/**
* Calculate the probability distribution for <b>P</b>(X<sub>i</sub> |
* mb(X<sub>i</sub>)), where mb(X<sub>i</sub>) is the Markov Blanket of
* X<sub>i</sub>. The probability of a variable given its Markov blanket is
* proportional to the probability of the variable given its parents times
* the probability of each child given its respective parents (see equation
* 14.12 pg. 538 AIMA3e):<br>
* <br>
* P(x'<sub>i</sub>|mb(Xi)) =
* αP(x'<sub>i</sub>|parents(X<sub>i</sub>)) *
* ∏<sub>Y<sub>j</sub> ∈ Children(X<sub>i</sub>)</sub>
* P(y<sub>j</sub>|parents(Y<sub>j</sub>))
*
* @param Xi
* a Node from a Bayesian network for the Random Variable
* X<sub>i</sub>.
* @param event
* comprising assignments for the Markov Blanket X<sub>i</sub>.
* @return a random sample from <b>P</b>(X<sub>i</sub> | mb(X<sub>i</sub>))
*/
public static double[] mbDistribution(Node Xi,
Map <RandomVariable, Object> evt)
{
FiniteDomain fd = (FiniteDomain)Xi.getRandomVariable().getDomain();
double[] X = new double[fd.size()];
for (int i = 0; i < fd.size(); i++)
{
// P(x'<sub>i</sub>|mb(Xi)) =
// αP(x'<sub>i</sub>|parents(X<sub>i</sub>)) *
// ∏<sub>Y<sub>j</sub> ∈ Children(X<sub>i</sub>)</sub>
// P(y<sub>j</sub>|parents(Y<sub>j</sub>))
double cprob = 1.0;
foreach (Node Yj in Xi.getChildren())
{
cprob *= Yj.getCPD().getValue(
getEventValuesForXiGivenParents(Yj, evt));
}
X[i] = Xi.getCPD()
.getValue(
getEventValuesForXiGivenParents(Xi,
fd.getValueAt(i), evt))
* cprob;
}
return(Util.normalize(X));
}
/**
* Calculate the probability distribution for <b>P</b>(X<sub>i</sub> |
* mb(X<sub>i</sub>)), where mb(X<sub>i</sub>) is the Markov Blanket of
* X<sub>i</sub>. The probability of a variable given its Markov blanket is
* proportional to the probability of the variable given its parents times
* the probability of each child given its respective parents (see equation
* 14.12 pg. 538 AIMA3e):<br>
* <br>
* P(x'<sub>i</sub>|mb(Xi)) =
* αP(x'<sub>i</sub>|parents(X<sub>i</sub>)) *
* ∏<sub>Y<sub>j</sub> ∈ Children(X<sub>i</sub>)</sub>
* P(y<sub>j</sub>|parents(Y<sub>j</sub>))
*
* @param Xi
* a Node from a Bayesian network for the Random Variable
* X<sub>i</sub>.
* @param event
* comprising assignments for the Markov Blanket X<sub>i</sub>.
* @return a random sample from <b>P</b>(X<sub>i</sub> | mb(X<sub>i</sub>))
*/
public static double[] mbDistribution(INode Xi, IMap <IRandomVariable, object> even)
{
IFiniteDomain fd = (IFiniteDomain)Xi.GetRandomVariable().getDomain();
double[] X = new double[fd.Size()];
/**
* As we iterate over the domain of a ramdom variable corresponding to Xi
* it is necessary to make the modified values of the variable visible
* to the child nodes of Xi in the computation of the markov blanket
* probabilities.
*/
//Copy contents of event to generatedEvent so as to leave event untouched
IMap <IRandomVariable, object> generatedEvent = CollectionFactory.CreateInsertionOrderedMap <IRandomVariable, object>();
foreach (var entry in even)
{
generatedEvent.Put(entry.GetKey(), entry.GetValue());
}
for (int i = 0; i < fd.Size(); ++i)
{
/** P(x'<sub>i</sub>|mb(Xi)) =
* αP(x'<sub>i</sub>|parents(X<sub>i</sub>)) *
* ∏<sub>Y<sub>j</sub> ∈ Children(X<sub>i</sub>)</sub>
* P(y<sub>j</sub>|parents(Y<sub>j</sub>))
*/
generatedEvent.Put(Xi.GetRandomVariable(), fd.GetValueAt(i));
double cprob = 1.0;
foreach (INode Yj in Xi.GetChildren())
{
cprob *= Yj.GetCPD().GetValue(
getEventValuesForXiGivenParents(Yj, generatedEvent));
}
X[i] = Xi.GetCPD()
.GetValue(
getEventValuesForXiGivenParents(Xi,
fd.GetValueAt(i), even))
* cprob;
}
return(Util.normalize(X));
}
