public void WordModel()
{
// We want to build a word model as a reasonably simple StringDistribution. It
// should satisfy the following:
// (1) The probability of a word of moderate length should not be
// significantly less than the probability of a shorter word.
// (2) The probability of a specific word conditioned on its length matches that of
// words in the target language.
// We achieve this by putting non-normalized character distributions on the edges. The
// StringDistribution is unaware that these are non-normalized.
// The StringDistribution itself is non-normalizable.
const double TargetProb1 = 0.05;
const double Ratio1 = 0.4;
const double TargetProb2 = TargetProb1 * Ratio1;
const double Ratio2 = 0.2;
const double TargetProb3 = TargetProb2 * Ratio2;
const double TargetProb4 = TargetProb3 * Ratio2;
const double TargetProb5 = TargetProb4 * Ratio2;
const double Ratio3 = 0.999;
const double TargetProb6 = TargetProb5 * Ratio3;
const double TargetProb7 = TargetProb6 * Ratio3;
const double TargetProb8 = TargetProb7 * Ratio3;
const double Ratio4 = 0.9;
const double TargetProb9 = TargetProb8 * Ratio4;
const double TargetProb10 = TargetProb9 * Ratio4;
var targetProbabilitiesPerLength = new double[]
{
TargetProb1, TargetProb2, TargetProb3, TargetProb4, TargetProb5, TargetProb6, TargetProb7, TargetProb8, TargetProb9, TargetProb10
};
var charDistUpper = DiscreteChar.Upper();
var charDistLower = DiscreteChar.Lower();
var charDistUpperNarrow = DiscreteChar.OneOf('A', 'B');
var charDistLowerNarrow = DiscreteChar.OneOf('a', 'b');
var charDistUpperScaled = DiscreteChar.Uniform();
var charDistLowerScaled1 = DiscreteChar.Uniform();
var charDistLowerScaled2 = DiscreteChar.Uniform();
var charDistLowerScaled3 = DiscreteChar.Uniform();
var charDistLowerScaledEnd = DiscreteChar.Uniform();
charDistUpperScaled.SetToPartialUniformOf(charDistUpper, Math.Log(TargetProb1));
charDistLowerScaled1.SetToPartialUniformOf(charDistLower, Math.Log(Ratio1));
charDistLowerScaled2.SetToPartialUniformOf(charDistLower, Math.Log(Ratio2));
charDistLowerScaled3.SetToPartialUniformOf(charDistLower, Math.Log(Ratio3));
charDistLowerScaledEnd.SetToPartialUniformOf(charDistLower, Math.Log(Ratio4));
var wordModel = StringDistribution.Concatenate(
new List <DiscreteChar>
{
charDistUpperScaled,
charDistLowerScaled1,
charDistLowerScaled2,
charDistLowerScaled2,
charDistLowerScaled2,
charDistLowerScaled3,
charDistLowerScaled3,
charDistLowerScaled3,
charDistLowerScaledEnd
},
true,
true);
const string Word = "Abcdefghij";
const double Eps = 1e-5;
var broadDist = StringDistribution.Char(charDistUpper);
var narrowDist = StringDistribution.Char(charDistUpperNarrow);
var narrowWord = "A";
var expectedProbForNarrow = 0.5;
for (var i = 0; i < targetProbabilitiesPerLength.Length; i++)
{
var currentWord = Word.Substring(0, i + 1);
var probCurrentWord = Math.Exp(wordModel.GetLogProb(currentWord));
Assert.Equal(targetProbabilitiesPerLength[i], probCurrentWord, Eps);
var logAvg = Math.Exp(wordModel.GetLogAverageOf(broadDist));
Assert.Equal(targetProbabilitiesPerLength[i], logAvg, Eps);
var prod = StringDistribution.Zero();
prod.SetToProduct(broadDist, wordModel);
Xunit.Assert.True(prod.GetWorkspaceOrPoint().HasElementLogValueOverrides);
probCurrentWord = Math.Exp(prod.GetLogProb(currentWord));
Assert.Equal(targetProbabilitiesPerLength[i], probCurrentWord, Eps);
prod.SetToProduct(narrowDist, wordModel);
Xunit.Assert.False(prod.GetWorkspaceOrPoint().HasElementLogValueOverrides);
var probNarrowWord = Math.Exp(prod.GetLogProb(narrowWord));
Assert.Equal(expectedProbForNarrow, probNarrowWord, Eps);
broadDist = broadDist.Append(charDistLower);
narrowDist = narrowDist.Append(charDistLowerNarrow);
narrowWord += "a";
expectedProbForNarrow *= 0.5;
}
// Copied model
var copiedModel = StringDistribution.FromWorkspace(StringTransducer.Copy().ProjectSource(wordModel.GetWorkspaceOrPoint()));
// Under transducer.
for (var i = 0; i < targetProbabilitiesPerLength.Length; i++)
{
var currentWord = Word.Substring(0, i + 1);
var probCurrentWord = Math.Exp(copiedModel.GetLogProb(currentWord));
Assert.Equal(targetProbabilitiesPerLength[i], probCurrentWord, Eps);
}
// Rescaled model
var scale = 0.5;
var newTargetProb1 = TargetProb1 * scale;
var charDistUpperScaled1 = DiscreteChar.Uniform();
charDistUpperScaled1.SetToPartialUniformOf(charDistUpper, Math.Log(newTargetProb1));
var reWeightingTransducer =
StringTransducer.Replace(StringDistribution.Char(charDistUpper).GetWorkspaceOrPoint(), StringDistribution.Char(charDistUpperScaled1).GetWorkspaceOrPoint())
.Append(StringTransducer.Copy());
var reWeightedWordModel = StringDistribution.FromWorkspace(reWeightingTransducer.ProjectSource(wordModel.GetWorkspaceOrPoint()));
for (var i = 0; i < targetProbabilitiesPerLength.Length; i++)
{
var currentWord = Word.Substring(0, i + 1);
var probCurrentWord = Math.Exp(reWeightedWordModel.GetLogProb(currentWord));
Assert.Equal(scale * targetProbabilitiesPerLength[i], probCurrentWord, Eps);
}
}
