package aima.core.probability.bayes.approx;
import java.util.LinkedHashMap;
import java.util.Map;
import aima.core.probability.FiniteProbabilityModel;
import aima.core.probability.RandomVariable;
import aima.core.probability.bayes.DynamicBayesianNetwork;
import aima.core.probability.bayes.exact.EliminationAsk;
import aima.core.probability.bayes.model.FiniteBayesModel;
import aima.core.probability.domain.FiniteIntegerDomain;
import aima.core.probability.proposition.AssignmentProposition;
import aima.core.probability.util.ProbUtil;
import aima.core.probability.util.RandVar;
import aima.core.util.JavaRandomizer;
import aima.core.util.Randomizer;
import aima.core.util.Util;
/**
* Artificial Intelligence A Modern Approach (3rd Edition): page 598.<br>
* <br>
*
* <pre>
* function PARTICLE-FILTERING(<b>e</b>, N, dbn) returns a set of samples for the next time step
* inputs: <b>e</b>, the new incoming evidence
* N, the number of samples to be maintained
* dbn, a DBN with prior <b>P</b>(<b>X</b><sub>0</sub>), transition model <b>P</b>(<b>X</b><sub>1</sub> | <b>X</b><sub>0</sub>), sensor model <b>P</b>(<b>E</b><sub>1</sub> | <b>X</b><sub>1</sub>)
* persistent: S, a vector of samples of size N, initially generated from <b>P</b>(<b>X</b><sub>0</sub>)
* local variables: W, a vector of weights of size N
*
* for i = 1 to N do
* S[i] <- sample from <b>P</b>(<b>X</b><sub>1</sub> | <b>X</b><sub>0</sub> = S[i]) /* step 1
* W[i] <- <b>P</b>(<b>e</b> | <b>X</b><sub>1</sub> = S[i]) /* step 2
* S <- WEIGHTED-SAMPLE-WITH-REPLACEMENT(N, S, W) /* step 3
* return S
* </pre>
*
* Figure 15.17 The particle filtering algorithm implemented as a recursive
* update operation with state (the set of samples). Each of the sampling
* operations involves sampling the relevant slice variables in topological
* order, much as in PRIOR-SAMPLE. The WEIGHTED-SAMPLE-WITH-REPLACEMENT
* operation can be implemented to run in O(N) expected time. The step numbers
* refer to the description in the text.
*
* <ol>
* <li>Each sample is propagated forward by sampling the next state value
* <b>x</b><sub>t+1</sub> given the current value <b>x</b><sub>t</sub> for the
* sample, based on the transition model <b>P</b>(<b>X</b><sub>t+1</sub> |
* <b>x</b><sub>t</sub>).</li>
* <li>Each sample is weighted by the likelihood it assigns to the new evidence,
* P(<b>e</b><sub>t+1</sub> | <b>x</b><sub>t+1</sub>).</li>
* <li>The population is resampled to generate a new population of N samples.
* Each new sample is selected from the current population; the probability that
* a particular sample is selected is proportional to its weight. The new
* samples are unweighted.</li>
* </ol>
*
* @author Ciaran O'Reilly
* @author Ravi Mohan
*
*/
public class ParticleFiltering {
private int N = 0;
private DynamicBayesianNetwork dbn = null;
private AssignmentProposition[][] S = new AssignmentProposition[0][0];
//
private Randomizer randomizer = null;
private PriorSample priorSampler = null;
private AssignmentProposition[][] S_tp1 = new AssignmentProposition[0][0];
private FiniteProbabilityModel sensorModel = null;
private RandomVariable sampleIndexes = null;
/**
* Construct a Particle Filtering instance.
*
* @param N
* the number of samples to be maintained
* @param dbn
* a DBN with prior <b>P</b>(<b>X</b><sub>0</sub>), transition
* model <b>P</b>(<b>X</b><sub>1</sub> | <b>X</b><sub>0</sub>),
* sensor model <b>P</b>(<b>E</b><sub>1</sub> |
* <b>X</b><sub>1</sub>)
*/
public ParticleFiltering(int N, DynamicBayesianNetwork dbn) {
this(N, dbn, new JavaRandomizer());
}
/**
* Construct a Particle Filtering instance.
*
* @param N
* the number of samples to be maintained
* @param dbn
* a DBN with prior <b>P</b>(<b>X</b><sub>0</sub>), transition
* model <b>P</b>(<b>X</b><sub>1</sub> | <b>X</b><sub>0</sub>),
* sensor model <b>P</b>(<b>E</b><sub>1</sub> |
* <b>X</b><sub>1</sub>)
* @param randomizer
* a Randomizer to be used for sampling purposes.
*/
public ParticleFiltering(int N, DynamicBayesianNetwork dbn,
Randomizer randomizer) {
this.randomizer = randomizer;
this.priorSampler = new PriorSample(this.randomizer);
initPersistent(N, dbn);
}
/**
* 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;
}
/**
* Reset this instances persistent variables to be used between called to
* particleFiltering().
*
* @param N
* the number of samples to be maintained
* @param dbn
* a DBN with prior <b>P</b>(<b>X</b><sub>0</sub>), transition
* model <b>P</b>(<b>X</b><sub>1</sub> | <b>X</b><sub>0</sub>),
* sensor model <b>P</b>(<b>E</b><sub>1</sub> |
* <b>X</b><sub>1</sub>)
*/
public void initPersistent(int N, DynamicBayesianNetwork dbn) {
this.N = N;
this.dbn = dbn;
// persistent: S, a vector of samples of size N, initially generated
// from <b>P</b>(<b>X</b><sub>0</sub>)
S = new AssignmentProposition[N][this.dbn.getX_0().size()];
S_tp1 = new AssignmentProposition[N][this.dbn.getX_0().size()];
Integer[] indexes = new Integer[N];
for (int i = 0; i < N; i++) {
indexes[i] = i;
Map<RandomVariable, Object> sample = priorSampler
.priorSample(this.dbn.getPriorNetwork());
int idx = 0;
for (Map.Entry<RandomVariable, Object> sa : sample.entrySet()) {
S[i][idx] = new AssignmentProposition(this.dbn.getX_0_to_X_1()
.get(sa.getKey()), sa.getValue());
S_tp1[i][idx] = new AssignmentProposition(this.dbn
.getX_0_to_X_1().get(sa.getKey()), sa.getValue());
idx++;
}
}
sensorModel = new FiniteBayesModel(dbn, new EliminationAsk());
sampleIndexes = new RandVar("SAMPLE_INDEXES", new FiniteIntegerDomain(
indexes));
}
//
// PRIVATE METHODS
//
private void sampleFromTransitionModel(int i) {
// x <- an event initialized with S[i]
Map<RandomVariable, Object> x = new LinkedHashMap<RandomVariable, 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
for (RandomVariable X1_i : 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()));
}
}
/**
* The population is re-sampled to generate a new population of N samples.
* Each new sample is selected from the current population; the probability
* that a particular sample is selected is proportional to its weight. The
* new samples are un-weighted.
*
* @param N
* the number of samples
* @param S
* 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 sample for time t
* @param W
* a vector of weights of size N
*
* @return a new vector of samples of size N sampled from S based on W
*/
private AssignmentProposition[][] weightedSampleWithReplacement(int N,
AssignmentProposition[][] S, double[] W) {
AssignmentProposition[][] newS = new AssignmentProposition[N][this.dbn
.getX_0().size()];
double[] normalizedW = Util.normalize(W);
for (int i = 0; i < N; i++) {
int sample = (Integer) ProbUtil.sample(randomizer.nextDouble(),
sampleIndexes, normalizedW);
for (int idx = 0; idx < S_tp1[i].length; idx++) {
AssignmentProposition ap = S_tp1[sample][idx];
newS[i][idx] = new AssignmentProposition(ap.getTermVariable(),
ap.getValue());
}
}
return newS;
}
}