemData[observation]]).Named("bias");
Variable<double> affinity = (bias + Variable.Sum(products).Named("productSum")).Named("affinity");
Variable<double> noisyAffinity = Variable.GaussianFromMeanAndVariance(affinity, affinityNoiseVariance).Named("noisyAffinity");
VariableArray<double> noisyThresholds = Variable.Array<double>(level).Named("noisyThresholds");
noisyThresholds[level] = Variable.GaussianFromMeanAndVariance(userThresholds[userData[observation]][level], thresholdsNoiseVariance);
ratingData[observation][level] = noisyAffinity > noisyThresholds[level];
}
// Observe training data
GenerateData(numUsers, numItems, numTraits, numObservations.ObservedValue, numLevels,
userData, itemData, ratingData,
userTraitsPrior.ObservedValue, itemTraitsPrior.ObservedValue,
userBiasPrior.ObservedValue, itemBiasPrior.ObservedValue, userThresholdsPrior.ObservedValue,
affinityNoiseVariance.ObservedValue, thresholdsNoiseVariance.ObservedValue);
// Allow EP to process the product factor as if running VMP
// as in Stern, Herbrich, Graepel paper.
engine.Compiler.GivePriorityTo(typeof(GaussianProductOp_SHG09));
engine.Compiler.ShowWarnings = true;
// Run inference
var userTraitsPosterior = engine.Infer<Gaussian[][]>(userTraits);
var itemTraitsPosterior = engine.Infer<Gaussian[][]>(itemTraits);
var userBiasPosterior = engine.Infer<Gaussian[]>(userBias);
var itemBiasPosterior = engine.Infer<Gaussian[]>(itemBias);
var userThresholdsPosterior = engine.Infer<Gaussian[][]>(userThresholds);
// Feed in the inferred posteriors as the new priors
userTraitsPrior.ObservedValue = userTraitsPosterior;
itemTraitsPrior.ObservedValue = itemTraitsPosterior;
userBiasPrior.ObservedValue = userBiasPosterior;
itemBiasPrior.ObservedValue = itemBiasPosterior;
userThresholdsPrior.ObservedValue = userThresholdsPosterior;
// Make a prediction
numObservations.ObservedValue = 1;
userData.ObservedValue = new int[] { 5 };
itemData.ObservedValue = new int[] { 6 };
ratingData.ClearObservedValue();
Bernoulli[] predictedRating = engine.Infer<Bernoulli[][]>(ratingData)[0];
Console.WriteLine("Predicted rating:");
foreach (var rating in predictedRating) Console.WriteLine(rating);
}
private ShapeFittingInfo InferShapeFitting(InferenceEngine engine)
{
return new ShapeFittingInfo(
engine.Infer<GaussianArray2D>(this.shapeTraits),
engine.Infer<GaussianArray3D>(this.shapePartLocation),
engine.Infer<WishartArray2D>(this.shapePartOrientation),
engine.Infer<GaussianArray1D>(this.globalLogScale));
}
private ShapeModel InferShapeModel(InferenceEngine engine)
{
return new ShapeModel(
this.gridWidth.ObservedValue,
this.gridHeight.ObservedValue,
this.observationNoiseProbability.ObservedValue,
engine.Infer<GaussianArray1D>(this.shapeLocationMean),
engine.Infer<GammaArray1D>(this.shapeLocationPrecision),
engine.Infer<GaussianArray3D>(this.shapePartOffsetWeights),
engine.Infer<GaussianArray3D>(this.shapePartLogScaleWeights),
engine.Infer<GaussianArray2D>(this.shapePartAngleWeights),
engine.Infer<GammaArray2D>(this.shapePartOffsetPrecisions),
engine.Infer<GammaArray2D>(this.shapePartLogScalePrecisions),
engine.Infer<GammaArray1D>(this.shapePartAnglePrecisions));
}
private static void TrainCovariance(double[][] obs)
{
var r = new Range(obs[0].Length).Named("r");
var c = new Range(obs.Length).Named("c");
var data = Variable.Array<Vector>(r).Named("matrix");
var meansPrior = Variable.VectorGaussianFromMeanAndPrecision(Vector.FromArray(new double[obs.Length]), PositiveDefiniteMatrix.IdentityScaledBy(obs.Length, 10));
var covPrior = Variable.WishartFromShapeAndScale(1, PositiveDefiniteMatrix.Identity(c.SizeAsInt));
using (Variable.ForEach(r))
{
data[r] = Variable.VectorGaussianFromMeanAndPrecision(meansPrior, covPrior);
}
data.ObservedValue = GetRows(obs).Select(Vector.FromArray).ToArray();
var engine = new InferenceEngine(new VariationalMessagePassing());
var meansPosterior = engine.Infer<VectorGaussian>(meansPrior);
var covPosterior = engine.Infer<Wishart>(covPrior);
var covPosteriorVariance = covPosterior.GetMean().Inverse();
var verificationGaussian = new VectorGaussian(meansPosterior.GetMean(), covPosteriorVariance);
var verificationSamples = GetRows(Samples(verificationGaussian).Take(1000).ToArray()).ToArray();
var covM = GetCovarianceMatrix(verificationSamples);
var verificationCovariance = covM.GetVariance();
var actual = GetCovarianceMatrix(obs);
var actualMeans = actual.GetMean();
var actualCov = actual.GetVariance();
}
private static void FittingCurveWithBayesian(double[] input, double[] observed, int m)
{
if (input.Length != observed.Length)
{
throw new ArgumentException("input and observed arrays must be equal in length");
}
var rR = new Range(input.Length).Named("r");
var rM = new Range(m).Named("M");
var inputArr = new double[input.Length, m];
for (var r = 0; r < input.Length; r++)
{
for (var c = 0; c < m; c++)
{
inputArr[r, c] = Math.Pow(input[r], c);
}
}
var X = Variable.Array<double>(rR, rM).Named("X");
X.ObservedValue = inputArr;
var w = Variable.Array<double>(rM).Named("W");
w[rM] = Variable.GaussianFromMeanAndPrecision(0, 0.01).ForEach(rM);
var y = Variable.Array<double>(rR).Named("Y");
using (Variable.ForEach(rR))
{
var prods = Variable.Array<double>(rM);
using (Variable.ForEach(rM))
{
prods[rM] = X[rR, rM]*w[rM];
}
y[rR] = Variable.Sum(prods);
}
y.ObservedValue = observed;
var engine = new InferenceEngine();
var posteriorW = engine.Infer<DistributionStructArray<Gaussian, double>>(w);
Console.WriteLine("{0} deg poli weights\n{1}", m, posteriorW);
}
public override void Run()
{
var engine = new InferenceEngine();
var series = new List<LabelledSeries<Tuple<double, double>>>();
var rand = new Random();
var input = Enumerable.Range(-100, 200).Select(x => Convert.ToDouble(x) / 100.0).ToArray();
var expected = input.Select(x => Math.Sin(2 * Math.PI * x)).ToArray();
var observed = expected.Select(x => x + (rand.NextDouble() - 0.5)).ToArray();
series.Add(new LabelledSeries<Tuple<double, double>>("Actual sin(2x*Pi)", input.Zip(expected, (f, s) => Tuple.Create(f, s))));
var m = Variable.New<int>();
var rR = new Range(input.Length).Named("r");
var rM = new Range(m).Named("M");
var X = Variable.Array<double>(rR, rM).Named("X");
var w = Variable.Array<double>(rM).Named("W");
var noise = Variable.GammaFromShapeAndScale(1,5);
w[rM] = Variable.GaussianFromMeanAndPrecision(0, 0.01).ForEach(rM);
var y = Variable.Array<double>(rR).Named("Y");
using (Variable.ForEach(rR))
{
var prods = Variable.Array<double>(rM);
using (Variable.ForEach(rM))
{
prods[rM] = X[rR, rM] * w[rM];
}
y[rR] = Variable.Sum(prods);
}
for (var i = 3; i < 8; i++)
{
m.ObservedValue = i;
var inputArr = new double[input.Length, i];
for (var r = 0; r < input.Length; r++)
{
for (var c = 0; c < i; c++)
{
inputArr[r, c] = Math.Pow(input[r], c);
}
}
X.ObservedValue = inputArr;
y.ObservedValue = observed;
var posteriorW = engine.Infer<DistributionStructArray<Gaussian, double>>(w);
var weights = posteriorW.Select(d => d.GetMean()).ToArray();
var implied = new double[input.Length];
for (var r = 0; r < implied.Length; r++)
{
var val = 0.0;
for (var c = 0; c < i; c++)
{
val += Math.Pow(input[r], c) * weights[c];
}
implied[r] = val;
}
var polinomialLabelParts = new List<string>();
for (var c = 0; c < i; c++)
{
polinomialLabelParts.Add(Math.Round(weights[c], 4) + "*x^" + c);
}
var polinomialLabel = string.Join("+", polinomialLabelParts);
series.Add(new LabelledSeries<Tuple<double, double>>(string.Format("Inferred {0}", polinomialLabel), input.Zip(implied, (f, s) => Tuple.Create(f, s))) { IsScatter = false });
}
series.Add(new LabelledSeries<Tuple<double, double>>("Data", input.Zip(observed, (f, s) => Tuple.Create(f, s))) { IsScatter = true });
this.Series = series.Select(s => new LabelledSeries<Tuple<double, double>>(s.Label, s.Series.Skip(50).Take(100)) { IsScatter = s.IsScatter }).ToArray();
}
private static void TrainGaussian(double sourceMean, double sourcePrecision, int cycles)
{
var source = Gaussian.FromMeanAndPrecision(sourceMean, sourcePrecision);
// Prior distributions
var meanPriorDistr = Gaussian.FromMeanAndPrecision(0, 0.01);
var precisionPriorDistr = Gamma.FromMeanAndVariance(2, 5);
var meanPrior = Variable.Random(meanPriorDistr).Named("mean");
var precPrior = Variable.Random(precisionPriorDistr).Named("precision");
var engine = new InferenceEngine();
for (var i = 0; i < cycles; i++)
{
var x = Variable.GaussianFromMeanAndPrecision(meanPrior, precPrior);
x.ObservedValue = source.Sample();
}
var meanPost = engine.Infer<Gaussian>(meanPrior);
var precPost = engine.Infer<Gamma>(precPrior);
var estimate = Variable.GaussianFromMeanAndPrecision(meanPrior, precPrior);
var estimateDist = engine.Infer<Gaussian>(estimate);
Console.WriteLine("mean: {0}, prec: {1}", estimateDist.GetMean(), estimateDist.Precision);
}
private static double InferMixture(Vector[] observedData, int dimensions, int clusters)
{
var evidence = Variable.Bernoulli(0.5).Named("evidence");
var evidenceBlock = Variable.If(evidence);
var k = new Range(clusters).Named("k");
// Mixture component means
var means = Variable.Array<Vector>(k).Named("means");
means[k] = Variable.VectorGaussianFromMeanAndPrecision(
Vector.Zero(dimensions),
PositiveDefiniteMatrix.IdentityScaledBy(dimensions, 0.01)).ForEach(k);
// Mixture component precisions
var precs = Variable.Array<PositiveDefiniteMatrix>(k).Named("precs");
precs[k] = Variable.WishartFromShapeAndRate(100.0, PositiveDefiniteMatrix.IdentityScaledBy(dimensions, 0.01)).ForEach(k);
// Mixture weights
var weights = Variable.Dirichlet(k, Enumerable.Range(0, clusters).Select(_ => 1.0).ToArray()).Named("weights");
// Create a variable array which will hold the data
var n = new Range(observedData.Length).Named("n");
var data = Variable.Array<Vector>(n).Named("x");
// Create latent indicator variable for each data point
var z = Variable.Array<int>(n).Named("z");
// The mixture of Gaussians model
using (Variable.ForEach(n))
{
z[n] = Variable.Discrete(weights);
using (Variable.Switch(z[n]))
{
data[n] = Variable.VectorGaussianFromMeanAndPrecision(means[z[n]], precs[z[n]]);
}
}
// Initialise messages randomly so as to break symmetry
var zinit = new Discrete[n.SizeAsInt];
for (int i = 0; i < zinit.Length; i++)
zinit[i] = Discrete.PointMass(Rand.Int(k.SizeAsInt), k.SizeAsInt);
z.InitialiseTo(Distribution<int>.Array(zinit));
evidenceBlock.CloseBlock();
// Attach some generated data
data.ObservedValue = observedData.ToArray();
// The inference
var ie = new InferenceEngine(new VariationalMessagePassing());
ie.ShowProgress = false;
Console.WriteLine("Dist over pi=" + ie.Infer(weights));
Console.WriteLine("Dist over means=\n" + ie.Infer(means));
Console.WriteLine("Dist over precs=\n" + ie.Infer(precs));
var logEvidence = ie.Infer<Bernoulli>(evidence);
Console.WriteLine("The model log evidence is {0}", logEvidence.LogOdds);
return logEvidence.LogOdds;
}
