update model selection code and docs to match the math

Author: varunagrawal

gtsam/hybrid/HybridBayesNet.cpp

@@ -265,16 +265,10 @@ GaussianBayesNetValTree HybridBayesNet::assembleTree() const {
 /* ************************************************************************* */
 AlgebraicDecisionTree<Key> HybridBayesNet::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))),
+      To perform model selection, we need: q(mu; M, Z) = exp(-error)
       where error is computed at the corresponding MAP point, gbn.error(mu).
 
-      So we compute (error + log(k)) and exponentiate later
+      So we compute (-error) and exponentiate later
     */
 
   GaussianBayesNetValTree bnTree = assembleTree();
@@ -301,13 +295,16 @@ AlgebraicDecisionTree<Key> HybridBayesNet::modelSelection() const {
   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);
+  AlgebraicDecisionTree<Key> modelSelectionTerm = errorTree * -1;
+
+  // Exponentiate using our scheme
+  double max_log = modelSelectionTerm.max();
+  modelSelectionTerm = DecisionTree<Key, double>(
+      modelSelectionTerm,
+      [&max_log](const double &x) { return std::exp(x - max_log); });
+  modelSelectionTerm = modelSelectionTerm.normalize(modelSelectionTerm.sum());
+
   return modelSelectionTerm;
 }
 
@@ -531,20 +528,4 @@ AlgebraicDecisionTree<Key> computeLogNormConstants(
   return log_norm_constants;
 }
 
-/* ************************************************************************* */
-AlgebraicDecisionTree<Key> computeModelSelectionTerm(
-    const AlgebraicDecisionTree<Key> &errorTree,
-    const AlgebraicDecisionTree<Key> &log_norm_constants) {
-  AlgebraicDecisionTree<Key> modelSelectionTerm =
-      (errorTree + log_norm_constants) * -1;
-
-  double max_log = modelSelectionTerm.max();
-  modelSelectionTerm = DecisionTree<Key, double>(
-      modelSelectionTerm,
-      [&max_log](const double &x) { return std::exp(x - max_log); });
-  modelSelectionTerm = modelSelectionTerm.normalize(modelSelectionTerm.sum());
-
-  return modelSelectionTerm;
-}
-
 }  // namespace gtsam

gtsam/hybrid/HybridBayesNet.h

@@ -128,22 +128,17 @@ class GTSAM_EXPORT HybridBayesNet : public BayesNet<HybridConditional> {
    */
   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).
-  */
+  /**
+   * @brief Compute the model selection term q(μ_X; M, Z)
+   * given the error for each discrete assignment.
+   *
+   * The q(μ) terms are obtained as a result of elimination
+   * as part of the separator factor.
+   *
+   * Perform normalization to handle underflow issues.
+   *
+   * @return AlgebraicDecisionTree<Key>
+   */
   AlgebraicDecisionTree<Key> modelSelection() const;
 
   /**
@@ -301,18 +296,4 @@ GaussianBayesNetTree addGaussian(const GaussianBayesNetTree &gbnTree,
 AlgebraicDecisionTree<Key> computeLogNormConstants(
     const GaussianBayesNetValTree &bnTree);
 
-/**
- * @brief Compute the model selection term L(M; Z, X) given the error
- * and log normalization constants.
- *
- * Perform normalization to handle underflow issues.
- *
- * @param errorTree
- * @param log_norm_constants
- * @return AlgebraicDecisionTree<Key>
- */
-AlgebraicDecisionTree<Key> computeModelSelectionTerm(
-    const AlgebraicDecisionTree<Key> &errorTree,
-    const AlgebraicDecisionTree<Key> &log_norm_constants);
-
 }  // namespace gtsam

gtsam/hybrid/HybridBayesTree.cpp

@@ -111,13 +111,15 @@ AlgebraicDecisionTree<Key> HybridBayesTree::modelSelection() const {
   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);
+  AlgebraicDecisionTree<Key> modelSelectionTerm = errorTree * -1;
+
+  // Exponentiate using our scheme
+  double max_log = modelSelectionTerm.max();
+  modelSelectionTerm = DecisionTree<Key, double>(
+      modelSelectionTerm,
+      [&max_log](const double& x) { return std::exp(x - max_log); });
+  modelSelectionTerm = modelSelectionTerm.normalize(modelSelectionTerm.sum());
 
   return modelSelectionTerm;
 }