// OPTIMIZATION:
// cache the last list of factors, and the last set of messages passed, in case we can recycle some
/// <summary>Does tree shaped message passing.</summary>
/// <remarks>
/// Does tree shaped message passing. The algorithm calls for first passing down to the leaves, then passing back up
/// to the root.
/// </remarks>
/// <param name="marginalize">the method for marginalization, controls MAP or marginals</param>
/// <returns>the marginal messages</returns>
private CliqueTree.MarginalResult MessagePassing(CliqueTree.MarginalizationMethod marginalize, bool includeJointMarginalsAndPartition)
{
// Using the behavior of brute force factor multiplication as ground truth, the desired
// outcome of marginal calculation with an impossible factor is a uniform probability dist.,
// since we have a resulting factor of all 0s. That is of course assuming that normalizing
// all 0s gives you uniform, which is not real math, but that's a useful tolerance to include, so we do.
bool impossibleObservationMade = false;
// Message passing will look at fully observed cliques as non-entities, but their
// log-likelihood (the log-likelihood of the single observed value) is still relevant for the
// partition function.
double partitionFunction = 1.0;
if (includeJointMarginalsAndPartition)
{
foreach (GraphicalModel.Factor f in model.factors)
{
foreach (int n in f.neigborIndices)
{
if (!model.GetVariableMetaDataByReference(n).Contains(VariableObservedValue))
{
goto outer_continue;
}
}
int[] assignment = new int[f.neigborIndices.Length];
for (int i = 0; i < f.neigborIndices.Length; i++)
{
assignment[i] = System.Convert.ToInt32(model.GetVariableMetaDataByReference(f.neigborIndices[i])[VariableObservedValue]);
}
double assignmentValue = f.featuresTable.GetAssignmentValue(assignment).Get().DotProduct(weights);
if (double.IsInfinite(assignmentValue))
{
impossibleObservationMade = true;
}
else
{
partitionFunction *= Math.Exp(assignmentValue);
}
}
outer_break :;
}
// Create the cliques by multiplying out table factors
// TODO:OPT This could be made more efficient by observing first, then dot product
IList <TableFactor> cliquesList = new List <TableFactor>();
IDictionary <int, GraphicalModel.Factor> cliqueToFactor = new Dictionary <int, GraphicalModel.Factor>();
int numFactorsCached = 0;
foreach (GraphicalModel.Factor f_1 in model.factors)
{
bool allObserved = true;
int maxVar = 0;
foreach (int n in f_1.neigborIndices)
{
if (!model.GetVariableMetaDataByReference(n).Contains(VariableObservedValue))
{
allObserved = false;
}
if (n > maxVar)
{
maxVar = n;
}
}
if (allObserved)
{
continue;
}
TableFactor clique = null;
// Retrieve cache if exists and none of the observations have changed
if (cachedFactors.Contains(f_1))
{
CliqueTree.CachedFactorWithObservations obs = cachedFactors[f_1];
bool allConsistent = true;
for (int i = 0; i < f_1.neigborIndices.Length; i++)
{
int n_1 = f_1.neigborIndices[i];
if (model.GetVariableMetaDataByReference(n_1).Contains(VariableObservedValue) && (obs.observations[i] == -1 || System.Convert.ToInt32(model.GetVariableMetaDataByReference(n_1)[VariableObservedValue]) != obs.observations[i]))
{
allConsistent = false;
break;
}
// NOTE: This disqualifies lots of stuff for some reason...
if (!model.GetVariableMetaDataByReference(n_1).Contains(VariableObservedValue) && (obs.observations[i] != -1))
{
allConsistent = false;
break;
}
}
if (allConsistent)
{
clique = obs.cachedFactor;
numFactorsCached++;
if (obs.impossibleObservation)
{
impossibleObservationMade = true;
}
}
}
// Otherwise make a new cache
if (clique == null)
{
int[] observations = new int[f_1.neigborIndices.Length];
for (int i = 0; i < observations.Length; i++)
{
IDictionary <string, string> metadata = model.GetVariableMetaDataByReference(f_1.neigborIndices[i]);
if (metadata.Contains(VariableObservedValue))
{
int value = System.Convert.ToInt32(metadata[VariableObservedValue]);
observations[i] = value;
}
else
{
observations[i] = -1;
}
}
clique = new TableFactor(weights, f_1, observations);
CliqueTree.CachedFactorWithObservations cache = new CliqueTree.CachedFactorWithObservations();
cache.cachedFactor = clique;
cache.observations = observations;
// Check for an impossible observation
bool nonZeroValue = false;
foreach (int[] assignment in clique)
{
if (clique.GetAssignmentValue(assignment) > 0)
{
nonZeroValue = true;
break;
}
}
if (!nonZeroValue)
{
impossibleObservationMade = true;
cache.impossibleObservation = true;
}
cachedFactors[f_1] = cache;
}
cliqueToFactor[cliquesList.Count] = f_1;
cliquesList.Add(clique);
}
TableFactor[] cliques = Sharpen.Collections.ToArray(cliquesList, new TableFactor[cliquesList.Count]);
// If we made any impossible observations, we can just return a uniform distribution for all the variables that
// weren't observed, since that's the semantically correct thing to do (our 'probability' is broken at this
// point).
if (impossibleObservationMade)
{
int maxVar = 0;
foreach (TableFactor c in cliques)
{
foreach (int i in c.neighborIndices)
{
if (i > maxVar)
{
maxVar = i;
}
}
}
double[][] result = new double[maxVar + 1][];
foreach (TableFactor c_1 in cliques)
{
for (int i = 0; i < c_1.neighborIndices.Length; i++)
{
result[c_1.neighborIndices[i]] = new double[c_1.GetDimensions()[i]];
for (int j = 0; j < result[c_1.neighborIndices[i]].Length; j++)
{
result[c_1.neighborIndices[i]][j] = 1.0 / result[c_1.neighborIndices[i]].Length;
}
}
}
// Create a bunch of uniform joint marginals, constrained by observations, and fill up the joint marginals
// with them
IDictionary <GraphicalModel.Factor, TableFactor> jointMarginals = new IdentityHashMap <GraphicalModel.Factor, TableFactor>();
if (includeJointMarginalsAndPartition)
{
foreach (GraphicalModel.Factor f in model.factors)
{
TableFactor uniformZero = new TableFactor(f_1.neigborIndices, f_1.featuresTable.GetDimensions());
foreach (int[] assignment in uniformZero)
{
uniformZero.SetAssignmentValue(assignment, 0.0);
}
jointMarginals[f_1] = uniformZero;
}
}
return(new CliqueTree.MarginalResult(result, 1.0, jointMarginals));
}
// Find the largest contained variable, so that we can size arrays appropriately
int maxVar_1 = 0;
foreach (GraphicalModel.Factor fac in model.factors)
{
foreach (int i in fac.neigborIndices)
{
if (i > maxVar_1)
{
maxVar_1 = i;
}
}
}
// Indexed by (start-clique, end-clique), this array will remain mostly null in most graphs
TableFactor[][] messages = new TableFactor[cliques.Length][];
// OPTIMIZATION:
// check if we've only added one factor since the last time we ran marginal inference. If that's the case, we
// can use the new factor as the root, all the messages passed in from the leaves will not have changed. That
// means we can cut message passing computation in half.
bool[][] backwardPassedMessages = new bool[cliques.Length][];
int forceRootForCachedMessagePassing = -1;
int[] cachedCliquesBackPointers = null;
if (CacheMessages && (numFactorsCached == cliques.Length - 1) && (numFactorsCached > 0))
{
cachedCliquesBackPointers = new int[cliques.Length];
// Sometimes we'll have cached versions of the factors, but they're from inference steps a long time ago, so we
// don't get consistent backpointers to our cache of factors. This is a flag to indicate if this happens.
bool backPointersConsistent = true;
// Calculate the correspondence between the old cliques list and the new cliques list
for (int i = 0; i < cliques.Length; i++)
{
cachedCliquesBackPointers[i] = -1;
for (int j = 0; j < cachedCliqueList.Length; j++)
{
if (cliques[i] == cachedCliqueList[j])
{
cachedCliquesBackPointers[i] = j;
break;
}
}
if (cachedCliquesBackPointers[i] == -1)
{
if (forceRootForCachedMessagePassing != -1)
{
backPointersConsistent = false;
break;
}
forceRootForCachedMessagePassing = i;
}
}
if (!backPointersConsistent)
{
forceRootForCachedMessagePassing = -1;
}
}
// Create the data structures to hold the tree pattern
bool[] visited = new bool[cliques.Length];
int numVisited = 0;
int[] visitedOrder = new int[cliques.Length];
int[] parent = new int[cliques.Length];
for (int i_1 = 0; i_1 < parent.Length; i_1++)
{
parent[i_1] = -1;
}
// Figure out which cliques are connected to which trees. This is important for calculating the partition
// function later, since each tree will converge to its own partition function by multiplication, and we will
// need to multiply the partition function of each of the trees to get the global one.
int[] trees = new int[cliques.Length];
// Forward pass, record a BFS forest pattern that we can use for message passing
int treeIndex = -1;
bool[] seenVariable = new bool[maxVar_1 + 1];
while (numVisited < cliques.Length)
{
treeIndex++;
// Pick the largest connected graph remaining as the root for message passing
int root = -1;
// OPTIMIZATION: if there's a forced root for message passing (a node that we just added) then make it the
// root
if (CacheMessages && forceRootForCachedMessagePassing != -1 && !visited[forceRootForCachedMessagePassing])
{
root = forceRootForCachedMessagePassing;
}
else
{
for (int i = 0; i_1 < cliques.Length; i_1++)
{
if (!visited[i_1] && (root == -1 || cliques[i_1].neighborIndices.Length > cliques[root].neighborIndices.Length))
{
root = i_1;
}
}
}
System.Diagnostics.Debug.Assert((root != -1));
IQueue <int> toVisit = new ArrayDeque <int>();
toVisit.Add(root);
bool[] toVisitArray = new bool[cliques.Length];
toVisitArray[root] = true;
while (toVisit.Count > 0)
{
int cursor = toVisit.Poll();
// toVisitArray[cursor] = false;
trees[cursor] = treeIndex;
if (visited[cursor])
{
log.Info("Visited contains: " + cursor);
log.Info("Visited: " + Arrays.ToString(visited));
log.Info("To visit: " + toVisit);
}
System.Diagnostics.Debug.Assert((!visited[cursor]));
visited[cursor] = true;
visitedOrder[numVisited] = cursor;
foreach (int i in cliques[cursor].neighborIndices)
{
seenVariable[i_1] = true;
}
numVisited++;
for (int i_2 = 0; i_2 < cliques.Length; i_2++)
{
if (i_2 == cursor)
{
continue;
}
if (i_2 == parent[cursor])
{
continue;
}
if (DomainsOverlap(cliques[cursor], cliques[i_2]))
{
// Make sure that for every variable that we've already seen somewhere in the graph, if it's
// in the child, it's in the parent. Otherwise we'll break the property of continuous
// transmission of information about variables through messages.
foreach (int child in cliques[i_2].neighborIndices)
{
if (seenVariable[child])
{
foreach (int j in cliques[cursor].neighborIndices)
{
if (j == child)
{
goto childNeighborLoop_continue;
}
}
// If we get here it means that this clique is not good as a child, since we can't pass
// it all the information it needs from other elements of the tree
goto childLoop_continue;
}
}
childNeighborLoop_break :;
if (parent[i_2] == -1 && !visited[i_2])
{
if (!toVisitArray[i_2])
{
toVisit.Add(i_2);
toVisitArray[i_2] = true;
foreach (int j in cliques[i_2].neighborIndices)
{
seenVariable[j] = true;
}
}
parent[i_2] = cursor;
}
}
childLoop_continue :;
}
childLoop_break :;
}
// No cycles in the tree
System.Diagnostics.Debug.Assert((parent[root] == -1));
}
System.Diagnostics.Debug.Assert((numVisited == cliques.Length));
// Backward pass, run the visited list in reverse
for (int i_3 = numVisited - 1; i_3 >= 0; i_3--)
{
int cursor = visitedOrder[i_3];
if (parent[cursor] == -1)
{
continue;
}
backwardPassedMessages[cursor][parent[cursor]] = true;
// OPTIMIZATION:
// if these conditions are met we can avoid calculating the message, and instead retrieve from the cache,
// since they should be the same
if (CacheMessages && forceRootForCachedMessagePassing != -1 && cachedCliquesBackPointers[cursor] != -1 && cachedCliquesBackPointers[parent[cursor]] != -1 && cachedMessages[cachedCliquesBackPointers[cursor]][cachedCliquesBackPointers[parent[cursor
]]] != null && cachedBackwardPassedMessages[cachedCliquesBackPointers[cursor]][cachedCliquesBackPointers[parent[cursor]]])
{
messages[cursor][parent[cursor]] = cachedMessages[cachedCliquesBackPointers[cursor]][cachedCliquesBackPointers[parent[cursor]]];
}
else
{
// Calculate the message to the clique's parent, given all incoming messages so far
TableFactor message = cliques[cursor];
for (int k = 0; k < cliques.Length; k++)
{
if (k == parent[cursor])
{
continue;
}
if (messages[k][cursor] != null)
{
message = message.Multiply(messages[k][cursor]);
}
}
messages[cursor][parent[cursor]] = MarginalizeMessage(message, cliques[parent[cursor]].neighborIndices, marginalize);
// Invalidate any cached outgoing messages
if (CacheMessages && forceRootForCachedMessagePassing != -1 && cachedCliquesBackPointers[parent[cursor]] != -1)
{
for (int k_1 = 0; k_1 < cachedCliqueList.Length; k_1++)
{
cachedMessages[cachedCliquesBackPointers[parent[cursor]]][k_1] = null;
}
}
}
}
// Forward pass, run the visited list forward
for (int i_4 = 0; i_4 < numVisited; i_4++)
{
int cursor = visitedOrder[i_4];
for (int j = 0; j < cliques.Length; j++)
{
if (parent[j] != cursor)
{
continue;
}
TableFactor message = cliques[cursor];
for (int k = 0; k < cliques.Length; k++)
{
if (k == j)
{
continue;
}
if (messages[k][cursor] != null)
{
message = message.Multiply(messages[k][cursor]);
}
}
messages[cursor][j] = MarginalizeMessage(message, cliques[j].neighborIndices, marginalize);
}
}
// OPTIMIZATION:
// cache the messages, and the current list of cliques
cachedCliqueList = cliques;
cachedMessages = messages;
cachedBackwardPassedMessages = backwardPassedMessages;
// Calculate final marginals for each variable
double[][] marginals = new double[maxVar_1 + 1][];
// Include observed variables as deterministic
foreach (GraphicalModel.Factor fac_1 in model.factors)
{
for (int i = 0; i_4 < fac_1.neigborIndices.Length; i_4++)
{
int n = fac_1.neigborIndices[i_4];
if (model.GetVariableMetaDataByReference(n).Contains(VariableObservedValue))
{
double[] deterministic = new double[fac_1.featuresTable.GetDimensions()[i_4]];
int assignment = System.Convert.ToInt32(model.GetVariableMetaDataByReference(n)[VariableObservedValue]);
if (assignment > deterministic.Length)
{
throw new InvalidOperationException("Variable " + n + ": Can't have as assignment (" + assignment + ") that is out of bounds for dimension size (" + deterministic.Length + ")");
}
deterministic[assignment] = 1.0;
marginals[n] = deterministic;
}
}
}
IDictionary <GraphicalModel.Factor, TableFactor> jointMarginals_1 = new IdentityHashMap <GraphicalModel.Factor, TableFactor>();
if (marginalize == CliqueTree.MarginalizationMethod.Sum && includeJointMarginalsAndPartition)
{
bool[] partitionIncludesTrees = new bool[treeIndex + 1];
double[] treePartitionFunctions = new double[treeIndex + 1];
for (int i = 0; i_4 < cliques.Length; i_4++)
{
TableFactor convergedClique = cliques[i_4];
for (int j = 0; j < cliques.Length; j++)
{
if (i_4 == j)
{
continue;
}
if (messages[j][i_4] == null)
{
continue;
}
convergedClique = convergedClique.Multiply(messages[j][i_4]);
}
// Calculate the partition function when we're calculating marginals
// We need one contribution per tree in our forest graph
if (!partitionIncludesTrees[trees[i_4]])
{
partitionIncludesTrees[trees[i_4]] = true;
treePartitionFunctions[trees[i_4]] = convergedClique.ValueSum();
partitionFunction *= treePartitionFunctions[trees[i_4]];
}
else
{
// This is all just an elaborate assert
// Check that our partition function is the same as the trees we're attached to, or with %.1, for numerical reasons.
// Sometimes the partition function will explode in value, which can make a non-%-based assert worthless here
if (AssertsEnabled() && !TableFactor.UseExpApprox)
{
double valueSum = convergedClique.ValueSum();
if (double.IsFinite(valueSum) && double.IsFinite(treePartitionFunctions[trees[i_4]]))
{
if (Math.Abs(treePartitionFunctions[trees[i_4]] - valueSum) >= 1.0e-3 * treePartitionFunctions[trees[i_4]])
{
log.Info("Different partition functions for tree " + trees[i_4] + ": ");
log.Info("Pre-existing for tree: " + treePartitionFunctions[trees[i_4]]);
log.Info("This clique for tree: " + valueSum);
}
System.Diagnostics.Debug.Assert((Math.Abs(treePartitionFunctions[trees[i_4]] - valueSum) < 1.0e-3 * treePartitionFunctions[trees[i_4]]));
}
}
}
// Calculate the factor this clique corresponds to, and put in an entry for joint marginals
GraphicalModel.Factor f = cliqueToFactor[i_4];
System.Diagnostics.Debug.Assert((f_1 != null));
if (!jointMarginals_1.Contains(f_1))
{
int[] observedAssignments = GetObservedAssignments(f_1);
// Collect back pointers and check if this factor matches the clique we're using
int[] backPointers = new int[observedAssignments.Length];
int cursor = 0;
for (int j_1 = 0; j_1 < observedAssignments.Length; j_1++)
{
if (observedAssignments[j_1] == -1)
{
backPointers[j_1] = cursor;
cursor++;
}
else
{
// This is not strictly necessary but will trigger array OOB exception if things go wrong, so is nice
backPointers[j_1] = -1;
}
}
double sum = convergedClique.ValueSum();
TableFactor jointMarginal = new TableFactor(f_1.neigborIndices, f_1.featuresTable.GetDimensions());
// OPTIMIZATION:
// Rather than use the standard iterator, which creates lots of int[] arrays on the heap, which need to be GC'd,
// we use the fast version that just mutates one array. Since this is read once for us here, this is ideal.
IEnumerator <int[]> fastPassByReferenceIterator = convergedClique.FastPassByReferenceIterator();
int[] assignment = fastPassByReferenceIterator.Current;
while (true)
{
if (backPointers.Length == assignment.Length)
{
jointMarginal.SetAssignmentValue(assignment, convergedClique.GetAssignmentValue(assignment) / sum);
}
else
{
int[] jointAssignment = new int[backPointers.Length];
for (int j_2 = 0; j_2 < jointAssignment.Length; j_2++)
{
if (observedAssignments[j_2] != -1)
{
jointAssignment[j_2] = observedAssignments[j_2];
}
else
{
jointAssignment[j_2] = assignment[backPointers[j_2]];
}
}
jointMarginal.SetAssignmentValue(jointAssignment, convergedClique.GetAssignmentValue(assignment) / sum);
}
// Set the assignment arrays correctly
if (fastPassByReferenceIterator.MoveNext())
{
fastPassByReferenceIterator.Current;
}
else
{
break;
}
}
jointMarginals_1[f_1] = jointMarginal;
}
bool anyNull = false;
for (int j_3 = 0; j_3 < convergedClique.neighborIndices.Length; j_3++)
{
int k = convergedClique.neighborIndices[j_3];
if (marginals[k] == null)
{
anyNull = true;
}
}
if (anyNull)
{
double[][] cliqueMarginals = null;
switch (marginalize)
{
case CliqueTree.MarginalizationMethod.Sum:
{
cliqueMarginals = convergedClique.GetSummedMarginals();
break;
}
case CliqueTree.MarginalizationMethod.Max:
{
cliqueMarginals = convergedClique.GetMaxedMarginals();
break;
}
}
for (int j_1 = 0; j_1 < convergedClique.neighborIndices.Length; j_1++)
{
int k = convergedClique.neighborIndices[j_1];
if (marginals[k] == null)
{
marginals[k] = cliqueMarginals[j_1];
}
}
}
}
}
else
{
// If we don't care about joint marginals, we can be careful about not calculating more cliques than we need to,
// by explicitly sorting by which cliques are most profitable to calculate over. In this way we can avoid, in
// the case of a chain CRF, calculating almost half the joint factors.
// First do a pass where we only calculate all-null neighbors
for (int i = 0; i_4 < cliques.Length; i_4++)
{
bool allNull = true;
foreach (int k in cliques[i_4].neighborIndices)
{
if (marginals[k] != null)
{
allNull = false;
}
}
if (allNull)
{
TableFactor convergedClique = cliques[i_4];
for (int j = 0; j < cliques.Length; j++)
{
if (i_4 == j)
{
continue;
}
if (messages[j][i_4] == null)
{
continue;
}
convergedClique = convergedClique.Multiply(messages[j][i_4]);
}
double[][] cliqueMarginals = null;
switch (marginalize)
{
case CliqueTree.MarginalizationMethod.Sum:
{
cliqueMarginals = convergedClique.GetSummedMarginals();
break;
}
case CliqueTree.MarginalizationMethod.Max:
{
cliqueMarginals = convergedClique.GetMaxedMarginals();
break;
}
}
for (int j_1 = 0; j_1 < convergedClique.neighborIndices.Length; j_1++)
{
int k_1 = convergedClique.neighborIndices[j_1];
if (marginals[k_1] == null)
{
marginals[k_1] = cliqueMarginals[j_1];
}
}
}
}
// Now we calculate any remaining cliques with any non-null variables
for (int i_2 = 0; i_2 < cliques.Length; i_2++)
{
bool anyNull = false;
for (int j = 0; j < cliques[i_2].neighborIndices.Length; j++)
{
int k = cliques[i_2].neighborIndices[j];
if (marginals[k] == null)
{
anyNull = true;
}
}
if (anyNull)
{
TableFactor convergedClique = cliques[i_2];
for (int j_1 = 0; j_1 < cliques.Length; j_1++)
{
if (i_2 == j_1)
{
continue;
}
if (messages[j_1][i_2] == null)
{
continue;
}
convergedClique = convergedClique.Multiply(messages[j_1][i_2]);
}
double[][] cliqueMarginals = null;
switch (marginalize)
{
case CliqueTree.MarginalizationMethod.Sum:
{
cliqueMarginals = convergedClique.GetSummedMarginals();
break;
}
case CliqueTree.MarginalizationMethod.Max:
{
cliqueMarginals = convergedClique.GetMaxedMarginals();
break;
}
}
for (int j_2 = 0; j_2 < convergedClique.neighborIndices.Length; j_2++)
{
int k = convergedClique.neighborIndices[j_2];
if (marginals[k] == null)
{
marginals[k] = cliqueMarginals[j_2];
}
}
}
}
}
// Add any factors to the joint marginal map that were fully observed and so didn't get cliques
if (marginalize == CliqueTree.MarginalizationMethod.Sum && includeJointMarginalsAndPartition)
{
foreach (GraphicalModel.Factor f in model.factors)
{
if (!jointMarginals_1.Contains(f_1))
{
// This implies that every variable in the factor is observed. If that's the case, we need to construct
// a one hot TableFactor representing the deterministic distribution.
TableFactor deterministicJointMarginal = new TableFactor(f_1.neigborIndices, f_1.featuresTable.GetDimensions());
int[] observedAssignment = GetObservedAssignments(f_1);
foreach (int i in observedAssignment)
{
System.Diagnostics.Debug.Assert((i_4 != -1));
}
deterministicJointMarginal.SetAssignmentValue(observedAssignment, 1.0);
jointMarginals_1[f_1] = deterministicJointMarginal;
}
}
}
return(new CliqueTree.MarginalResult(marginals, partitionFunction, jointMarginals_1));
}