//
// START-ForwardBackwardInference
public virtual ICollection <ICategoricalDistribution> forwardBackward(ICollection <ICollection <AssignmentProposition> > ev,
ICategoricalDistribution prior)
{
// local variables: fv, a vector of forward messages for steps 0,...,t
ICollection <Matrix> fv = CollectionFactory.CreateQueue <Matrix>();
// b, a representation of the backward message, initially all 1s
Matrix b = hmm.createUnitMessage();
// sv, a vector of smoothed estimates for steps 1,...,t
ICollection <Matrix> sv = CollectionFactory.CreateQueue <Matrix>();
// fv[0] <- prior
fv.Add(hmm.convert(prior));
// for i = 1 to t do
for (int i = 0; i < ev.Size(); ++i)
{
// fv[i] <- FORWARD(fv[i-1], ev[i])
fv.Add(forward(fv.Get(i), hmm.getEvidence(ev.Get(i))));
}
// for i = t downto 1 do
for (int i = ev.Size() - 1; i >= 0; i--)
{
// sv[i] <- NORMALIZE(fv[i] * b)
sv.Insert(0, hmm.normalize(fv.Get(i + 1).ArrayTimes(b)));
// b <- BACKWARD(b, ev[i])
b = backward(b, hmm.getEvidence(ev.Get(i)));
}
// return sv
return(hmm.convert(sv));
}
/**
* Algorithm for smoothing with a fixed time lag of d steps, implemented as
* an online algorithm that outputs the new smoothed estimate given the
* observation for a new time step.
*
* @param et
* the current evidence from time step t
* @return a distribution over <b>X</b><sub>t-d</sub>
*/
public ICategoricalDistribution fixedLagSmoothing(ICollection <AssignmentProposition> et)
{
// local variables: <b>O</b><sub>t-d</sub>, <b>O</b><sub>t</sub>,
// diagonal matrices containing the sensor model information
Matrix O_tmd, O_t;
// add e<sub>t</sub> to the end of e<sub>t-d:t</sub>
e_tmd_to_t.Add(hmm.getEvidence(et));
// <b>O</b><sub>t</sub> <- diagonal matrix containing
// <b>P</b>(e<sub>t</sub> | X<sub>t</sub>)
O_t = e_tmd_to_t.Get(e_tmd_to_t.Size() - 1);
// if t > d then
if (t > d)
{
// remove e<sub>t-d-1</sub> from the beginning of e<sub>t-d:t</sub>
e_tmd_to_t.RemoveAt(0);
// <b>O</b><sub>t-d</sub> <- diagonal matrix containing
// <b>P</b>(e<sub>t-d</sub> | X<sub>t-d</sub>)
O_tmd = e_tmd_to_t.Get(0);
// <b>f</b> <- FORWARD(<b>f</b>, e<sub>t-d</sub>)
f = forward(f, O_tmd);
// <b>B</b> <-
// <b>O</b><sup>-1</sup><sub>t-d</sub><b>B</b><b>T</b><b>O</b><sub>t</sub>
B = O_tmd.Inverse().Times(hmm.getTransitionModel().Inverse()).Times(B).Times(hmm.getTransitionModel()).Times(O_t);
}
else
{
// else <b>B</b> <- <b>BTO</b><sub>t</sub>
B = B.Times(hmm.getTransitionModel()).Times(O_t);
}
// if t > d then return NORMALIZE(<b>f</b> * <b>B1</b>) else return null
ICategoricalDistribution rVal = null;
if (t > d)
{
rVal = hmm.convert(hmm.normalize(f.ArrayTimes(B.Times(unitMessage))));
}
// t <- t + 1
t = t + 1;
return(rVal);
}