Example #1
0
        /// <summary>This is a key step in message passing.</summary>
        /// <remarks>
        /// This is a key step in message passing. When we are calculating a message, we want to marginalize out all variables
        /// not relevant to the recipient of the message. This function does that.
        /// </remarks>
        /// <param name="message">the message to marginalize</param>
        /// <param name="relevant">the variables that are relevant</param>
        /// <param name="marginalize">whether to use sum of max marginalization, for marginal or MAP inference</param>
        /// <returns>the marginalized message</returns>
        private static TableFactor MarginalizeMessage(TableFactor message, int[] relevant, CliqueTree.MarginalizationMethod marginalize)
        {
            TableFactor result = message;

            foreach (int i in message.neighborIndices)
            {
                bool contains = false;
                foreach (int j in relevant)
                {
                    if (i == j)
                    {
                        contains = true;
                        break;
                    }
                }
                if (!contains)
                {
                    switch (marginalize)
                    {
                    case CliqueTree.MarginalizationMethod.Sum:
                    {
                        result = result.SumOut(i);
                        break;
                    }

                    case CliqueTree.MarginalizationMethod.Max:
                    {
                        result = result.MaxOut(i);
                        break;
                    }
                    }
                }
            }
            return(result);
        }
Example #2
0
        // 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));
        }