def TwoCoins():
firstCoin = Variable.Bernoulli(0.5)
secondCoin = Variable.Bernoulli(0.5)
bothHeads = firstCoin.op_BitwiseAnd(firstCoin, secondCoin)
engine = InferenceEngine()
print("Probability both coins are heads: %s" % engine.Infer(bothHeads))
bothHeads.ObservedValue = False
print("Probability distribution over firstCoin: %s" % engine.Infer(firstCoin))
def TruncatedGaussianEfficient():
threshold = Variable.New[Double]()
x = Variable.GaussianFromMeanAndVariance(0.0, 1.0)
Variable.ConstrainTrue(x.op_GreaterThan(x,threshold))
engine = InferenceEngine()
for thresh in [i*0.1 for i in range(11)]:
threshold.ObservedValue = thresh
print("Dist over x given thresh of %s = %s" % (thresh, engine.Infer(x)))
def BayesPointMachine(incomes, ages, w, y):
j = y.Range
xData = [Vector.FromArray(income, age, 1) for income, age in zip(incomes, ages)]
x = VariableObserved(xData, j)
# The following does not work in pythonnet:
#x = Variable.Observed[Vector](Array[Vector](xData))
noise = 0.1
ip = Variable.InnerProduct(w, x.get_Item(j))
v = Variable.GaussianFromMeanAndVariance(ip, noise)
v = v.op_GreaterThan(v, 0.0)
y.set_Item(j, v)
def HelloStrings():
str1 = Variable.StringUniform()
str2 = Variable.StringUniform()
# TODO: text = str1 + " " + str2
text = str1.op_Addition(str1, " ")
text = text.op_Addition(text, str2)
text.ObservedValue = "hello uncertain world"
engine = InferenceEngine()
print(f"str1: {engine.Infer(str1)}")
print(f"str2: {engine.Infer(str2)}")
dist_of_str1 = engine.Infer(str1)
for s in ["hello", "hello uncertain", "hello uncertain world"]:
print(f"P(str1 = '{s}') = {dist_of_str1.GetProb(s)}")
def LearningAGaussian():
# Restart the infer.NET random number generator
Rand.Restart(12347)
data = [Rand.Normal(0.0, 1.0) for i in range(100)]
mean = Variable.GaussianFromMeanAndVariance(0.0, 1.0).Named("mean")
precision = Variable.GammaFromShapeAndScale(1.0, 1.0).Named("precision")
for i in range(len(data)):
x = Variable.GaussianFromMeanAndPrecision(mean, precision)
x.ObservedValue = data[i]
engine = InferenceEngine()
print("mean=%s" % engine.Infer(mean))
print("precision=%s" % engine.Infer(precision))
def LearningAGaussianWithRanges():
# Restart the infer.NET random number generator
Rand.Restart(12347)
data = [Rand.Normal(0.0, 1.0) for i in range(100)]
mean = Variable.GaussianFromMeanAndVariance(0.0, 1.0).Named("mean")
precision = Variable.GammaFromShapeAndScale(1.0, 1.0).Named("precision")
data_range = Range(len(data)).Named("n")
x = Variable.Array[Double](data_range)
v = Variable.GaussianFromMeanAndPrecision(mean, precision).ForEach(data_range)
x.set_Item(data_range, v)
x.ObservedValue = data
engine = InferenceEngine()
print("mean=%s" % engine.Infer(mean))
print("precision=%s" %engine.Infer(precision))
def ClinicalTrial():
# Data from clinical trial
control_group_data = [False, False, True, False, False]
control_group = VariableObserved(control_group_data)
treated_group_data = [True, False, True, True, True]
treated_group = VariableObserved(treated_group_data)
i = control_group.Range
j = treated_group.Range
# Prior on being effective treatment
is_effective = Variable.Bernoulli(0.5)
# if block
if_var = Variable.If(is_effective)
# Model if treatment is effective
probIfControl = Variable.Beta(1.0, 1.0)
t = Variable.Bernoulli(probIfControl).ForEach(i)
control_group.set_Item(i, t)
probIfTreated = Variable.Beta(1.0, 1.0)
t = Variable.Bernoulli(probIfTreated).ForEach(j)
treated_group.set_Item(j, t)
if_var.Dispose()
# A bit of background
if_var = Variable.IfNot(is_effective)
# Model if treatment is not effective
prob_all = Variable.Beta(1.0, 1.0)
control_group.set_Item(i, Variable.Bernoulli(prob_all).ForEach(i))
treated_group.set_Item(j, Variable.Bernoulli(prob_all).ForEach(j))
if_var.Dispose()
# Clinical accuracy
engine = InferenceEngine()
print("Probability treatment has an effect = %s" %
engine.Infer(is_effective))
print("Probability of good outcome if given treatment = %s" %
engine.Infer[Beta](probIfTreated).GetMean())
print("Probability of good outcome if control = %s" %
engine.Infer[Beta](probIfControl).GetMean())
def MixtureOfGaussians():
# Define a range for the number of mixture components
k = Range(2)
# Mixture component means
means = Variable.Array[Vector](k)
means_k = Variable.VectorGaussianFromMeanAndPrecision(
Vector.FromArray(0.0, 0.0),
PositiveDefiniteMatrix.IdentityScaledBy(2, 0.01)).ForEach(k)
means.set_Item(k, means_k)
# Mixture component precisions
precs = Variable.Array[PositiveDefiniteMatrix](k).Named("precs")
precs_k = Variable.WishartFromShapeAndScale(
100.0, PositiveDefiniteMatrix.IdentityScaledBy(2, 0.01)).ForEach(k)
precs.set_Item(k, precs_k)
# Mixture weights
weights = Variable.Dirichlet(k, [1.0, 1.0]).Named("weights")
# Create a variable array which will hold the data
n = Range(300).Named("n")
data = Variable.Array[Vector](n).Named("x")
# Create latent indicator variable for each data point
z = Variable.Array[Int32](n).Named("z")
# The mixture of Gaussians model
forEachBlock = Variable.ForEach(n)
z.set_Item(n, Variable.Discrete(weights))
switchBlock = Variable.Switch(z.get_Item(n))
data.set_Item(
n,
Variable.VectorGaussianFromMeanAndPrecision(
means.get_Item(z.get_Item(n)), precs.get_Item(z.get_Item(n))))
switchBlock.CloseBlock()
forEachBlock.CloseBlock()
# Attach some generated data
data.ObservedValue = GenerateData(n.SizeAsInt)
# Initialise messages randomly to break symmetry
zInit = Variable.Array[Discrete](n).Named("zInit")
zInit.ObservedValue = [
Discrete.PointMass(Rand.Int(k.SizeAsInt), k.SizeAsInt)
for i in range(n.SizeAsInt)
]
# The following does not work in pythonnet:
#z.get_Item(n).InitialiseTo[Discrete].Overloads[Variable[Discrete]](zInit.get_Item(n))
InitialiseTo(z.get_Item(n), zInit.get_Item(n))
# The inference
engine = InferenceEngine()
print("Dist over pi=%s" % engine.Infer(weights))
print("Dist over means=\n%s" % engine.Infer(means))
print("Dist over precs=\n%s" % engine.Infer(precs))
def StringFormat():
# Infer argument
name = Variable.StringCapitalized()
text = VariableStringFormat("My name is {0}.", name)
text.ObservedValue = "My name is John."
engine = InferenceEngine()
engine.Compiler.RecommendedQuality = QualityBand.Experimental
print(f"name is '{engine.Infer(name)}'")
# Infer template
name = Variable.StringCapitalized()
# The following does not work in pythonnet:
#template = Variable.StringUniform() + Variable.CharNonWord()
template = Variable.StringUniform().op_Addition(Variable.StringUniform(), Variable.CharNonWord())
template = template.op_Addition(template, "{0}")
template = template.op_Addition(template, Variable.CharNonWord())
template = template.op_Addition(template, Variable.StringUniform())
text = VariableStringFormat(template, name)
text.ObservedValue = "Hello, mate! I'm Dave."
print(f"name is '{engine.Infer(name)}'")
print(f"template is '{engine.Infer(template)}'")
# With a slightly different observation.
text.ObservedValue = "Hi! My name is John."
print(f"name is '{engine.Infer(name)}'")
print(f"template is '{engine.Infer(template)}'")
# Provide more data to reduce ambiguity.
name2 = Variable.StringCapitalized()
text2 = VariableStringFormat(template, name2)
text2.ObservedValue = "Hi! My name is Tom."
print(f"name is '{engine.Infer(name)}'")
print(f"name2 is '{engine.Infer(name2)}'")
print(f"template is '{engine.Infer(template)}'")
# Generate text with the learned template.
text3 = VariableStringFormat(template, "Boris")
print(f"text3 is '{engine.Infer(text3)}'")
def MotifFinder():
Rand.Restart(1337)
SequenceCount = 50
SequenceLength = 25
MotifPresenceProbability = 0.8
trueMotifNucleobaseDist = [
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),
]
backgroundNucleobaseDist = NucleobaseDist(a=0.25, c=0.25, g=0.25, t=0.25)
sequenceData, motifPositionData = SampleMotifData(SequenceCount, SequenceLength,
MotifPresenceProbability,
trueMotifNucleobaseDist,
backgroundNucleobaseDist)
assert(sequenceData[0] == "CTACTTCGAATTTACCCCTATATTT")
# should be CTACTTCGAATTTACCCCTATATTT
assert(len(sequenceData) == 50)
assert(motifPositionData[:10] ==[2, 15, -1, 0, 14, 5, -1, 5, 1, 9])
assert(len(motifPositionData) == 50)
# Char.MaxValue is a string '\uffff', so we convert the hex to decimal.
motif_nucleobase_pseudo_counts = PiecewiseVector.Constant(int('ffff', 16) + 1, 1e-6)
# Cannot call managed PiecewiseVector object's indexer with ['A'], i.e. cannot do
# motif_nucleobase_pseudo_counts['A'] = 2.0
motif_nucleobase_pseudo_counts[ord('A')] = 2.0
motif_nucleobase_pseudo_counts[ord('C')] = 2.0
motif_nucleobase_pseudo_counts[ord('G')] = 2.0
motif_nucleobase_pseudo_counts[ord('T')] = 2.0
motifLength = len(trueMotifNucleobaseDist) # Assume we know the true motif length.
motifCharsRange = Range(motifLength)
motifNucleobaseProbs = Variable.Array[Vector](motifCharsRange)
# Cannot do motifNucleobaseProbs[motifCharsRange] = Variable.Dirichlet...
motifNucleobaseProbs.set_Item(motifCharsRange, Variable.Dirichlet(motif_nucleobase_pseudo_counts).ForEach(motifCharsRange))
sequenceRange = Range(SequenceCount)
sequences = Variable.Array[str](sequenceRange)
motifPositions = Variable.Array[int](sequenceRange)
motifPositions.set_Item(sequenceRange, Variable.DiscreteUniform(SequenceLength - motifLength + 1).ForEach(sequenceRange))
motifPresence = Variable.Array[bool](sequenceRange)
motifPresence.set_Item(sequenceRange, Variable.Bernoulli(MotifPresenceProbability).ForEach(sequenceRange))
forEachBlock = Variable.ForEach(sequenceRange)
ifVar = Variable.If(motifPresence.get_Item(sequenceRange))
motifChars = Variable.Array[Char](motifCharsRange)
motifChars.set_Item(motifCharsRange, Variable.Char(motifNucleobaseProbs.get_Item(motifCharsRange)))
motif = Variable.StringFromArray(motifChars)
motifPos = motifPositions.get_Item(sequenceRange)
backgroundLengthRight = motifPos.op_Subtraction(SequenceLength - motifLength, motifPositions.get_Item(sequenceRange))
backgroundLeft = VariableStringOfLength(motifPositions.get_Item(sequenceRange), backgroundNucleobaseDist)
backgroundRight = VariableStringOfLength(backgroundLengthRight, backgroundNucleobaseDist)
added_vars = backgroundLeft.op_Addition(backgroundLeft, motif)
added_vars = added_vars.op_Addition(added_vars, backgroundRight)
sequences.set_Item(sequenceRange, added_vars)
ifVar.Dispose()
ifNotVar = Variable.IfNot(motifPresence.get_Item(sequenceRange))
sequences.set_Item(sequenceRange, VariableStringOfLength(SequenceLength, backgroundNucleobaseDist))
ifNotVar.Dispose()
forEachBlock.CloseBlock()
sequences.ObservedValue = sequenceData
engine = InferenceEngine()
engine.NumberOfIterations = 30 #30
engine.Compiler.RecommendedQuality = QualityBand.Experimental
motifNucleobaseProbsPosterior = engine.Infer[Array[Dirichlet]](motifNucleobaseProbs)
motifPresencePosterior = engine.Infer[Array[Bernoulli]](motifPresence)
motifPositionPosterior = engine.Infer[Array[Discrete]](motifPositions)
# PrintMotifInferenceResults
PrintPositionFrequencyMatrix("\nTrue position frequency matrix:",
trueMotifNucleobaseDist,
lambda dist, c: dist[c]) # Distributions.DiscreteChar indexer is implemented.
PrintPositionFrequencyMatrix("\nInferred position frequency matrix mean:",
motifNucleobaseProbsPosterior, # Array of Distribtions.Dirichlet; mean of each is a PiecewiseVector
lambda dist, c: dist.GetMean()[ord(c)]) # PiecewiseVector indexer is implemented, but not for strings...
# TypeError: No method matches given arguments for get_Item: (<class 'str'>) -> need to do ord(c)
# Tried importing Console and ConsoleColor from System which works in powershell but not in VS console.
printc("\nPREDICTION ", ConsoleColor.Yellow)
printc("GROUND TRUTH ", ConsoleColor.Red)
printc("OVERLAP \n\n", ConsoleColor.Green)
for i in range(min(SequenceCount, 30)):
motifPos = motifPositionPosterior[i].GetMode() if motifPresencePosterior[i].GetProbTrue() > 0.5 else -1
inPrediction, inGroundTruth = False, False
for j in range(SequenceLength):
if j == motifPos:
inPrediction = True
elif j == motifPos + motifLength:
inPrediction = False
if j == motifPositionData[i]:
inGroundTruth = True
elif j == motifPositionData[i] + motifLength:
inGroundTruth = False
color = Console.ForegroundColor
if (inPrediction and inGroundTruth):
color = ConsoleColor.Green
elif (inPrediction):
color = ConsoleColor.Yellow
elif inGroundTruth:
color = ConsoleColor.Red
printc(sequenceData[i][j], color)
print(f" P(has motif) = {motifPresencePosterior[i].GetProbTrue():.2f}", end="");
if (motifPos != -1):
print(f" P(pos={motifPos}) = {motifPositionPosterior[i][motifPos]:.2f}", end="");
print()