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#ifndef OPENGM_SWENDSENWANG_HXX
#define OPENGM_SWENDSENWANG_HXX
#include <vector>
#include <set>
#include <stack>
#include <cmath>
#include <algorithm>
#include <iostream>
#include "opengm/opengm.hxx"
#include "opengm/operations/adder.hxx"
#include "opengm/operations/multiplier.hxx"
#include "opengm/operations/minimizer.hxx"
#include "opengm/operations/maximizer.hxx"
#include "opengm/utilities/random.hxx"
#include "opengm/utilities/indexing.hxx"
#include "opengm/datastructures/randomaccessset.hxx"
#include "opengm/datastructures/partition.hxx"
#include "opengm/inference/movemaker.hxx"
#include "opengm/inference/visitors/visitor.hxx"
#include "opengm/functions/view_convert_function.hxx"
namespace opengm {
/// \cond suppress doxygen
namespace detail_swendsenwang {
template<class OPERATOR, class ACCUMULATOR, class PROBABILITY>
struct ValueToProbability;
template<class PROBABILITY>
struct ValueToProbability<Multiplier, Maximizer, PROBABILITY>
{
typedef PROBABILITY ProbabilityType;
template<class T>
static ProbabilityType convert(const T x)
{ return static_cast<ProbabilityType>(x); }
};
template<class PROBABILITY>
struct ValueToProbability<Adder, Minimizer, PROBABILITY>
{
typedef PROBABILITY ProbabilityType;
template<class T>
static ProbabilityType convert(const T x)
{ return static_cast<ProbabilityType>(std::exp(-x)); }
};
}
/// \endcond no longer suppress doxygen
/// \brief Visitor
template<class SW>
class SwendsenWangEmptyVisitor {
public:
typedef SW SwendsenWangType;
void operator()(const SwendsenWangType&, const size_t, const size_t,
const bool, const bool) const;
};
/// \brief Visitor
template<class SW>
class SwendsenWangVerboseVisitor
{
public:
typedef SW SwendsenWangType;
void operator()(const SwendsenWangType&, const size_t, const size_t,
const bool, const bool) const;
};
/// \brief Visitor
template<class SW>
class SwendsenWangMarginalVisitor {
public:
typedef SW SwendsenWangType;
typedef typename SwendsenWangType::ValueType ValueType;
typedef typename SwendsenWangType::GraphicalModelType GraphicalModelType;
typedef typename GraphicalModelType::IndependentFactorType IndependentFactorType;
// construction
SwendsenWangMarginalVisitor();
SwendsenWangMarginalVisitor(const GraphicalModelType&);
void assign(const GraphicalModelType&);
// manipulation
template<class VariableIndexIterator>
size_t addMarginal(VariableIndexIterator, VariableIndexIterator);
size_t addMarginal(const size_t);
void operator()(const SwendsenWangType&, const size_t, const size_t,
const bool, const bool);
// query
size_t numberOfSamples() const;
size_t numberOfAcceptedSamples() const;
size_t numberOfRejectedSamples() const;
size_t numberOfMarginals() const;
const IndependentFactorType& marginal(const size_t) const;
private:
const GraphicalModelType* gm_;
size_t numberOfSamples_;
size_t numberOfAcceptedSamples_;
size_t numberOfRejectedSamples_;
std::vector<IndependentFactorType> marginals_;
std::vector<typename GraphicalModelType::LabelType> stateCache_;
};
/// \brief Generalized Swendsen-Wang sampling\n\n
/// A. Barbu, S. Zhu, "Generalizing swendsen-wang to sampling arbitrary posterior probabilities", PAMI 27:1239-1253, 2005
///
/// \ingroup inference
template<class GM, class ACC>
class SwendsenWang
: public Inference<GM, ACC> {
public:
typedef GM GraphicalModelType;
typedef ACC AccumulationType;
OPENGM_GM_TYPE_TYPEDEFS;
typedef double ProbabilityType;
typedef SwendsenWangEmptyVisitor<SwendsenWang<GM, ACC> > EmptyVisitorType;
typedef SwendsenWangVerboseVisitor<SwendsenWang<GM, ACC> > VerboseVisitorType;
typedef TimingVisitor<SwendsenWang<GM, ACC> > TimingVisitorType;
struct Parameter
{
Parameter
(
const size_t maxNumberOfSamplingSteps = 1e5,
const size_t numberOfBurnInSteps = 1e5,
ProbabilityType lowestAllowedProbability = 1e-6,
const std::vector<LabelType>& initialState = std::vector<LabelType>()
)
: maxNumberOfSamplingSteps_(maxNumberOfSamplingSteps),
numberOfBurnInSteps_(numberOfBurnInSteps),
lowestAllowedProbability_(lowestAllowedProbability),
initialState_(initialState)
{}
size_t maxNumberOfSamplingSteps_;
size_t numberOfBurnInSteps_;
ProbabilityType lowestAllowedProbability_;
std::vector<LabelType> initialState_;
};
SwendsenWang(const GraphicalModelType&, const Parameter& param = Parameter());
virtual std::string name() const;
virtual const GraphicalModelType& graphicalModel() const;
virtual void reset();
virtual InferenceTermination infer();
template<class VISITOR>
InferenceTermination infer(VISITOR&);
virtual InferenceTermination arg(std::vector<LabelType>&, const size_t = 1) const;
LabelType markovState(const size_t) const;
ValueType markovValue() const;
LabelType currentBestState(const size_t) const;
ValueType currentBestValue() const;
private:
void computeEdgeProbabilities();
void cluster(Partition<size_t>&) const;
template<bool BURNED_IN, class VARIABLE_ITERATOR, class STATE_ITERATOR>
bool move(VARIABLE_ITERATOR, VARIABLE_ITERATOR, STATE_ITERATOR);
Parameter parameter_;
const GraphicalModelType& gm_;
Movemaker<GraphicalModelType> movemaker_;
std::vector<RandomAccessSet<size_t> > variableAdjacency_;
std::vector<std::vector<ProbabilityType> > edgeProbabilities_;
std::vector<LabelType> currentBestState_;
ValueType currentBestValue_;
};
template<class GM, class ACC>
inline
SwendsenWang<GM, ACC>::SwendsenWang
(
const typename SwendsenWang<GM, ACC>::GraphicalModelType& gm,
const typename SwendsenWang<GM, ACC>::Parameter& param
)
: parameter_(param),
gm_(gm),
movemaker_(param.initialState_.size() == gm.numberOfVariables() ? Movemaker<GM>(gm, param.initialState_.begin()) : Movemaker<GM>(gm)),
variableAdjacency_(gm.numberOfVariables()),
edgeProbabilities_(gm.numberOfVariables()),
currentBestState_(gm.numberOfVariables()),
currentBestValue_(movemaker_.value())
{
if(parameter_.initialState_.size() != 0 && parameter_.initialState_.size() != gm.numberOfVariables()) {
throw RuntimeError("The size of the initial state does not match the number of variables.");
}
gm.variableAdjacencyList(variableAdjacency_);
for(size_t j=0; j<gm_.numberOfVariables(); ++j) {
edgeProbabilities_[j].resize(variableAdjacency_[j].size());
}
computeEdgeProbabilities();
}
template<class GM, class ACC>
inline void
SwendsenWang<GM, ACC>::reset()
{
if(parameter_.initialState_.size() == gm_.numberOfVariables()) {
movemaker_.initialize(parameter_.initialState_.begin());
currentBestState_.assign(parameter_.initialState_.begin(),parameter_.initialState_.end());
}
else if(parameter_.initialState_.size() != 0) {
throw RuntimeError("The size of the initial state does not match the number of variables.");
}
else{
movemaker_.reset();
std::fill(currentBestState_.begin(),currentBestState_.end(),0);
}
currentBestValue_ = movemaker_.value();
computeEdgeProbabilities();
}
template<class GM, class ACC>
inline std::string
SwendsenWang<GM, ACC>::name() const
{
return "SwendsenWang";
}
template<class GM, class ACC>
inline const typename SwendsenWang<GM, ACC>::GraphicalModelType&
SwendsenWang<GM, ACC>::graphicalModel() const
{
return gm_;
}
template<class GM, class ACC>
template<class VISITOR>
InferenceTermination
SwendsenWang<GM, ACC>::infer
(
VISITOR& visitor
)
{
Partition<size_t> partition(gm_.numberOfVariables());
std::vector<size_t> representatives(gm_.numberOfVariables());
std::vector<bool> visited(gm_.numberOfVariables());
std::stack<size_t> stack;
std::vector<size_t> variablesInCluster;
std::vector<size_t> variablesAroundCluster;
for(size_t j=0; j<parameter_.numberOfBurnInSteps_ + parameter_.maxNumberOfSamplingSteps_; ++j) {
// cluster the variable adjacency graph by randomly removing edges
cluster(partition);
// draw one cluster at random
partition.representatives(representatives.begin());
RandomUniform<size_t> randomNumberGeneratorCluster(0, partition.numberOfSets());
const size_t representative = representatives[randomNumberGeneratorCluster()];
// collect all variables in and around the drawn cluster
variablesInCluster.clear();
variablesAroundCluster.clear();
visited[representative] = true;
stack.push(representative);
while(!stack.empty()) {
const size_t variable = stack.top();
stack.pop();
variablesInCluster.push_back(variable);
for(size_t k=0; k<variableAdjacency_[variable].size(); ++k) {
const size_t adjacentVariable = variableAdjacency_[variable][k];
if(!visited[adjacentVariable]) {
visited[adjacentVariable] = true;
if(partition.find(adjacentVariable) == representative) { // if in cluster
stack.push(adjacentVariable);
}
else {
variablesAroundCluster.push_back(adjacentVariable);
}
}
}
}
// clean vector visited
for(size_t k=0; k<variablesInCluster.size(); ++k) {
visited[variablesInCluster[k]] = false;
}
for(size_t k=0; k<variablesAroundCluster.size(); ++k) {
visited[variablesAroundCluster[k]] = false;
}
// assertion testing
if(!NO_DEBUG) {
for(size_t k=0; k<visited.size(); ++k) {
OPENGM_ASSERT(!visited[k]);
}
for(size_t k=0; k<variablesInCluster.size(); ++k) {
OPENGM_ASSERT(gm_.numberOfLabels(variablesInCluster[k]) == gm_.numberOfLabels(representative));
}
}
// draw a new label at random
RandomUniform<size_t> randomNumberGeneratorState(0, gm_.numberOfLabels(representative));
size_t targetLabel = randomNumberGeneratorState();
std::vector<size_t> targetLabels(variablesInCluster.size(), targetLabel); // TODO add simpler function to movemaker
if(j < parameter_.numberOfBurnInSteps_) {
move<false>(variablesInCluster.begin(), variablesInCluster.end(), targetLabels.begin());
visitor(*this, j, variablesInCluster.size(), true, true);
continue;
}
// evaluate probability density function
const ProbabilityType currentPDF =
detail_swendsenwang::ValueToProbability<OperatorType, AccumulationType, ProbabilityType>::convert
(movemaker_.value());
const ProbabilityType targetPDF =
detail_swendsenwang::ValueToProbability<OperatorType, AccumulationType, ProbabilityType>::convert
(movemaker_.valueAfterMove(variablesInCluster.begin(), variablesInCluster.end(), targetLabels.begin()));
// evaluate proposal density
ProbabilityType currentValueProposal = 1;
ProbabilityType targetValueProposal = 1;
for(std::vector<size_t>::const_iterator vi = variablesAroundCluster.begin(); vi != variablesAroundCluster.end(); ++vi) {
if(movemaker_.state(*vi) == movemaker_.state(representative)) { // *vi has old label
for(size_t k=0; k<variableAdjacency_[*vi].size(); ++k) {
const size_t nvi = variableAdjacency_[*vi][k];
if(partition.find(nvi) == representative) { // if *nvi is in cluster
currentValueProposal *= (1.0 - edgeProbabilities_[*vi][k]);
}
}
}
else if(movemaker_.state(*vi) == targetLabel) { // *vi has new label
for(size_t k=0; k<variableAdjacency_[*vi].size(); ++k) {
const size_t nvi = variableAdjacency_[*vi][k];
if(partition.find(nvi) == representative) { // if *nvi is in cluster
targetValueProposal *= (1.0 - edgeProbabilities_[*vi][k]);
}
}
}
}
// accept or reject re-labeling
const ProbabilityType metropolisHastingsProbability = (targetValueProposal / currentValueProposal) * (targetPDF / currentPDF);
OPENGM_ASSERT(metropolisHastingsProbability > 0);
if(metropolisHastingsProbability >= 1) { // accept
move<true>(variablesInCluster.begin(), variablesInCluster.end(), targetLabels.begin());
visitor(*this, j, variablesInCluster.size(), true, false);
}
else {
RandomUniform<ProbabilityType> randomNumberGeneratorAcceptance(0, 1);
if(metropolisHastingsProbability >= randomNumberGeneratorAcceptance()) { // accept
move<true>(variablesInCluster.begin(), variablesInCluster.end(), targetLabels.begin());
visitor(*this, j, variablesInCluster.size(), true, false);
}
else { // reject
visitor(*this, j, variablesInCluster.size(), false, false);
}
}
}
return NORMAL;
}
template<class GM, class ACC>
inline InferenceTermination
SwendsenWang<GM, ACC>::infer()
{
EmptyVisitorType visitor;
return infer(visitor);
}
template<class GM, class ACC>
inline InferenceTermination
SwendsenWang<GM, ACC>::arg
(
std::vector<LabelType>& x,
const size_t N
) const {
if(N == 1) {
x = currentBestState_;
return NORMAL;
}
else {
return UNKNOWN;
}
}
template<class GM, class ACC>
inline typename SwendsenWang<GM, ACC>::LabelType
SwendsenWang<GM, ACC>::markovState
(
const size_t j
) const
{
OPENGM_ASSERT(j < gm_.numberOfVariables());
return movemaker_.state(j);
}
template<class GM, class ACC>
inline typename SwendsenWang<GM, ACC>::ValueType
SwendsenWang<GM, ACC>::markovValue() const
{
return movemaker_.value();
}
template<class GM, class ACC>
inline typename SwendsenWang<GM, ACC>::LabelType
SwendsenWang<GM, ACC>::currentBestState
(
const size_t j
) const
{
OPENGM_ASSERT(j < gm_.numberOfVariables());
return currentBestState_[j];
}
template<class GM, class ACC>
inline typename SwendsenWang<GM, ACC>::ValueType
SwendsenWang<GM, ACC>::currentBestValue() const
{
return currentBestValue_;
}
template<class GM, class ACC>
template<bool BURNED_IN, class VARIABLE_ITERATOR, class STATE_ITERATOR>
inline bool SwendsenWang<GM, ACC>::move
(
VARIABLE_ITERATOR begin,
VARIABLE_ITERATOR end,
STATE_ITERATOR it
)
{
movemaker_.move(begin, end, it);
if(BURNED_IN) {
if(ACC::bop(movemaker_.value(), currentBestValue_)) {
currentBestValue_ = movemaker_.value();
std::copy(movemaker_.stateBegin(), movemaker_.stateEnd(), currentBestState_.begin());
return true;
}
}
return false;
}
template<class GM, class ACC>
void
SwendsenWang<GM, ACC>::computeEdgeProbabilities()
{
std::set<size_t> factors;
std::set<size_t> connectedVariables;
size_t variables[] = {0, 0};
for(variables[0] = 0; variables[0] < gm_.numberOfVariables(); ++variables[0]) {
for(size_t j = 0; j < variableAdjacency_[variables[0]].size(); ++j) {
variables[1] = variableAdjacency_[variables[0]][j];
if(gm_.numberOfLabels(variables[0]) == gm_.numberOfLabels(variables[1])) {
// for all pairs of connected variables, variables[0] and variables[1],
// that have the same number of states, identify
// - all factors connected to variables[0] or variables[1] (or both)
// - all variables connected to these factors
factors.clear();
connectedVariables.clear();
// factors that depend on at least variables[0] OR variables[1]
for(size_t k = 0; k < 2; ++k) {
for(typename GraphicalModelType::ConstFactorIterator it = gm_.factorsOfVariableBegin(variables[k]);
it != gm_.factorsOfVariableEnd(variables[k]); ++it) {
factors.insert(*it);
for(size_t m = 0; m < gm_[*it].numberOfVariables(); ++m) {
connectedVariables.insert(gm_[*it].variableIndex(m));
}
}
}
// factors that depend on at least variables[0] AND variables[1]
/*
for(typename GraphicalModelType::ConstFactorIterator it = gm_.factorsOfVariableBegin(variables[0]);
it != gm_.factorsOfVariableEnd(variables[0]); ++it) {
for(size_t k = 0; k<gm_[*it].numberOfVariables(); ++k) {
if(gm_[*it].variableIndex(k) == variables[1]) {
factors.insert(*it);
for(size_t m = 0; m < gm_[*it].numberOfVariables(); ++m) {
connectedVariables.insert(gm_[*it].variableIndex(m));
}
break;
}
}
}
*/
// operate all found factors up
IndependentFactorType localFactor(gm_,
connectedVariables.begin(),
connectedVariables.end(),
OperatorType::template neutral<ValueType>());
for(std::set<size_t>::const_iterator it = factors.begin(); it != factors.end(); ++it) {
OperatorType::op(gm_[*it], localFactor);
}
// marginalize
size_t indices[] = {0, 0};
for(size_t k = 0; k < localFactor.numberOfVariables(); ++k) {
if(localFactor.variableIndex(k) == variables[0]) {
indices[0] = k;
}
else if(localFactor.variableIndex(k) == variables[1]) {
indices[1] = k;
}
}
ProbabilityType probEqual = 0;
ProbabilityType probUnequal = 0;
ShapeWalker< typename IndependentFactorType::ShapeIteratorType>
walker(localFactor.shapeBegin(), localFactor.numberOfVariables());
for(size_t k = 0; k < localFactor.size(); ++k, ++walker) {
const ValueType value = localFactor(walker.coordinateTuple().begin());
const ProbabilityType p = detail_swendsenwang::ValueToProbability<OperatorType, AccumulationType, ProbabilityType>::convert(value);
if(walker.coordinateTuple()[indices[0]] == walker.coordinateTuple()[indices[1]]) {
probEqual += p;
}
else {
probUnequal += p;
}
}
// normalize
ProbabilityType sum = probEqual + probUnequal;
if(sum == 0.0) {
throw RuntimeError("Some local probabilities are exactly zero.");
}
probEqual /= sum;
probUnequal /= sum;
if(probEqual < parameter_.lowestAllowedProbability_ || probUnequal < parameter_.lowestAllowedProbability_) {
throw RuntimeError("Marginal probabilities are smaller than the allowed minimum.");
}
edgeProbabilities_[variables[0]][j] = probUnequal;
}
}
}
}
template<class GM, class ACC>
void
SwendsenWang<GM, ACC>::cluster
(
Partition<size_t>& out
) const
{
// randomly merge variables
out.reset(gm_.numberOfVariables());
opengm::RandomUniform<ProbabilityType> randomNumberGenerator(0.0, 1.0);
size_t variables[] = {0, 0};
for(variables[0] = 0; variables[0] < gm_.numberOfVariables(); ++variables[0]) {
for(size_t j = 0; j < variableAdjacency_[variables[0]].size(); ++j) {
variables[1] = variableAdjacency_[variables[0]][j];
if(variables[0] < variables[1]) { // only once for each pair
if(movemaker_.state(variables[0]) == movemaker_.state(variables[1])) {
if(edgeProbabilities_[variables[0]][j] > randomNumberGenerator()) {
// turn edge on with probability edgeProbabilities_[variables[0]][variables[1]]
out.merge(variables[0], variables[1]);
}
}
}
}
}
}
template<class SW>
inline void
SwendsenWangEmptyVisitor<SW>::operator()(
const typename SwendsenWangEmptyVisitor<SW>::SwendsenWangType& sw,
const size_t iteration,
const size_t clusterSize,
const bool accepted,
const bool burningIn
) const {
}
template<class SW>
inline void
SwendsenWangVerboseVisitor<SW>::operator()(
const typename SwendsenWangVerboseVisitor<SW>::SwendsenWangType& sw,
const size_t iteration,
const size_t clusterSize,
const bool accepted,
const bool burningIn
) const {
std::cout << "Step " << iteration
<< ": " << "V_opt=" << sw.currentBestValue()
<< ", " << "V_markov=" << sw.markovValue()
<< ", " << "cs=" << clusterSize
<< ", " << (accepted ? "accepted" : "rejected")
<< ", " << (burningIn ? "burning in" : "sampling")
<< std::endl;
//std::cout << " arg_opt: ";
//for(size_t j=0; j<sw.graphicalModel().numberOfVariables(); ++j) {
// std::cout << sw.currentBestState(j) << ' ';
//}
//std::cout << std::endl;
//
//std::cout << " arg_markov: ";
//for(size_t j=0; j<sw.graphicalModel().numberOfVariables(); ++j) {
// std::cout << sw.markovState(j) << ' ';
//std::cout << std::endl;
}
template<class SW>
inline
SwendsenWangMarginalVisitor<SW>::SwendsenWangMarginalVisitor()
: gm_(NULL),
numberOfSamples_(0),
numberOfAcceptedSamples_(0),
numberOfRejectedSamples_(0),
marginals_(),
stateCache_()
{}
template<class SW>
inline
SwendsenWangMarginalVisitor<SW>::SwendsenWangMarginalVisitor(
const typename SwendsenWangMarginalVisitor<SW>::GraphicalModelType& gm
)
: gm_(&gm),
numberOfSamples_(0),
numberOfAcceptedSamples_(0),
numberOfRejectedSamples_(0),
marginals_(),
stateCache_()
{}
template<class SW>
inline void
SwendsenWangMarginalVisitor<SW>::assign(
const typename SwendsenWangMarginalVisitor<SW>::GraphicalModelType& gm
)
{
gm_ = &gm;
}
template<class SW>
inline void
SwendsenWangMarginalVisitor<SW>::operator()(
const typename SwendsenWangMarginalVisitor<SW>::SwendsenWangType& sw,
const size_t iteration,
const size_t clusterSize,
const bool accepted,
const bool burningIn
) {
if(!burningIn) {
++numberOfSamples_;
if(accepted) {
++numberOfAcceptedSamples_;
}
else {
++numberOfRejectedSamples_;
}
for(size_t j = 0; j < marginals_.size(); ++j) {
for(size_t k = 0; k < marginals_[j].numberOfVariables(); ++k) {
stateCache_[k] = sw.markovState(marginals_[j].variableIndex(k));
}
++marginals_[j](stateCache_.begin());
}
}
}
template<class SW>
template<class VariableIndexIterator>
inline size_t
SwendsenWangMarginalVisitor<SW>::addMarginal(
VariableIndexIterator begin,
VariableIndexIterator end
) {
marginals_.push_back(IndependentFactorType(*gm_, begin, end));
if(marginals_.back().numberOfVariables() > stateCache_.size()) {
stateCache_.resize(marginals_.back().numberOfVariables());
}
return marginals_.size() - 1;
}
template<class SW>
inline size_t
SwendsenWangMarginalVisitor<SW>::addMarginal(
const size_t variableIndex
) {
size_t variableIndices[] = {variableIndex};
return addMarginal(variableIndices, variableIndices + 1);
}
template<class SW>
inline size_t
SwendsenWangMarginalVisitor<SW>::numberOfSamples() const {
return numberOfSamples_;
}
template<class SW>
inline size_t
SwendsenWangMarginalVisitor<SW>::numberOfAcceptedSamples() const {
return numberOfAcceptedSamples_;
}
template<class SW>
inline size_t
SwendsenWangMarginalVisitor<SW>::numberOfRejectedSamples() const {
return numberOfRejectedSamples_;
}
template<class SW>
inline size_t
SwendsenWangMarginalVisitor<SW>::numberOfMarginals() const {
return marginals_.size();
}
template<class SW>
inline const typename SwendsenWangMarginalVisitor<SW>::IndependentFactorType&
SwendsenWangMarginalVisitor<SW>::marginal(
const size_t setIndex
) const {
return marginals_[setIndex];
}
} // namespace opengm
#endif // #ifndef OPENGM_SWENDSENWANG_HXX
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