// function WEIGHTED-SAMPLE(bn, e) returns an event and a weight
/**
* The WEIGHTED-SAMPLE function in Figure 14.15.
*
* @param e
* observed values for variables E
* @param bn
* a Bayesian network specifying joint distribution
* <b>P</b>(X<sub>1</sub>,...,X<sub>n</sub>)
* @return return <b>x</b>, w - an event with its associated weight.
*/
public Pair <IMap <IRandomVariable, object>, double> weightedSample(IBayesianNetwork bn, AssignmentProposition[] e)
{
// w <- 1;
double w = 1.0;
// <b>x</b> <- an event with n elements initialized from e
IMap <IRandomVariable, object> x = CollectionFactory.CreateInsertionOrderedMap <IRandomVariable, object>();
foreach (AssignmentProposition ap in e)
{
x.Put(ap.getTermVariable(), ap.getValue());
}
// foreach variable X<sub>i</sub> in X<sub>1</sub>,...,X<sub>n</sub> do
foreach (IRandomVariable Xi in bn.GetVariablesInTopologicalOrder())
{
// if X<sub>i</sub> is an evidence variable with value x<sub>i</sub>
// in e
if (x.ContainsKey(Xi))
{
// then w <- w * P(X<sub>i</sub> = x<sub>i</sub> |
// parents(X<sub>i</sub>))
w *= bn.GetNode(Xi)
.GetCPD()
.GetValue(ProbUtil.getEventValuesForXiGivenParents(bn.GetNode(Xi), x));
}
else
{
// else <b>x</b>[i] <- a random sample from
// <b>P</b>(X<sub>i</sub> | parents(X<sub>i</sub>))
x.Put(Xi, ProbUtil.randomSample(bn.GetNode(Xi), x, randomizer));
}
}
// return <b>x</b>, w
return(new Pair <IMap <IRandomVariable, object>, double>(x, w));
}
private void sampleFromTransitionModel(int i)
{
// x <- an event initialized with S[i]
IMap <IRandomVariable, object> x = CollectionFactory.CreateInsertionOrderedMap <IRandomVariable, object>();
for (int n = 0; n < S[i].Length; n++)
{
AssignmentProposition x1 = S[i][n];
x.Put(this.dbn.GetX_1_to_X_0().Get(x1.getTermVariable()), x1.getValue());
}
// foreach variable X<sub>1<sub>i</sub></sub> in
// X<sub>1<sub>1</sub></sub>,...,X<sub>1<sub>n<</sub>/sub> do
foreach (IRandomVariable X1_i in dbn.GetX_1_VariablesInTopologicalOrder())
{
// x1[i] <- a random sample from
// <b>P</b>(X<sub>1<sub>i</sub></sub> |
// parents(X<sub>1<sub>i</sub></sub>))
x.Put(X1_i, ProbUtil.randomSample(dbn.GetNode(X1_i), x, randomizer));
}
// S[i] <- sample from <b>P</b>(<b>X</b><sub>1</sub> |
// <b>X</b><sub>0</sub> = S[i])
for (int n = 0; n < S_tp1[i].Length; n++)
{
AssignmentProposition x1 = S_tp1[i][n];
x1.setValue(x.Get(x1.getTermVariable()));
}
}
// function GIBBS-ASK(X, e, bn, N) returns an estimate of <b>P</b>(X|e)
/**
* The GIBBS-ASK algorithm in Figure 14.16. For answering queries given
* evidence in a Bayesian Network.
*
* @param X
* the query variables
* @param e
* observed values for variables E
* @param bn
* a Bayesian network specifying joint distribution
* <b>P</b>(X<sub>1</sub>,...,X<sub>n</sub>)
* @param Nsamples
* the total number of samples to be generated
* @return an estimate of <b>P</b>(X|e)
*/
public CategoricalDistribution gibbsAsk(RandomVariable[] X,
AssignmentProposition[] e, BayesianNetwork bn, int Nsamples)
{
// local variables: <b>N</b>, a vector of counts for each value of X,
// initially zero
double[] N = new double[ProbUtil
.expectedSizeOfCategoricalDistribution(X)];
// Z, the nonevidence variables in bn
Set <RandomVariable> Z = new Set <RandomVariable>(
bn.getVariablesInTopologicalOrder());
foreach (AssignmentProposition ap in e)
{
Z.Remove(ap.getTermVariable());
}
// <b>x</b>, the current state of the network, initially copied from e
Map <RandomVariable, Object> x = new LinkedHashMap <RandomVariable, Object>();
foreach (AssignmentProposition ap in e)
{
x.Add(ap.getTermVariable(), ap.getValue());
}
// initialize <b>x</b> with random values for the variables in Z
foreach (RandomVariable Zi in
Z)
{
x.put(Zi, ProbUtil.randomSample(bn.getNode(Zi), x, randomizer));
}
// for j = 1 to N do
for (int j = 0; j < Nsamples; j++)
{
// for each Z<sub>i</sub> in Z do
foreach (RandomVariable Zi in
Z)
{
// set the value of Z<sub>i</sub> in <b>x</b> by sampling from
// <b>P</b>(Z<sub>i</sub>|mb(Z<sub>i</sub>))
x.put(Zi,
ProbUtil.mbRandomSample(bn.getNode(Zi), x, randomizer));
}
// Note: moving this outside the previous for loop,
// as described in fig 14.6, as will only work
// correctly in the case of a single query variable X.
// However, when multiple query variables, rare events
// will get weighted incorrectly if done above. In case
// of single variable this does not happen as each possible
// value gets * |Z| above, ending up with the same ratios
// when normalized (i.e. its still more efficient to place
// outside the loop).
//
// <b>N</b>[x] <- <b>N</b>[x] + 1
// where x is the value of X in <b>x</b>
N[ProbUtil.indexOf(X, x)] += 1.0;
}
// return NORMALIZE(<b>N</b>)
return(new ProbabilityTable(N, X).normalize());
}
// function PRIOR-SAMPLE(bn) returns an event sampled from the prior
// specified by bn
/**
* The PRIOR-SAMPLE algorithm in Figure 14.13. A sampling algorithm that
* generates events from a Bayesian network. Each variable is sampled
* according to the conditional distribution given the values already
* sampled for the variable's parents.
*
* @param bn
* a Bayesian network specifying joint distribution
* <b>P</b>(X<sub>1</sub>,...,X<sub>n</sub>)
* @return an event sampled from the prior specified by bn
*/
public IMap <IRandomVariable, object> priorSample(IBayesianNetwork bn)
{
// x <- an event with n elements
IMap <IRandomVariable, object> x = CollectionFactory.CreateInsertionOrderedMap <IRandomVariable, object>();
// foreach variable X<sub>i</sub> in X<sub>1</sub>,...,X<sub>n</sub> do
foreach (IRandomVariable Xi in bn.GetVariablesInTopologicalOrder())
{
// x[i] <- a random sample from
// <b>P</b>(X<sub>i</sub> | parents(X<sub>i</sub>))
x.Put(Xi, ProbUtil.randomSample(bn.GetNode(Xi), x, randomizer));
}
// return x
return(x);
}
// function PRIOR-SAMPLE(bn) returns an event sampled from the prior
// specified by bn
/**
* The PRIOR-SAMPLE algorithm in Figure 14.13. A sampling algorithm that
* generates events from a Bayesian network. Each variable is sampled
* according to the conditional distribution given the values already
* sampled for the variable's parents.
*
* @param bn
* a Bayesian network specifying joint distribution
* <b>P</b>(X<sub>1</sub>,...,X<sub>n</sub>)
* @return an event sampled from the prior specified by bn
*/
public Map <RandomVariable, Object> priorSample(BayesianNetwork bn)
{
// x <- an event with n elements
Map <RandomVariable, Object> x = new LinkedHashMap <RandomVariable, Object>();
// foreach variable X<sub>i</sub> in X<sub>1</sub>,...,X<sub>n</sub> do
foreach (RandomVariable Xi in bn.getVariablesInTopologicalOrder())
{
// x[i] <- a random sample from
// <b>P</b>(X<sub>i</sub> | parents(X<sub>i</sub>))
x.Add(Xi, ProbUtil.randomSample(bn.getNode(Xi), x, randomizer));
}
// return x
return(x);
}
