/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="SingleOp"]/message_doc[@name="CharacterAverageConditional(StringDistribution)"]/*'/>
public static DiscreteChar CharacterAverageConditional(StringDistribution str)
{
Argument.CheckIfNotNull(str, "str");
if (str.IsPointMass)
{
return(CharacterAverageConditional(str.Point));
}
Vector resultLogProb = PiecewiseVector.Constant(char.MaxValue + 1, double.NegativeInfinity);
StringAutomaton probFunc = str.GetWorkspaceOrPoint();
StringAutomaton.EpsilonClosure startEpsilonClosure = new Automaton <string, char, DiscreteChar, StringManipulator, StringAutomaton> .EpsilonClosure(probFunc, probFunc.Start);
for (int stateIndex = 0; stateIndex < startEpsilonClosure.Size; ++stateIndex)
{
StringAutomaton.State state = startEpsilonClosure.GetStateByIndex(stateIndex);
Weight stateLogWeight = startEpsilonClosure.GetStateWeightByIndex(stateIndex);
foreach (var transition in state.Transitions)
{
if (!transition.IsEpsilon)
{
StringAutomaton.State destState = probFunc.States[transition.DestinationStateIndex];
StringAutomaton.EpsilonClosure destStateClosure = new Automaton <string, char, DiscreteChar, StringManipulator, StringAutomaton> .EpsilonClosure(probFunc, destState);
if (!destStateClosure.EndWeight.IsZero)
{
Weight weight = Weight.Product(stateLogWeight, transition.Weight, destStateClosure.EndWeight);
var logProbs = transition.ElementDistribution.Value.GetProbs();
logProbs.SetToFunction(logProbs, Math.Log);
resultLogProb = LogSumExp(resultLogProb, logProbs, weight);
}
}
}
}
if (resultLogProb.All(double.IsNegativeInfinity))
{
throw new AllZeroException("An input distribution assigns zero probability to all single character strings.");
}
Vector resultProb = PiecewiseVector.Zero(char.MaxValue + 1);
double logNormalizer = resultLogProb.LogSumExp();
resultProb.SetToFunction(resultLogProb, lp => Math.Exp(lp - logNormalizer));
return(DiscreteChar.FromVector(resultProb));
}
/// <summary>EP message to <c>character</c>.</summary>
/// <param name="str">Incoming message from <c>str</c>.</param>
/// <returns>The outgoing EP message to the <c>character</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is a distribution matching the moments of <c>character</c> as the random arguments are varied. The formula is <c>proj[p(character) sum_(str) p(str) factor(character,str)]/p(character)</c>.</para>
/// </remarks>
public static DiscreteChar CharacterAverageConditional(StringDistribution str)
{
Argument.CheckIfNotNull(str, "str");
Vector resultlogProb = PiecewiseVector.Constant(char.MaxValue + 1, double.NegativeInfinity);
StringAutomaton probFunc = str.GetProbabilityFunction();
StringAutomaton.EpsilonClosure startEpsilonClosure = probFunc.Start.GetEpsilonClosure();
for (int stateIndex = 0; stateIndex < startEpsilonClosure.Size; ++stateIndex)
{
StringAutomaton.State state = startEpsilonClosure.GetStateByIndex(stateIndex);
double stateLogWeight = startEpsilonClosure.GetStateLogWeightByIndex(stateIndex);
for (int transitionIndex = 0; transitionIndex < state.Transitions.Count; ++transitionIndex)
{
StringAutomaton.Transition transition = state.Transitions[transitionIndex];
if (!transition.IsEpsilon)
{
StringAutomaton.State destState = probFunc.States[transition.DestinationStateIndex];
StringAutomaton.EpsilonClosure destStateClosure = destState.GetEpsilonClosure();
if (!double.IsNegativeInfinity(destStateClosure.EndLogWeight))
{
double logWeight = stateLogWeight + transition.LogWeight + destStateClosure.EndLogWeight;
resultlogProb = LogSumExp(resultlogProb, transition.ElementDistribution.GetInternalDiscrete().GetLogProbs(), logWeight);
}
}
}
}
if (resultlogProb.All(double.IsNegativeInfinity))
{
throw new AllZeroException("An input distribution assigns zero probability to all single character strings.");
}
Vector resultProb = PiecewiseVector.Zero(char.MaxValue + 1);
resultProb.SetToFunction(resultlogProb, Math.Exp);
return(DiscreteChar.FromVector(resultProb));
}
/// <summary>
/// Creates a distribution which is uniform over all characters
/// that have zero probability under this distribution
/// i.e. that are not 'in' this distribution.
/// </summary>
/// <remarks>
/// This is useful for defining characters that are not in a particular distribution
/// e.g. not a letter or not a word character.
/// </remarks>
/// <returns>The created distribution.</returns>
public DiscreteChar Complement()
{
// This creates a vector whose common value is not zero,
// but where the piece values are zero. This is useful when
// displaying the distribution (to show that it is a 'complement')
// but may have unforeseen side effects e.g. on performance.
// todo: consider revisiting this design.
PiecewiseVector res;
if (this.IsPointMass)
{
res = PiecewiseVector.Constant(this.Dimension, 1.0);
res[this.Point] = 0;
}
else
{
res = PiecewiseVector.Zero(this.Dimension);
res.SetToFunction(this.disc.GetWorkspace(), x => x == 0.0 ? 1.0 : 0.0);
}
var comp = DiscreteChar.FromVector(res);
return(comp);
}
/// <summary>
/// The entry point of the motif finder.
/// </summary>
public static void Main()
{
Rand.Restart(1337);
const int SequenceCount = 50;
const int SequenceLength = 25;
const double MotifPresenceProbability = 0.8;
//// Sample some data
var trueMotifNucleobaseDist = new[]
{
NucleobaseDist(a: 0.8, c: 0.1, g: 0.05, t: 0.05),
NucleobaseDist(a: 0.0, c: 0.9, g: 0.05, t: 0.05),
NucleobaseDist(a: 0.0, c: 0.0, g: 0.5, t: 0.5),
NucleobaseDist(a: 0.25, c: 0.25, g: 0.25, t: 0.25),
NucleobaseDist(a: 0.1, c: 0.1, g: 0.1, t: 0.7),
NucleobaseDist(a: 0.0, c: 0.0, g: 0.9, t: 0.1),
NucleobaseDist(a: 0.9, c: 0.05, g: 0.0, t: 0.05),
NucleobaseDist(a: 0.5, c: 0.5, g: 0.0, t: 0.0),
};
int motifLength = trueMotifNucleobaseDist.Length;
var backgroundNucleobaseDist = NucleobaseDist(a: 0.25, c: 0.25, g: 0.25, t: 0.25);
string[] sequenceData;
int[] motifPositionData;
SampleMotifData(
SequenceCount,
SequenceLength,
MotifPresenceProbability,
trueMotifNucleobaseDist,
backgroundNucleobaseDist,
out sequenceData,
out motifPositionData);
//// Specify the model
Vector motifNucleobasePseudoCounts = PiecewiseVector.Constant(char.MaxValue + 1, 1e-6);
motifNucleobasePseudoCounts['A'] = motifNucleobasePseudoCounts['C'] = motifNucleobasePseudoCounts['G'] = motifNucleobasePseudoCounts['T'] = 2.0;
Range motifCharsRange = new Range(motifLength);
VariableArray <Vector> motifNucleobaseProbs = Variable.Array <Vector>(motifCharsRange);
motifNucleobaseProbs[motifCharsRange] = Variable.Dirichlet(motifNucleobasePseudoCounts).ForEach(motifCharsRange);
var sequenceRange = new Range(SequenceCount);
VariableArray <string> sequences = Variable.Array <string>(sequenceRange);
VariableArray <int> motifPositions = Variable.Array <int>(sequenceRange);
motifPositions[sequenceRange] = Variable.DiscreteUniform(SequenceLength - motifLength + 1).ForEach(sequenceRange);
VariableArray <bool> motifPresence = Variable.Array <bool>(sequenceRange);
motifPresence[sequenceRange] = Variable.Bernoulli(MotifPresenceProbability).ForEach(sequenceRange);
using (Variable.ForEach(sequenceRange))
{
using (Variable.If(motifPresence[sequenceRange]))
{
var motifChars = Variable.Array <char>(motifCharsRange);
motifChars[motifCharsRange] = Variable.Char(motifNucleobaseProbs[motifCharsRange]);
var motif = Variable.StringFromArray(motifChars);
var backgroundLengthRight = SequenceLength - motifLength - motifPositions[sequenceRange];
var backgroundLeft = Variable.StringOfLength(motifPositions[sequenceRange], backgroundNucleobaseDist);
var backgroundRight = Variable.StringOfLength(backgroundLengthRight, backgroundNucleobaseDist);
sequences[sequenceRange] = backgroundLeft + motif + backgroundRight;
}
using (Variable.IfNot(motifPresence[sequenceRange]))
{
sequences[sequenceRange] = Variable.StringOfLength(SequenceLength, backgroundNucleobaseDist);
}
}
//// Infer the motif from sampled data
sequences.ObservedValue = sequenceData;
var engine = new InferenceEngine();
engine.Algorithm = new ExpectationPropagation();
engine.NumberOfIterations = 30;
engine.Compiler.RecommendedQuality = QualityBand.Experimental;
var motifNucleobaseProbsPosterior = engine.Infer <IList <Dirichlet> >(motifNucleobaseProbs);
var motifPresencePosterior = engine.Infer <IList <Bernoulli> >(motifPresence);
var motifPositionPosterior = engine.Infer <IList <Discrete> >(motifPositions);
//// Output inference results
PrintMotifInferenceResults(
sequenceData,
motifPositionData,
trueMotifNucleobaseDist,
motifNucleobaseProbsPosterior,
motifPresencePosterior,
motifPositionPosterior);
//// Keep the application alive until the user enters a keystroke
Console.ReadKey();
}