protected static void demoBurglaryAlarmModel(IFiniteProbabilityModel model)
{
System.Console.WriteLine("--------------------");
System.Console.WriteLine("Burglary Alarm Model");
System.Console.WriteLine("--------------------");
AssignmentProposition aburglary = new AssignmentProposition(
ExampleRV.BURGLARY_RV, true);
AssignmentProposition anotburglary = new AssignmentProposition(
ExampleRV.BURGLARY_RV, false);
AssignmentProposition anotearthquake = new AssignmentProposition(
ExampleRV.EARTHQUAKE_RV, false);
AssignmentProposition aalarm = new AssignmentProposition(
ExampleRV.ALARM_RV, true);
AssignmentProposition anotalarm = new AssignmentProposition(
ExampleRV.ALARM_RV, false);
AssignmentProposition ajohnCalls = new AssignmentProposition(
ExampleRV.JOHN_CALLS_RV, true);
AssignmentProposition amaryCalls = new AssignmentProposition(
ExampleRV.MARY_CALLS_RV, true);
// AIMA3e pg. 514
System.Console.WriteLine("P(j,m,a,~b,~e) = "
+ model.prior(ajohnCalls, amaryCalls, aalarm, anotburglary,
anotearthquake));
System.Console.WriteLine("P(j,m,~a,~b,~e) = "
+ model.prior(ajohnCalls, amaryCalls, anotalarm, anotburglary,
anotearthquake));
// AIMA3e. pg. 514
// P<>(Alarm | JohnCalls = true, MaryCalls = true, Burglary = false,
// Earthquake = false)
// = <0.558, 0.442>
System.Console
.WriteLine("P<>(Alarm | JohnCalls = true, MaryCalls = true, Burglary = false, Earthquake = false) = "
+ model.posteriorDistribution(ExampleRV.ALARM_RV,
ajohnCalls, amaryCalls, anotburglary,
anotearthquake));
// AIMA3e pg. 523
// P<>(Burglary | JohnCalls = true, MaryCalls = true) = <0.284, 0.716>
System.Console
.WriteLine("P<>(Burglary | JohnCalls = true, MaryCalls = true) = "
+ model.posteriorDistribution(ExampleRV.BURGLARY_RV,
ajohnCalls, amaryCalls));
// AIMA3e pg. 528
// P<>(JohnCalls | Burglary = true)
System.Console.WriteLine("P<>(JohnCalls | Burglary = true) = "
+ model.posteriorDistribution(ExampleRV.JOHN_CALLS_RV,
aburglary));
}
protected static void demoToothacheCavityCatchModel(IFiniteProbabilityModel model)
{
System.Console.WriteLine("Toothache, Cavity, and Catch Model");
System.Console.WriteLine("----------------------------------");
AssignmentProposition atoothache = new AssignmentProposition(
ExampleRV.TOOTHACHE_RV, true);
AssignmentProposition acavity = new AssignmentProposition(
ExampleRV.CAVITY_RV, true);
AssignmentProposition anotcavity = new AssignmentProposition(
ExampleRV.CAVITY_RV, false);
AssignmentProposition acatch = new AssignmentProposition(
ExampleRV.CATCH_RV, true);
// AIMA3e pg. 485
System.Console.WriteLine("P(cavity) = " + model.prior(acavity));
System.Console.WriteLine("P(cavity | toothache) = "
+ model.posterior(acavity, atoothache));
// AIMA3e pg. 492
DisjunctiveProposition cavityOrToothache = new DisjunctiveProposition(
acavity, atoothache);
System.Console.WriteLine("P(cavity OR toothache) = "
+ model.prior(cavityOrToothache));
// AIMA3e pg. 493
System.Console.WriteLine("P(~cavity | toothache) = "
+ model.posterior(anotcavity, atoothache));
// AIMA3e pg. 493
// P<>(Cavity | toothache) = <0.6, 0.4>
System.Console.WriteLine("P<>(Cavity | toothache) = "
+ model.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache));
// AIMA3e pg. 497
// P<>(Cavity | toothache AND catch) = <0.871, 0.129>
System.Console.WriteLine("P<>(Cavity | toothache AND catch) = "
+ model.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache,
acatch));
}
protected void test_BurglaryAlarmModel_Distributions(
IFiniteProbabilityModel model)
{
AssignmentProposition aburglary = new AssignmentProposition(
ExampleRV.BURGLARY_RV, true);
AssignmentProposition anotburglary = new AssignmentProposition(
ExampleRV.BURGLARY_RV, false);
AssignmentProposition anotearthquake = new AssignmentProposition(
ExampleRV.EARTHQUAKE_RV, false);
AssignmentProposition ajohnCalls = new AssignmentProposition(
ExampleRV.JOHN_CALLS_RV, true);
AssignmentProposition amaryCalls = new AssignmentProposition(
ExampleRV.MARY_CALLS_RV, true);
// AIMA3e. pg. 514
// P<>(Alarm | JohnCalls = true, MaryCalls = true, Burglary = false,
// Earthquake = false)
// = <0.558, 0.442>
assertArrayEquals(
new double[] { 0.5577689243027888, 0.44223107569721115 },
model.posteriorDistribution(ExampleRV.ALARM_RV, ajohnCalls,
amaryCalls, anotburglary, anotearthquake).getValues(),
DELTA_THRESHOLD);
// AIMA3e pg. 523
// P<>(Burglary | JohnCalls = true, MaryCalls = true) = <0.284, 0.716>
assertArrayEquals(
new double[] { 0.2841718353643929, 0.7158281646356071 },
model.posteriorDistribution(ExampleRV.BURGLARY_RV, ajohnCalls,
amaryCalls).getValues(), DELTA_THRESHOLD);
// AIMA3e pg. 528
// P<>(JohnCalls | Burglary = true)
assertArrayEquals(new double[] { 0.8490169999999999,
0.15098299999999998 },
model.posteriorDistribution(ExampleRV.JOHN_CALLS_RV, aburglary)
.getValues(), DELTA_THRESHOLD);
}
public void iterate(IMap <IRandomVariable, object> possibleWorld, double probability)
{
// <b>P</b>(X<sub>t+1</sub> | x<sub>t</sub>)*
// P(x<sub>t</sub> | e<sub>1:t</sub>)
foreach (var av in possibleWorld)
{
xtVarAssignMap.Get(av.GetKey()).setValue(av.GetValue());
}
int i = 0;
foreach (double tp in transitionModel.posteriorDistribution(xtp1, xt).getValues())
{
s1.setValue(i, s1.getValues()[i] + (tp * probability));
++i;
}
}
// AIMA3e pg. 496
protected void test_MeningitisStiffNeckModel_Distributions(
IFiniteProbabilityModel model)
{
AssignmentProposition astiffNeck = new AssignmentProposition(
ExampleRV.STIFF_NECK_RV, true);
// AIMA3e pg. 497
// P<>(Mengingitis | stiffneck) = α<P(s | m)P(m), P(s | ~m)P(~m)>
ICategoricalDistribution dMeningitisGivenStiffNeck = model
.posteriorDistribution(ExampleRV.MENINGITIS_RV, astiffNeck);
Assert.AreEqual(2, dMeningitisGivenStiffNeck.getValues().Length);
Assert.AreEqual(0.0014, dMeningitisGivenStiffNeck.getValues()[0],
DELTA_THRESHOLD);
Assert.AreEqual(0.9986, dMeningitisGivenStiffNeck.getValues()[1],
DELTA_THRESHOLD);
}
public ICategoricalDistribution forward(ICategoricalDistribution f1_t, ICollection <AssignmentProposition> e_tp1)
{
ICategoricalDistribution s1 = new ProbabilityTable(f1_t.getFor());
// Set up required working variables
IProposition[] props = new IProposition[s1.getFor().Size()];
int i = 0;
foreach (IRandomVariable rv in s1.getFor())
{
props[i] = new RandVar(rv.getName(), rv.getDomain());
++i;
}
IProposition Xtp1 = ProbUtil.constructConjunction(props);
AssignmentProposition[] xt = new AssignmentProposition[tToTm1StateVarMap.Size()];
IMap <IRandomVariable, AssignmentProposition> xtVarAssignMap = CollectionFactory.CreateInsertionOrderedMap <IRandomVariable, AssignmentProposition>();
i = 0;
foreach (IRandomVariable rv in tToTm1StateVarMap.GetKeys())
{
xt[i] = new AssignmentProposition(tToTm1StateVarMap.Get(rv), "<Dummy Value>");
xtVarAssignMap.Put(rv, xt[i]);
++i;
}
// Step 1: Calculate the 1 time step prediction
// ∑<sub>x<sub>t</sub></sub>
CategoricalDistributionIterator if1_t = new CategoricalDistributionIteratorImpl(transitionModel,
xtVarAssignMap, s1, Xtp1, xt);
f1_t.iterateOver(if1_t);
// Step 2: multiply by the probability of the evidence
// and normalize
// <b>P</b>(e<sub>t+1</sub> | X<sub>t+1</sub>)
ICategoricalDistribution s2 = sensorModel.posteriorDistribution(ProbUtil
.constructConjunction(e_tp1.ToArray()), Xtp1);
return(s2.multiplyBy(s1).normalize());
}
public void iterate(IMap <IRandomVariable, object> possibleWorld, double probability)
{
// Assign current values for x<sub>k+1</sub>
foreach (var av in possibleWorld)
{
x_kp1VarAssignMap.Get(av.GetKey()).setValue(av.GetValue());
}
// P(e<sub>k+1</sub> | x<sub>k+1</sub>)
// P(e<sub>k+2:t</sub> | x<sub>k+1</sub>)
double p = sensorModel.posterior(pe_kp1, x_kp1) * probability;
// <b>P</b>(x<sub>k+1</sub> | X<sub>k</sub>)
int i = 0;
foreach (double tp in transitionModel.posteriorDistribution(x_kp1, xk).getValues())
{
b_kp1t.setValue(i, b_kp1t.getValues()[i] + (tp * p));
++i;
}
}
//
// PROTECTED
//
protected void test_RollingPairFairDiceModel_Distributions(IFiniteProbabilityModel model)
{
AssignmentProposition ad1_1 = new AssignmentProposition(ExampleRV.DICE_1_RV, 1);
ICategoricalDistribution dD1_1 = model.priorDistribution(ad1_1);
assertArrayEquals(new double[] { 1.0 / 6.0 }, dD1_1.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dPriorDice1 = model.priorDistribution(ExampleRV.DICE_1_RV);
assertArrayEquals(new double[] { 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0 },
dPriorDice1.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dPriorDice2 = model.priorDistribution(ExampleRV.DICE_2_RV);
assertArrayEquals(new double[] { 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0 },
dPriorDice2.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dJointDice1Dice2 = model.jointDistribution(ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV);
Assert.AreEqual(36, dJointDice1Dice2.getValues().Length);
for (int i = 0; i < dJointDice1Dice2.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 36.0, dJointDice1Dice2.getValues()[i], DELTA_THRESHOLD);
}
ICategoricalDistribution dJointDice2Dice1 = model.jointDistribution(ExampleRV.DICE_2_RV, ExampleRV.DICE_1_RV);
Assert.AreEqual(36, dJointDice2Dice1.getValues().Length);
for (int i = 0; i < dJointDice2Dice1.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 36.0, dJointDice2Dice1.getValues()[i], DELTA_THRESHOLD);
}
//
// Test Sets of events
IntegerSumProposition total11 = new IntegerSumProposition("Total",
new FiniteIntegerDomain(11), ExampleRV.DICE_1_RV,
ExampleRV.DICE_2_RV);
// P<>(Total = 11) = <2.0/36.0>
assertArrayEquals(new double[] { 2.0 / 36.0 }, model.priorDistribution(total11).getValues(), DELTA_THRESHOLD);
// P<>(Dice1, Total = 11)
// = <0.0, 0.0, 0.0, 0.0, 1.0/36.0, 1.0/36.0>
assertArrayEquals(new double[] { 0, 0, 0, 0, 1.0 / 36.0, 1.0 / 36.0 },
model.priorDistribution(ExampleRV.DICE_1_RV, total11)
.getValues(), DELTA_THRESHOLD);
EquivalentProposition doubles = new EquivalentProposition("Doubles",
ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV);
// P(Doubles) = <1.0/6.0>
assertArrayEquals(new double[] { 1.0 / 6.0 }, model
.priorDistribution(doubles).getValues(), DELTA_THRESHOLD);
//
// Test posterior
//
// P<>(Dice1, Total = 11)
// = <0.0, 0.0, 0.0, 0.0, 0.5, 0.5>
assertArrayEquals(new double[] { 0, 0, 0, 0, 0.5, 0.5 }, model
.posteriorDistribution(ExampleRV.DICE_1_RV, total11)
.getValues(), DELTA_THRESHOLD);
// P<>(Dice1 | Doubles) = <1/6, 1/6, 1/6, 1/6, 1/6, 1/6>
assertArrayEquals(new double[] { 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0 }, model
.posteriorDistribution(ExampleRV.DICE_1_RV, doubles)
.getValues(), DELTA_THRESHOLD);
ICategoricalDistribution dPosteriorDice1GivenDice2 = model
.posteriorDistribution(ExampleRV.DICE_1_RV, ExampleRV.DICE_2_RV);
Assert.AreEqual(36, dPosteriorDice1GivenDice2.getValues().Length);
for (int i = 0; i < dPosteriorDice1GivenDice2.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 6.0, dPosteriorDice1GivenDice2.getValues()[i], DELTA_THRESHOLD);
}
ICategoricalDistribution dPosteriorDice2GivenDice1 = model
.posteriorDistribution(ExampleRV.DICE_2_RV, ExampleRV.DICE_1_RV);
Assert.AreEqual(36, dPosteriorDice2GivenDice1.getValues().Length);
for (int i = 0; i < dPosteriorDice2GivenDice1.getValues().Length; i++)
{
Assert.AreEqual(1.0 / 6.0, dPosteriorDice2GivenDice1.getValues()[i], DELTA_THRESHOLD);
}
}
protected void test_ToothacheCavityCatchModel_Distributions(IFiniteProbabilityModel model)
{
AssignmentProposition atoothache = new AssignmentProposition(ExampleRV.TOOTHACHE_RV, true);
AssignmentProposition anottoothache = new AssignmentProposition(ExampleRV.TOOTHACHE_RV, false);
AssignmentProposition acatch = new AssignmentProposition(ExampleRV.CATCH_RV, true);
AssignmentProposition anotcatch = new AssignmentProposition(ExampleRV.CATCH_RV, false);
// AIMA3e pg. 493
// P<>(Cavity | toothache) = <0.6, 0.4>
assertArrayEquals(new double[] { 0.6, 0.4 }, model
.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache)
.getValues(), DELTA_THRESHOLD);
// AIMA3e pg. 497
// P<>(Cavity | toothache AND catch) = <0.871, 0.129>
assertArrayEquals(new double[] { 0.8709677419354839, 0.12903225806451615 },
model.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache,
acatch).getValues(), DELTA_THRESHOLD);
// AIMA3e pg. 498
// (13.17)
// P<>(toothache AND catch | Cavity)
// = P<>(toothache | Cavity)P<>(catch | Cavity)
ConjunctiveProposition toothacheAndCatch = new ConjunctiveProposition(atoothache, acatch);
assertArrayEquals(model.posteriorDistribution(toothacheAndCatch,
ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(atoothache, ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(acatch,
ExampleRV.CAVITY_RV)).getValues(),
DELTA_THRESHOLD);
// (13.18)
// P<>(Cavity | toothache AND catch)
// = αP<>(toothache | Cavity)P<>(catch | Cavity)P(Cavity)
assertArrayEquals(model.posteriorDistribution(ExampleRV.CAVITY_RV,
toothacheAndCatch).getValues(),
model.posteriorDistribution(atoothache, ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(acatch,
ExampleRV.CAVITY_RV))
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.normalize().getValues(), DELTA_THRESHOLD);
// (13.19)
// P<>(Toothache, Catch | Cavity)
// = P<>(Toothache | Cavity)P<>(Catch | Cavity)
ConjunctiveProposition toothacheAndCatchRV = new ConjunctiveProposition(ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV);
assertArrayEquals(model.posteriorDistribution(toothacheAndCatchRV,
ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV)
.multiplyByPOS(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV),
ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV).getValues(),
DELTA_THRESHOLD);
// (product rule)
// P<>(Toothache, Catch, Cavity)
// = P<>(Toothache, Catch | Cavity)P<>(Cavity)
assertArrayEquals(model.priorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CATCH_RV, ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(toothacheAndCatchRV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.getValues(), DELTA_THRESHOLD);
// (using 13.19)
// P<>(Toothache, Catch | Cavity)P<>(Cavity)
// = P<>(Toothache | Cavity)P<>(Catch | Cavity)P<>(Cavity)
assertArrayEquals(model.posteriorDistribution(toothacheAndCatchRV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.getValues(),
model.posteriorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV)
.multiplyByPOS(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV)),
ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV).getValues(),
DELTA_THRESHOLD);
//
// P<>(Toothache, Catch, Cavity)
// = P<>(Toothache | Cavity)P<>(Catch | Cavity)P<>(Cavity)
assertArrayEquals(model.priorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CATCH_RV, ExampleRV.CAVITY_RV).getValues(),
model.posteriorDistribution(ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV)
.multiplyByPOS(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV),
ExampleRV.TOOTHACHE_RV, ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV)
.multiplyBy(
model.priorDistribution(ExampleRV.CAVITY_RV))
.getValues(), DELTA_THRESHOLD);
// AIMA3e pg. 496
// General case of Bayes' Rule
// P<>(Y | X) = P<>(X | Y)P<>(Y)/P<>(X)
// Note: Performing in this order -
// P<>(Y | X) = (P<>(Y)P<>(X | Y))/P<>(X)
// as default multiplication of distributions are not commutative (could
// also use pointwiseProductPOS() to specify the order).
assertArrayEquals(model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.TOOTHACHE_RV).getValues(),
model.priorDistribution(ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV))
.divideBy(
model.priorDistribution(ExampleRV.TOOTHACHE_RV))
.getValues(), DELTA_THRESHOLD);
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.CATCH_RV).getValues(),
model.priorDistribution(ExampleRV.CAVITY_RV)
.multiplyBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV))
.divideBy(model.priorDistribution(ExampleRV.CATCH_RV))
.getValues(), DELTA_THRESHOLD);
// General Bayes' Rule conditionalized on background evidence e (13.3)
// P<>(Y | X, e) = P<>(X | Y, e)P<>(Y|e)/P<>(X | e)
// Note: Performing in this order -
// P<>(Y | X, e) = (P<>(Y|e)P<>(X | Y, e)))/P<>(X | e)
// as default multiplication of distributions are not commutative (could
// also use pointwiseProductPOS() to specify the order).
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.TOOTHACHE_RV, acatch).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, acatch)
.multiplyBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV, acatch))
.divideBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV, acatch))
.getValues(), DELTA_THRESHOLD);
//
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.TOOTHACHE_RV, anotcatch).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, anotcatch)
.multiplyBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV,
ExampleRV.CAVITY_RV, anotcatch))
.divideBy(
model.posteriorDistribution(
ExampleRV.TOOTHACHE_RV, anotcatch))
.getValues(), DELTA_THRESHOLD);
//
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.CATCH_RV, atoothache).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, atoothache)
.multiplyBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV, atoothache))
.divideBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
atoothache)).getValues(),
DELTA_THRESHOLD);
assertArrayEquals(
model.posteriorDistribution(ExampleRV.CAVITY_RV,
ExampleRV.CATCH_RV, anottoothache).getValues(),
model.posteriorDistribution(ExampleRV.CAVITY_RV, anottoothache)
.multiplyBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
ExampleRV.CAVITY_RV, anottoothache))
.divideBy(
model.posteriorDistribution(ExampleRV.CATCH_RV,
anottoothache)).getValues(),
DELTA_THRESHOLD);
}
