model selection for HybridBayesTree

gtsam/hybrid/HybridBayesTree.cpp

@@ -38,19 +38,116 @@ bool HybridBayesTree::equals(const This& other, double tol) const {
   return Base::equals(other, tol);
 }
 
+GaussianBayesNetTree& HybridBayesTree::addCliqueToTree(
+    const sharedClique& clique, GaussianBayesNetTree& result) const {
+  // Perform bottom-up inclusion
+  for (sharedClique child : clique->children) {
+    result = addCliqueToTree(child, result);
+  }
+
+  auto f = clique->conditional();
+
+  if (auto hc = std::dynamic_pointer_cast<HybridConditional>(f)) {
+    if (auto gm = hc->asMixture()) {
+      result = gm->add(result);
+    } else if (auto g = hc->asGaussian()) {
+      result = addGaussian(result, g);
+    } else {
+      // Has to be discrete, which we don't add.
+    }
+  }
+  return result;
+}
+
+/* ************************************************************************ */
+GaussianBayesNetValTree HybridBayesTree::assembleTree() const {
+  GaussianBayesNetTree result;
+  for (auto&& root : roots_) {
+    result = addCliqueToTree(root, result);
+  }
+
+  GaussianBayesNetValTree resultTree(result, [](const GaussianBayesNet& gbn) {
+    return std::make_pair(gbn, 0.0);
+  });
+  return resultTree;
+}
+
+/* ************************************************************************* */
+AlgebraicDecisionTree<Key> HybridBayesTree::modelSelection() const {
+  /*
+      To perform model selection, we need:
+      q(mu; M, Z) * sqrt((2*pi)^n*det(Sigma))
+
+      If q(mu; M, Z) = exp(-error) & k = 1.0 / sqrt((2*pi)^n*det(Sigma))
+      thus, q * sqrt((2*pi)^n*det(Sigma)) = q/k = exp(log(q/k))
+      = exp(log(q) - log(k)) = exp(-error - log(k))
+      = exp(-(error + log(k))),
+      where error is computed at the corresponding MAP point, gbt.error(mu).
+
+      So we compute (error + log(k)) and exponentiate later
+    */
+
+  GaussianBayesNetValTree bnTree = assembleTree();
+
+  GaussianBayesNetValTree bn_error = bnTree.apply(
+      [this](const Assignment<Key>& assignment,
+             const std::pair<GaussianBayesNet, double>& gbnAndValue) {
+        //  Compute the X* of each assignment
+        VectorValues mu = gbnAndValue.first.optimize();
+
+        // mu is empty if gbn had nullptrs
+        if (mu.size() == 0) {
+          return std::make_pair(gbnAndValue.first,
+                                std::numeric_limits<double>::max());
+        }
+
+        // Compute the error for X* and the assignment
+        double error =
+            this->error(HybridValues(mu, DiscreteValues(assignment)));
+
+        return std::make_pair(gbnAndValue.first, error);
+      });
+
+  auto trees = unzip(bn_error);
+  AlgebraicDecisionTree<Key> errorTree = trees.second;
+
+  // Only compute logNormalizationConstant
+  AlgebraicDecisionTree<Key> log_norm_constants =
+      computeLogNormConstants(bnTree);
+
+  // Compute model selection term (with help from ADT methods)
+  AlgebraicDecisionTree<Key> modelSelectionTerm =
+      computeModelSelectionTerm(errorTree, log_norm_constants);
+
+  return modelSelectionTerm;
+}
+
 /* ************************************************************************* */
 HybridValues HybridBayesTree::optimize() const {
-  DiscreteBayesNet dbn;
+  DiscreteFactorGraph discrete_fg;
   DiscreteValues mpe;
 
+  // Compute model selection term
+  AlgebraicDecisionTree<Key> modelSelectionTerm = modelSelection();
+
   auto root = roots_.at(0);
   // Access the clique and get the underlying hybrid conditional
   HybridConditional::shared_ptr root_conditional = root->conditional();
 
-  // The root should be discrete only, we compute the MPE
+  // Get the set of all discrete keys involved in model selection
+  std::set<DiscreteKey> discreteKeySet;
+
+  //  The root should be discrete only, we compute the MPE
   if (root_conditional->isDiscrete()) {
-    dbn.push_back(root_conditional->asDiscrete());
+    discrete_fg.push_back(root_conditional->asDiscrete());
-    mpe = DiscreteFactorGraph(dbn).optimize();
+
+    // Only add model_selection if we have discrete keys
+    if (discreteKeySet.size() > 0) {
+      discrete_fg.push_back(DecisionTreeFactor(
+          DiscreteKeys(discreteKeySet.begin(), discreteKeySet.end()),
+          modelSelectionTerm));
+    }
+    mpe = discrete_fg.optimize();
   } else {
     throw std::runtime_error(
         "HybridBayesTree root is not discrete-only. Please check elimination "

gtsam/hybrid/HybridBayesTree.h

@@ -84,6 +84,51 @@ class GTSAM_EXPORT HybridBayesTree : public BayesTree<HybridBayesTreeClique> {
    */
   GaussianBayesTree choose(const DiscreteValues& assignment) const;
 
+  /** Error for all conditionals. */
+  double error(const HybridValues& values) const {
+    return HybridGaussianFactorGraph(*this).error(values);
+  }
+
+  /**
+   * @brief Helper function to add a clique of hybrid conditionals to the passed
+   * in GaussianBayesNetTree. Operates recursively on the clique in a bottom-up
+   * fashion, adding the children first.
+   *
+   * @param clique The
+   * @param result
+   * @return GaussianBayesNetTree&
+   */
+  GaussianBayesNetTree& addCliqueToTree(const sharedClique& clique,
+                                        GaussianBayesNetTree& result) const;
+
+  /**
+   * @brief Assemble a DecisionTree of (GaussianBayesTree, double) leaves for
+   * each discrete assignment.
+   * The included double value is used to make
+   * constructing the model selection term cleaner and more efficient.
+   *
+   * @return GaussianBayesNetValTree
+   */
+  GaussianBayesNetValTree assembleTree() const;
+
+  /*
+    Compute L(M;Z), the likelihood of the discrete model M
+    given the measurements Z.
+    This is called the model selection term.
+
+    To do so, we perform the integration of L(M;Z) ∝ L(X;M,Z)P(X|M).
+
+    By Bayes' rule, P(X|M,Z) ∝ L(X;M,Z)P(X|M),
+    hence L(X;M,Z)P(X|M) is the unnormalized probabilty of
+    the joint Gaussian distribution.
+
+    This can be computed by multiplying all the exponentiated errors
+    of each of the conditionals.
+
+    Return a tree where each leaf value is L(M_i;Z).
+  */
+  AlgebraicDecisionTree<Key> modelSelection() const;
+
   /**
    * @brief Optimize the hybrid Bayes tree by computing the MPE for the current
    * set of discrete variables and using it to compute the best continuous