public virtual ICategoricalDistribution jointDistribution(params IProposition[] propositions)
{
ProbabilityTable d = null;
IProposition conjProp = ProbUtil.constructConjunction(propositions);
ISet <IRandomVariable> vars = CollectionFactory.CreateSet <IRandomVariable>(conjProp.getUnboundScope());
if (vars.Size() > 0)
{
IRandomVariable[] distVars = new IRandomVariable[vars.Size()];
int i = 0;
foreach (IRandomVariable rv in vars)
{
distVars[i] = rv;
++i;
}
ProbabilityTable ud = new ProbabilityTable(distVars);
object[] values = new object[vars.Size()];
CategoricalDistributionIterator di = new CategoricalDistributionIteratorJointDistribution(conjProp, vars, ud, values);
IRandomVariable[] X = conjProp.getScope().ToArray();
bayesInference.Ask(X, new AssignmentProposition[0], bayesNet).iterateOver(di);
d = ud;
}
else
{
// No Unbound Variables, therefore just return
// the singular probability related to the proposition.
d = new ProbabilityTable();
d.setValue(0, prior(propositions));
}
return(d);
}
public ICategoricalDistribution jointDistribution(params IProposition[] propositions)
{
ProbabilityTable d = null;
IProposition conjProp = ProbUtil.constructConjunction(propositions);
ISet <IRandomVariable> vars = CollectionFactory.CreateSet <IRandomVariable>(conjProp.getUnboundScope());
if (vars.Size() > 0)
{
IRandomVariable[] distVars = vars.ToArray();
ProbabilityTable ud = new ProbabilityTable(distVars);
object[] values = new object[vars.Size()];
ProbabilityTable.ProbabilityTableIterator di = new ProbabilityTableIterator(conjProp, ud, values, vars);
distribution.iterateOverTable(di);
d = ud;
}
else
{
// No Unbound Variables, therefore just return
// the singular probability related to the proposition.
d = new ProbabilityTable();
d.setValue(0, prior(propositions));
}
return(d);
}
public virtual ICategoricalDistribution posteriorDistribution(IProposition phi, params IProposition[] evidence)
{
IProposition conjEvidence = ProbUtil.constructConjunction(evidence);
// P(A | B) = P(A AND B)/P(B) - (13.3 AIMA3e)
ICategoricalDistribution dAandB = jointDistribution(phi, conjEvidence);
ICategoricalDistribution dEvidence = jointDistribution(conjEvidence);
ICategoricalDistribution rVal = dAandB.divideBy(dEvidence);
// Note: Need to ensure normalize() is called
// in order to handle the case where an approximate
// algorithm is used (i.e. won't evenly divide
// as will have calculated on separate approximate
// runs). However, this should only be done
// if the all of the evidences scope are bound (if not
// you are returning in essence a set of conditional
// distributions, which you do not want normalized).
bool unboundEvidence = false;
foreach (IProposition e in evidence)
{
if (e.getUnboundScope().Size() > 0)
{
unboundEvidence = true;
break;
}
}
if (!unboundEvidence)
{
rVal.normalize();
}
return(rVal);
}
public ICategoricalDistribution posteriorDistribution(IProposition phi,
params IProposition[] evidence)
{
IProposition conjEvidence = ProbUtil.constructConjunction(evidence);
// P(A | B) = P(A AND B)/P(B) - (13.3 AIMA3e)
ICategoricalDistribution dAandB = jointDistribution(phi, conjEvidence);
ICategoricalDistribution dEvidence = jointDistribution(conjEvidence);
return(dAandB.divideBy(dEvidence));
}
public virtual double posterior(IProposition phi, params IProposition[] evidence)
{
IProposition conjEvidence = ProbUtil.constructConjunction(evidence);
// P(A | B) = P(A AND B)/P(B) - (13.3 AIMA3e)
IProposition aAndB = new ConjunctiveProposition(phi, conjEvidence);
double probabilityOfEvidence = prior(conjEvidence);
if (0 != probabilityOfEvidence)
{
return(prior(aAndB) / probabilityOfEvidence);
}
return(0);
}
public CategoricalDistribution jointDistribution(
params IProposition[] propositions)
{
ProbabilityTable d = null;
IProposition conjProp = ProbUtil
.constructConjunction(propositions);
LinkedHashSet <RandomVariable> vars = new LinkedHashSet <RandomVariable>(
conjProp.getUnboundScope());
if (vars.Count > 0)
{
RandomVariable[] distVars = new RandomVariable[vars.Count];
vars.CopyTo(distVars);
ProbabilityTable ud = new ProbabilityTable(distVars);
Object[] values = new Object[vars.Count];
//ProbabilityTable.Iterator di = new ProbabilityTable.Iterator() {
// public void iterate(Map<RandomVariable, Object> possibleWorld,
// double probability) {
// if (conjProp.holds(possibleWorld)) {
// int i = 0;
// for (RandomVariable rv : vars) {
// values[i] = possibleWorld.get(rv);
// i++;
// }
// int dIdx = ud.getIndex(values);
// ud.setValue(dIdx, ud.getValues()[dIdx] + probability);
// }
// }
//};
//distribution.iterateOverTable(di);
// TODO:
d = ud;
}
else
{
// No Unbound Variables, therefore just return
// the singular probability related to the proposition.
d = new ProbabilityTable();
d.setValue(0, prior(propositions));
}
return(d);
}
public virtual double prior(params IProposition[] phi)
{
// Calculating the prior, therefore no relevant evidence
// just query over the scope of proposition phi in order
// to get a joint distribution for these
IProposition conjunct = ProbUtil.constructConjunction(phi);
IRandomVariable[] X = conjunct.getScope().ToArray();
ICategoricalDistribution d = bayesInference.Ask(X, new AssignmentProposition[0], bayesNet);
// Then calculate the probability of the propositions phi
// be seeing where they hold.
double[] probSum = new double[1];
CategoricalDistributionIterator di = new CategoricalDistributionIteraorPrior(conjunct, probSum);
d.iterateOver(di);
return(probSum[0]);
}
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 ICategoricalDistribution backward(ICategoricalDistribution b_kp2t, ICollection <AssignmentProposition> e_kp1)
{
ICategoricalDistribution b_kp1t = new ProbabilityTable(b_kp2t.getFor());
// Set up required working variables
IProposition[] props = new IProposition[b_kp1t.getFor().Size()];
int i = 0;
foreach (IRandomVariable rv in b_kp1t.getFor())
{
IRandomVariable prv = tToTm1StateVarMap.Get(rv);
props[i] = new RandVar(prv.getName(), prv.getDomain());
++i;
}
IProposition Xk = ProbUtil.constructConjunction(props);
AssignmentProposition[] ax_kp1 = new AssignmentProposition[tToTm1StateVarMap.Size()];
IMap <IRandomVariable, AssignmentProposition> x_kp1VarAssignMap = CollectionFactory.CreateInsertionOrderedMap <IRandomVariable, AssignmentProposition>();
i = 0;
foreach (IRandomVariable rv in b_kp1t.getFor())
{
ax_kp1[i] = new AssignmentProposition(rv, "<Dummy Value>");
x_kp1VarAssignMap.Put(rv, ax_kp1[i]);
++i;
}
IProposition x_kp1 = ProbUtil.constructConjunction(ax_kp1);
props = e_kp1.ToArray();
IProposition pe_kp1 = ProbUtil.constructConjunction(props);
// ∑<sub>x<sub>k+1</sub></sub>
CategoricalDistributionIterator ib_kp2t = new CategoricalDistributionIteratorImpl2(x_kp1VarAssignMap,
sensorModel, transitionModel, b_kp1t, pe_kp1, Xk, x_kp1);
b_kp2t.iterateOver(ib_kp2t);
return(b_kp1t);
}
/**
* The particle filtering algorithm implemented as a recursive update
* operation with state (the set of samples).
*
* @param e
* <b>e</b>, the new incoming evidence
* @return a vector of samples of size N, where each sample is a vector of
* assignment propositions for the X_1 state variables, which is
* intended to represent the generated sample for time t.
*/
public AssignmentProposition[][] particleFiltering(AssignmentProposition[] e)
{
// local variables: W, a vector of weights of size N
double[] W = new double[N];
// for i = 1 to N do
for (int i = 0; i < N; ++i)
{
/* step 1 */
// S[i] <- sample from <b>P</b>(<b>X</b><sub>1</sub> |
// <b>X</b><sub>0</sub> = S[i])
sampleFromTransitionModel(i);
/* step 2 */
// W[i] <- <b>P</b>(<b>e</b> | <b>X</b><sub>1</sub> = S[i])
W[i] = sensorModel.posterior(ProbUtil.constructConjunction(e), S_tp1[i]);
}
/* step 3 */
// S <- WEIGHTED-SAMPLE-WITH-REPLACEMENT(N, S, W)
S = weightedSampleWithReplacement(N, S, W);
// return S
return(S);
}
public double prior(params IProposition[] phi)
{
return(probabilityOf(ProbUtil.constructConjunction(phi)));
}