Merge branch 'working-hybrid' into model-selection-bayestree

gtsam/hybrid/GaussianMixture.cpp

@@ -24,6 +24,7 @@
 #include <gtsam/hybrid/GaussianMixtureFactor.h>
 #include <gtsam/hybrid/HybridValues.h>
 #include <gtsam/inference/Conditional-inst.h>
+#include <gtsam/linear/GaussianBayesNet.h>
 #include <gtsam/linear/GaussianFactorGraph.h>
 
 namespace gtsam {
@@ -318,8 +319,15 @@ AlgebraicDecisionTree<Key> GaussianMixture::logProbability(
 AlgebraicDecisionTree<Key> GaussianMixture::errorTree(
     const VectorValues &continuousValues) const {
   auto errorFunc = [&](const GaussianConditional::shared_ptr &conditional) {
+    // Check if valid pointer
+    if (conditional) {
       return conditional->error(continuousValues) +  //
              logConstant_ - conditional->logNormalizationConstant();
+    } else {
+      // If not valid, pointer, it means this conditional was pruned,
+      // so we return maximum error.
+      return std::numeric_limits<double>::max();
+    }
   };
   DecisionTree<Key, double> error_tree(conditionals_, errorFunc);
   return error_tree;
@@ -327,10 +335,33 @@ AlgebraicDecisionTree<Key> GaussianMixture::errorTree(
 
 /* *******************************************************************************/
 double GaussianMixture::error(const HybridValues &values) const {
+  // Check if discrete keys in discrete assignment are
+  // present in the GaussianMixture
+  KeyVector dKeys = this->discreteKeys_.indices();
+  bool valid_assignment = false;
+  for (auto &&kv : values.discrete()) {
+    if (std::find(dKeys.begin(), dKeys.end(), kv.first) != dKeys.end()) {
+      valid_assignment = true;
+      break;
+    }
+  }
+
+  // The discrete assignment is not valid so we throw an error.
+  if (!valid_assignment) {
+    throw std::runtime_error(
+        "Invalid discrete values in values. Not all discrete keys specified.");
+  }
+
   // Directly index to get the conditional, no need to build the whole tree.
   auto conditional = conditionals_(values.discrete());
+  if (conditional) {
     return conditional->error(values.continuous()) +  //
            logConstant_ - conditional->logNormalizationConstant();
+  } else {
+    // If not valid, pointer, it means this conditional was pruned,
+    // so we return maximum error.
+    return std::numeric_limits<double>::max();
+  }
 }
 
 /* *******************************************************************************/

gtsam/hybrid/GaussianMixture.h

@@ -67,7 +67,7 @@ class GTSAM_EXPORT GaussianMixture
   double logConstant_;         ///< log of the normalization constant.
 
   /**
-   * @brief Convert a DecisionTree of factors into
+   * @brief Convert a GaussianMixture of conditionals into
    * a DecisionTree of Gaussian factor graphs.
    */
   GaussianFactorGraphTree asGaussianFactorGraphTree() const;

gtsam/hybrid/GaussianMixtureFactor.cpp

@@ -54,7 +54,9 @@ bool GaussianMixtureFactor::equals(const HybridFactor &lf, double tol) const {
 /* *******************************************************************************/
 void GaussianMixtureFactor::print(const std::string &s,
                                   const KeyFormatter &formatter) const {
-  HybridFactor::print(s, formatter);
+  std::cout << (s.empty() ? "" : s + "\n");
+  std::cout << "GaussianMixtureFactor" << std::endl;
+  HybridFactor::print("", formatter);
   std::cout << "{\n";
   if (factors_.empty()) {
     std::cout << "  empty" << std::endl;
@@ -117,6 +119,5 @@ double GaussianMixtureFactor::error(const HybridValues &values) const {
   const sharedFactor gf = factors_(values.discrete());
   return gf->error(values.continuous());
 }
-/* *******************************************************************************/
 
 }  // namespace gtsam

gtsam/hybrid/GaussianMixtureFactor.h

@@ -80,8 +80,8 @@ class GTSAM_EXPORT GaussianMixtureFactor : public HybridFactor {
    * @param continuousKeys A vector of keys representing continuous variables.
    * @param discreteKeys A vector of keys representing discrete variables and
    * their cardinalities.
-   * @param factors The decision tree of Gaussian factors stored as the mixture
+   * @param factors The decision tree of Gaussian factors stored
-   * density.
+   * as the mixture density.
    */
   GaussianMixtureFactor(const KeyVector &continuousKeys,
                         const DiscreteKeys &discreteKeys,
@@ -107,9 +107,8 @@ class GTSAM_EXPORT GaussianMixtureFactor : public HybridFactor {
 
   bool equals(const HybridFactor &lf, double tol = 1e-9) const override;
 
-  void print(
+  void print(const std::string &s = "", const KeyFormatter &formatter =
-      const std::string &s = "GaussianMixtureFactor\n",
+                                            DefaultKeyFormatter) const override;
-      const KeyFormatter &formatter = DefaultKeyFormatter) const override;
 
   /// @}
   /// @name Standard API

gtsam/hybrid/HybridBayesNet.cpp

@@ -220,15 +220,16 @@ GaussianBayesNet HybridBayesNet::choose(
 /* ************************************************************************* */
 HybridValues HybridBayesNet::optimize() const {
   // Collect all the discrete factors to compute MPE
-  DiscreteBayesNet discrete_bn;
+  DiscreteFactorGraph discrete_fg;
+
   for (auto &&conditional : *this) {
     if (conditional->isDiscrete()) {
-      discrete_bn.push_back(conditional->asDiscrete());
+      discrete_fg.push_back(conditional->asDiscrete());
     }
   }
 
   // Solve for the MPE
-  DiscreteValues mpe = DiscreteFactorGraph(discrete_bn).optimize();
+  DiscreteValues mpe = discrete_fg.optimize();
 
   // Given the MPE, compute the optimal continuous values.
   return HybridValues(optimize(mpe), mpe);

gtsam/hybrid/HybridFactor.h

@@ -13,6 +13,7 @@
  *  @file HybridFactor.h
  *  @date Mar 11, 2022
  *  @author Fan Jiang
+ *  @author Varun Agrawal
  */
 
 #pragma once

gtsam/hybrid/HybridGaussianFactorGraph.cpp

@@ -242,6 +242,18 @@ discreteElimination(const HybridGaussianFactorGraph &factors,
   for (auto &f : factors) {
     if (auto df = dynamic_pointer_cast<DiscreteFactor>(f)) {
       dfg.push_back(df);
+    } else if (auto gmf = dynamic_pointer_cast<GaussianMixtureFactor>(f)) {
+      // Case where we have a GaussianMixtureFactor with no continuous keys.
+      // In this case, compute discrete probabilities.
+      auto probability =
+          [&](const GaussianFactor::shared_ptr &factor) -> double {
+        if (!factor) return 0.0;
+        return exp(-factor->error(VectorValues()));
+      };
+      dfg.emplace_shared<DecisionTreeFactor>(
+          gmf->discreteKeys(),
+          DecisionTree<Key, double>(gmf->factors(), probability));
+
     } else if (auto orphan = dynamic_pointer_cast<OrphanWrapper>(f)) {
       // Ignore orphaned clique.
       // TODO(dellaert): is this correct? If so explain here.
@@ -279,21 +291,37 @@ GaussianFactorGraphTree removeEmpty(const GaussianFactorGraphTree &sum) {
 using Result = std::pair<std::shared_ptr<GaussianConditional>,
                          GaussianMixtureFactor::sharedFactor>;
 
-// Integrate the probability mass in the last continuous conditional using
+/**
-// the unnormalized probability q(μ;m) = exp(-error(μ;m)) at the mean.
+ * Compute the probability q(μ;m) = exp(-error(μ;m)) * sqrt(det(2π Σ_m)
-//   discrete_probability = exp(-error(μ;m)) * sqrt(det(2π Σ_m))
+ * from the residual error at the mean μ.
+ * The residual error contains no keys, and only
+ * depends on the discrete separator if present.
+ */
 static std::shared_ptr<Factor> createDiscreteFactor(
     const DecisionTree<Key, Result> &eliminationResults,
     const DiscreteKeys &discreteSeparator) {
-  auto probability = [&](const Result &pair) -> double {
+  auto logProbability = [&](const Result &pair) -> double {
     const auto &[conditional, factor] = pair;
     static const VectorValues kEmpty;
     // If the factor is not null, it has no keys, just contains the residual.
     if (!factor) return 1.0;  // TODO(dellaert): not loving this.
-    return exp(-factor->error(kEmpty)) / conditional->normalizationConstant();
+
+    // Logspace version of:
+    // exp(-factor->error(kEmpty)) / conditional->normalizationConstant();
+    // We take negative of the logNormalizationConstant `log(1/k)`
+    // to get `log(k)`.
+    return -factor->error(kEmpty) + (-conditional->logNormalizationConstant());
   };
 
-  DecisionTree<Key, double> probabilities(eliminationResults, probability);
+  AlgebraicDecisionTree<Key> logProbabilities(
+      DecisionTree<Key, double>(eliminationResults, logProbability));
+
+  // Perform normalization
+  double max_log = logProbabilities.max();
+  AlgebraicDecisionTree probabilities = DecisionTree<Key, double>(
+      logProbabilities,
+      [&max_log](const double x) { return exp(x - max_log); });
+  probabilities = probabilities.normalize(probabilities.sum());
 
   return std::make_shared<DecisionTreeFactor>(discreteSeparator, probabilities);
 }

gtsam/hybrid/tests/testGaussianMixtureFactor.cpp

@@ -22,9 +22,13 @@
 #include <gtsam/discrete/DiscreteValues.h>
 #include <gtsam/hybrid/GaussianMixture.h>
 #include <gtsam/hybrid/GaussianMixtureFactor.h>
+#include <gtsam/hybrid/HybridBayesNet.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
 #include <gtsam/hybrid/HybridValues.h>
 #include <gtsam/inference/Symbol.h>
 #include <gtsam/linear/GaussianFactorGraph.h>
+#include <gtsam/nonlinear/PriorFactor.h>
+#include <gtsam/slam/BetweenFactor.h>
 
 // Include for test suite
 #include <CppUnitLite/TestHarness.h>
@@ -34,6 +38,7 @@ using namespace gtsam;
 using noiseModel::Isotropic;
 using symbol_shorthand::M;
 using symbol_shorthand::X;
+using symbol_shorthand::Z;
 
 /* ************************************************************************* */
 // Check iterators of empty mixture.
@@ -56,7 +61,6 @@ TEST(GaussianMixtureFactor, Sum) {
   auto b = Matrix::Zero(2, 1);
   Vector2 sigmas;
   sigmas << 1, 2;
-  auto model = noiseModel::Diagonal::Sigmas(sigmas, true);
 
   auto f10 = std::make_shared<JacobianFactor>(X(1), A1, X(2), A2, b);
   auto f11 = std::make_shared<JacobianFactor>(X(1), A1, X(2), A2, b);
@@ -106,7 +110,8 @@ TEST(GaussianMixtureFactor, Printing) {
   GaussianMixtureFactor mixtureFactor({X(1), X(2)}, {m1}, factors);
 
   std::string expected =
-      R"(Hybrid [x1 x2; 1]{
+      R"(GaussianMixtureFactor
+Hybrid [x1 x2; 1]{
  Choice(1) 
  0 Leaf :
   A[x1] = [
@@ -178,7 +183,8 @@ TEST(GaussianMixtureFactor, Error) {
   continuousValues.insert(X(2), Vector2(1, 1));
 
   // error should return a tree of errors, with nodes for each discrete value.
-  AlgebraicDecisionTree<Key> error_tree = mixtureFactor.errorTree(continuousValues);
+  AlgebraicDecisionTree<Key> error_tree =
+      mixtureFactor.errorTree(continuousValues);
 
   std::vector<DiscreteKey> discrete_keys = {m1};
   // Error values for regression test
@@ -191,8 +197,422 @@ TEST(GaussianMixtureFactor, Error) {
   DiscreteValues discreteValues;
   discreteValues[m1.first] = 1;
   EXPECT_DOUBLES_EQUAL(
-      4.0, mixtureFactor.error({continuousValues, discreteValues}),
+      4.0, mixtureFactor.error({continuousValues, discreteValues}), 1e-9);
-      1e-9);
+}
+
+/* ************************************************************************* */
+/**
+ * Test a simple Gaussian Mixture Model represented as P(m)P(z|m)
+ * where m is a discrete variable and z is a continuous variable.
+ * m is binary and depending on m, we have 2 different means
+ * μ1 and μ2 for the Gaussian distribution around which we sample z.
+ *
+ * The resulting factor graph should eliminate to a Bayes net
+ * which represents a sigmoid function.
+ */
+TEST(GaussianMixtureFactor, GaussianMixtureModel) {
+  double mu0 = 1.0, mu1 = 3.0;
+  double sigma = 2.0;
+  auto model = noiseModel::Isotropic::Sigma(1, sigma);
+
+  DiscreteKey m(M(0), 2);
+  Key z = Z(0);
+
+  auto c0 = make_shared<GaussianConditional>(z, Vector1(mu0), I_1x1, model),
+       c1 = make_shared<GaussianConditional>(z, Vector1(mu1), I_1x1, model);
+
+  auto gm = new GaussianMixture({z}, {}, {m}, {c0, c1});
+  auto mixing = new DiscreteConditional(m, "0.5/0.5");
+
+  HybridBayesNet hbn;
+  hbn.emplace_back(gm);
+  hbn.emplace_back(mixing);
+
+  // The result should be a sigmoid.
+  // So should be m = 0.5 at z=3.0 - 1.0=2.0
+  VectorValues given;
+  given.insert(z, Vector1(mu1 - mu0));
+
+  HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
+  HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
+
+  HybridBayesNet expected;
+  expected.emplace_back(new DiscreteConditional(m, "0.5/0.5"));
+
+  EXPECT(assert_equal(expected, *bn));
+}
+
+/* ************************************************************************* */
+/**
+ * Test a simple Gaussian Mixture Model represented as P(m)P(z|m)
+ * where m is a discrete variable and z is a continuous variable.
+ * m is binary and depending on m, we have 2 different means
+ * and covariances each for the
+ * Gaussian distribution around which we sample z.
+ *
+ * The resulting factor graph should eliminate to a Bayes net
+ * which represents a sigmoid function leaning towards
+ * the tighter covariance Gaussian.
+ */
+TEST(GaussianMixtureFactor, GaussianMixtureModel2) {
+  double mu0 = 1.0, mu1 = 3.0;
+  auto model0 = noiseModel::Isotropic::Sigma(1, 8.0);
+  auto model1 = noiseModel::Isotropic::Sigma(1, 4.0);
+
+  DiscreteKey m(M(0), 2);
+  Key z = Z(0);
+
+  auto c0 = make_shared<GaussianConditional>(z, Vector1(mu0), I_1x1, model0),
+       c1 = make_shared<GaussianConditional>(z, Vector1(mu1), I_1x1, model1);
+
+  auto gm = new GaussianMixture({z}, {}, {m}, {c0, c1});
+  auto mixing = new DiscreteConditional(m, "0.5/0.5");
+
+  HybridBayesNet hbn;
+  hbn.emplace_back(gm);
+  hbn.emplace_back(mixing);
+
+  // The result should be a sigmoid leaning towards model1
+  // since it has the tighter covariance.
+  // So should be m = 0.34/0.66 at z=3.0 - 1.0=2.0
+  VectorValues given;
+  given.insert(z, Vector1(mu1 - mu0));
+  HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
+  HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
+
+  HybridBayesNet expected;
+  expected.emplace_back(
+      new DiscreteConditional(m, "0.338561851224/0.661438148776"));
+
+  EXPECT(assert_equal(expected, *bn));
+}
+
+/* ************************************************************************* */
+/**
+ * Test a model P(x0)P(z0|x0)p(x1|m1)p(z1|x1)p(m1).
+ *
+ * p(x1|m1) has different means and same covariance.
+ *
+ * Converting to a factor graph gives us
+ * P(x0)ϕ(x0)P(x1|m1)ϕ(x1)P(m1)
+ *
+ * If we only have a measurement on z0, then
+ * the probability of x1 should be 0.5/0.5.
+ * Getting a measurement on z1 gives use more information.
+ */
+TEST(GaussianMixtureFactor, TwoStateModel) {
+  double mu0 = 1.0, mu1 = 3.0;
+  auto model = noiseModel::Isotropic::Sigma(1, 2.0);
+
+  DiscreteKey m1(M(1), 2);
+  Key z0 = Z(0), z1 = Z(1), x0 = X(0), x1 = X(1);
+
+  auto c0 = make_shared<GaussianConditional>(x1, Vector1(mu0), I_1x1, model),
+       c1 = make_shared<GaussianConditional>(x1, Vector1(mu1), I_1x1, model);
+
+  auto p_x0 = new GaussianConditional(x0, Vector1(0.0), I_1x1,
+                                      noiseModel::Isotropic::Sigma(1, 1.0));
+  auto p_z0x0 = new GaussianConditional(z0, Vector1(0.0), I_1x1, x0, -I_1x1,
+                                        noiseModel::Isotropic::Sigma(1, 1.0));
+  auto p_x1m1 = new GaussianMixture({x1}, {}, {m1}, {c0, c1});
+  auto p_z1x1 = new GaussianConditional(z1, Vector1(0.0), I_1x1, x1, -I_1x1,
+                                        noiseModel::Isotropic::Sigma(1, 3.0));
+  auto p_m1 = new DiscreteConditional(m1, "0.5/0.5");
+
+  HybridBayesNet hbn;
+  hbn.emplace_back(p_x0);
+  hbn.emplace_back(p_z0x0);
+  hbn.emplace_back(p_x1m1);
+  hbn.emplace_back(p_m1);
+
+  VectorValues given;
+  given.insert(z0, Vector1(0.5));
+
+  {
+    // Start with no measurement on x1, only on x0
+    HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
+    HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
+
+    // Since no measurement on x1, we hedge our bets
+    DiscreteConditional expected(m1, "0.5/0.5");
+
+    EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete())));
+  }
+
+  {
+    // Now we add a measurement z1 on x1
+    hbn.emplace_back(p_z1x1);
+
+    given.insert(z1, Vector1(2.2));
+    HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
+    HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
+
+    // Since we have a measurement on z2, we get a definite result
+    DiscreteConditional expected(m1, "0.4923083/0.5076917");
+
+    EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 1e-6));
+  }
+}
+
+/* ************************************************************************* */
+/**
+ * Test a model P(x0)P(z0|x0)p(x1|m1)p(z1|x1)p(m1).
+ *
+ * p(x1|m1) has different means and different covariances.
+ *
+ * Converting to a factor graph gives us
+ * P(x0)ϕ(x0)P(x1|m1)ϕ(x1)P(m1)
+ *
+ * If we only have a measurement on z0, then
+ * the probability of x1 should be the ratio of covariances.
+ * Getting a measurement on z1 gives use more information.
+ */
+TEST(GaussianMixtureFactor, TwoStateModel2) {
+  double mu0 = 1.0, mu1 = 3.0;
+  auto model0 = noiseModel::Isotropic::Sigma(1, 6.0);
+  auto model1 = noiseModel::Isotropic::Sigma(1, 4.0);
+
+  DiscreteKey m1(M(1), 2);
+  Key z0 = Z(0), z1 = Z(1), x0 = X(0), x1 = X(1);
+
+  auto c0 = make_shared<GaussianConditional>(x1, Vector1(mu0), I_1x1, model0),
+       c1 = make_shared<GaussianConditional>(x1, Vector1(mu1), I_1x1, model1);
+
+  auto p_x0 = new GaussianConditional(x0, Vector1(0.0), I_1x1,
+                                      noiseModel::Isotropic::Sigma(1, 1.0));
+  auto p_z0x0 = new GaussianConditional(z0, Vector1(0.0), I_1x1, x0, -I_1x1,
+                                        noiseModel::Isotropic::Sigma(1, 1.0));
+  auto p_x1m1 = new GaussianMixture({x1}, {}, {m1}, {c0, c1});
+  auto p_z1x1 = new GaussianConditional(z1, Vector1(0.0), I_1x1, x1, -I_1x1,
+                                        noiseModel::Isotropic::Sigma(1, 3.0));
+  auto p_m1 = new DiscreteConditional(m1, "0.5/0.5");
+
+  HybridBayesNet hbn;
+  hbn.emplace_back(p_x0);
+  hbn.emplace_back(p_z0x0);
+  hbn.emplace_back(p_x1m1);
+  hbn.emplace_back(p_m1);
+
+  VectorValues given;
+  given.insert(z0, Vector1(0.5));
+
+  {
+    // Start with no measurement on x1, only on x0
+    HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
+    HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
+
+    // Since no measurement on x1, we get the ratio of covariances.
+    DiscreteConditional expected(m1, "0.6/0.4");
+
+    EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete())));
+  }
+
+  {
+    // Now we add a measurement z1 on x1
+    hbn.emplace_back(p_z1x1);
+
+    given.insert(z1, Vector1(2.2));
+    HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
+    HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
+
+    // Since we have a measurement on z2, we get a definite result
+    DiscreteConditional expected(m1, "0.52706646/0.47293354");
+
+    EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 1e-6));
+  }
+}
+
+/**
+ * @brief Helper function to specify a Hybrid Bayes Net
+ * {P(X1) P(Z1 | X1, X2, M1)} and convert it to a Hybrid Factor Graph
+ * {P(X1)L(X1, X2, M1; Z1)} by converting to likelihoods given Z1.
+ *
+ * We can specify either different means or different sigmas,
+ * or both for each hybrid factor component.
+ *
+ * @param values Initial values for linearization.
+ * @param means The mean values for the conditional components.
+ * @param sigmas Noise model sigma values (standard deviation).
+ * @param m1 The discrete mode key.
+ * @param z1 The measurement value.
+ * @return HybridGaussianFactorGraph
+ */
+HybridGaussianFactorGraph GetFactorGraphFromBayesNet(
+    const gtsam::Values &values, const std::vector<double> &means,
+    const std::vector<double> &sigmas, DiscreteKey &m1, double z1 = 0.0) {
+  // Noise models
+  auto model0 = noiseModel::Isotropic::Sigma(1, sigmas[0]);
+  auto model1 = noiseModel::Isotropic::Sigma(1, sigmas[1]);
+  auto prior_noise = noiseModel::Isotropic::Sigma(1, 1e-3);
+
+  // GaussianMixtureFactor component factors
+  auto f0 =
+      std::make_shared<BetweenFactor<double>>(X(1), X(2), means[0], model0);
+  auto f1 =
+      std::make_shared<BetweenFactor<double>>(X(1), X(2), means[1], model1);
+  std::vector<NonlinearFactor::shared_ptr> factors{f0, f1};
+
+  /// Get terms for each p^m(z1 | x1, x2)
+  Matrix H0_1, H0_2, H1_1, H1_2;
+  double x1 = values.at<double>(X(1)), x2 = values.at<double>(X(2));
+  Vector d0 = f0->evaluateError(x1, x2, &H0_1, &H0_2);
+  std::vector<std::pair<Key, Matrix>> terms0 = {{Z(1), gtsam::I_1x1 /*Rx*/},
+                                                //
+                                                {X(1), H0_1 /*Sp1*/},
+                                                {X(2), H0_2 /*Tp2*/}};
+
+  Vector d1 = f1->evaluateError(x1, x2, &H1_1, &H1_2);
+  std::vector<std::pair<Key, Matrix>> terms1 = {{Z(1), gtsam::I_1x1 /*Rx*/},
+                                                //
+                                                {X(1), H1_1 /*Sp1*/},
+                                                {X(2), H1_2 /*Tp2*/}};
+  // Create conditional P(Z1 | X1, X2, M1)
+  auto gm = new gtsam::GaussianMixture(
+      {Z(1)}, {X(1), X(2)}, {m1},
+      {std::make_shared<GaussianConditional>(terms0, 1, -d0, model0),
+       std::make_shared<GaussianConditional>(terms1, 1, -d1, model1)});
+  gtsam::HybridBayesNet bn;
+  bn.emplace_back(gm);
+  // bn.print();
+
+  // Create FG via toFactorGraph
+  gtsam::VectorValues measurements;
+  measurements.insert(Z(1), gtsam::I_1x1 * z1);  // Set Z1 = 0
+  HybridGaussianFactorGraph mixture_fg = bn.toFactorGraph(measurements);
+
+  // Linearized prior factor on X1
+  auto prior = PriorFactor<double>(X(1), x1, prior_noise).linearize(values);
+  mixture_fg.push_back(prior);
+
+  return mixture_fg;
+}
+
+/* ************************************************************************* */
+/**
+ * @brief Test components with differing means.
+ *
+ * We specify a hybrid Bayes network P(Z | X, M) =p(X1)p(Z1 | X1, X2, M1),
+ * which is then converted to a factor graph by specifying Z1.
+ * This is a different case since now we have a hybrid factor
+ * with 2 continuous variables ϕ(x1, x2, m1).
+ * p(Z1 | X1, X2, M1) has 2 factors each for the binary
+ * mode m1, with only the means being different.
+ */
+TEST(GaussianMixtureFactor, DifferentMeans) {
+  DiscreteKey m1(M(1), 2);
+
+  Values values;
+  double x1 = 0.0, x2 = 1.75;
+  values.insert(X(1), x1);
+  values.insert(X(2), x2);
+
+  // Different means, same sigma
+  std::vector<double> means{0.0, 2.0}, sigmas{1e-0, 1e-0};
+
+  HybridGaussianFactorGraph hfg =
+      GetFactorGraphFromBayesNet(values, means, sigmas, m1, 0.0);
+
+  {
+    // With no measurement on X2, each mode should be equally likely
+    auto bn = hfg.eliminateSequential();
+    HybridValues actual = bn->optimize();
+
+    HybridValues expected(
+        VectorValues{{X(1), Vector1(0.0)}, {X(2), Vector1(-1.75)}},
+        DiscreteValues{{M(1), 0}});
+
+    EXPECT(assert_equal(expected, actual));
+
+    {
+      DiscreteValues dv{{M(1), 0}};
+      VectorValues cont = bn->optimize(dv);
+      double error = bn->error(HybridValues(cont, dv));
+      // regression
+      EXPECT_DOUBLES_EQUAL(0.69314718056, error, 1e-9);
+    }
+    {
+      DiscreteValues dv{{M(1), 1}};
+      VectorValues cont = bn->optimize(dv);
+      double error = bn->error(HybridValues(cont, dv));
+      // regression
+      EXPECT_DOUBLES_EQUAL(0.69314718056, error, 1e-9);
+    }
+  }
+  {
+    // If we add a measurement on X2, we have more information to work with.
+    // Add a measurement on X2
+    auto prior_noise = noiseModel::Isotropic::Sigma(1, 1e-3);
+    GaussianConditional meas_z2(Z(2), Vector1(2.0), I_1x1, X(2), I_1x1,
+                                prior_noise);
+    auto prior_x2 = meas_z2.likelihood(Vector1(x2));
+
+    hfg.push_back(prior_x2);
+
+    auto bn = hfg.eliminateSequential();
+    HybridValues actual = bn->optimize();
+
+    HybridValues expected(
+        VectorValues{{X(1), Vector1(0.0)}, {X(2), Vector1(0.25)}},
+        DiscreteValues{{M(1), 1}});
+
+    EXPECT(assert_equal(expected, actual));
+
+    {
+      DiscreteValues dv{{M(1), 0}};
+      VectorValues cont = bn->optimize(dv);
+      double error = bn->error(HybridValues(cont, dv));
+      // regression
+      EXPECT_DOUBLES_EQUAL(2.12692448787, error, 1e-9);
+    }
+    {
+      DiscreteValues dv{{M(1), 1}};
+      VectorValues cont = bn->optimize(dv);
+      double error = bn->error(HybridValues(cont, dv));
+      // regression
+      EXPECT_DOUBLES_EQUAL(0.126928487854, error, 1e-9);
+    }
+  }
+}
+
+/* ************************************************************************* */
+/**
+ * @brief Test components with differing covariances
+ * but with a Bayes net P(Z|X, M) converted to a FG.
+ * Same as the DifferentMeans example but in this case,
+ * we keep the means the same and vary the covariances.
+ */
+TEST(GaussianMixtureFactor, DifferentCovariances) {
+  DiscreteKey m1(M(1), 2);
+
+  Values values;
+  double x1 = 1.0, x2 = 1.0;
+  values.insert(X(1), x1);
+  values.insert(X(2), x2);
+
+  std::vector<double> means{0.0, 0.0}, sigmas{1e2, 1e-2};
+  HybridGaussianFactorGraph mixture_fg =
+      GetFactorGraphFromBayesNet(values, means, sigmas, m1);
+
+  auto hbn = mixture_fg.eliminateSequential();
+
+  VectorValues cv;
+  cv.insert(X(1), Vector1(0.0));
+  cv.insert(X(2), Vector1(0.0));
+
+  // Check that the error values at the MLE point μ.
+  AlgebraicDecisionTree<Key> errorTree = hbn->errorTree(cv);
+
+  DiscreteValues dv0{{M(1), 0}};
+  DiscreteValues dv1{{M(1), 1}};
+
+  // regression
+  EXPECT_DOUBLES_EQUAL(9.90348755254, errorTree(dv0), 1e-9);
+  EXPECT_DOUBLES_EQUAL(0.69314718056, errorTree(dv1), 1e-9);
+
+  DiscreteConditional expected_m1(m1, "0.5/0.5");
+  DiscreteConditional actual_m1 = *(hbn->at(2)->asDiscrete());
+
+  EXPECT(assert_equal(expected_m1, actual_m1));
 }
 
 /* ************************************************************************* */

gtsam/hybrid/tests/testHybridNonlinearFactorGraph.cpp

@@ -510,6 +510,7 @@ factor 0:
   b = [ -10 ]
   No noise model
 factor 1: 
+GaussianMixtureFactor
 Hybrid [x0 x1; m0]{
  Choice(m0) 
  0 Leaf :
@@ -534,6 +535,7 @@ Hybrid [x0 x1; m0]{
 
 }
 factor 2: 
+GaussianMixtureFactor
 Hybrid [x1 x2; m1]{
  Choice(m1) 
  0 Leaf :

gtsam/hybrid/tests/testMixtureFactor.cpp

@@ -18,6 +18,9 @@
 
 #include <gtsam/base/TestableAssertions.h>
 #include <gtsam/discrete/DiscreteValues.h>
+#include <gtsam/hybrid/HybridBayesNet.h>
+#include <gtsam/hybrid/HybridGaussianFactorGraph.h>
+#include <gtsam/hybrid/HybridNonlinearFactorGraph.h>
 #include <gtsam/hybrid/MixtureFactor.h>
 #include <gtsam/inference/Symbol.h>
 #include <gtsam/slam/BetweenFactor.h>
@@ -115,6 +118,156 @@ TEST(MixtureFactor, Dim) {
   EXPECT_LONGS_EQUAL(1, mixtureFactor.dim());
 }
 
+/* ************************************************************************* */
+// Test components with differing means
+TEST(MixtureFactor, DifferentMeans) {
+  DiscreteKey m1(M(1), 2), m2(M(2), 2);
+
+  Values values;
+  double x1 = 0.0, x2 = 1.75, x3 = 2.60;
+  values.insert(X(1), x1);
+  values.insert(X(2), x2);
+  values.insert(X(3), x3);
+
+  auto model0 = noiseModel::Isotropic::Sigma(1, 1e-0);
+  auto model1 = noiseModel::Isotropic::Sigma(1, 1e-0);
+  auto prior_noise = noiseModel::Isotropic::Sigma(1, 1e-0);
+
+  auto f0 = std::make_shared<BetweenFactor<double>>(X(1), X(2), 0.0, model0);
+  auto f1 = std::make_shared<BetweenFactor<double>>(X(1), X(2), 2.0, model1);
+  std::vector<NonlinearFactor::shared_ptr> factors{f0, f1};
+
+  MixtureFactor mixtureFactor({X(1), X(2)}, {m1}, factors);
+  HybridNonlinearFactorGraph hnfg;
+  hnfg.push_back(mixtureFactor);
+
+  f0 = std::make_shared<BetweenFactor<double>>(X(2), X(3), 0.0, model0);
+  f1 = std::make_shared<BetweenFactor<double>>(X(2), X(3), 2.0, model1);
+  std::vector<NonlinearFactor::shared_ptr> factors23{f0, f1};
+  hnfg.push_back(MixtureFactor({X(2), X(3)}, {m2}, factors23));
+
+  auto prior = PriorFactor<double>(X(1), x1, prior_noise);
+  hnfg.push_back(prior);
+
+  hnfg.emplace_shared<PriorFactor<double>>(X(2), 2.0, prior_noise);
+
+  auto hgfg = hnfg.linearize(values);
+  auto bn = hgfg->eliminateSequential();
+  HybridValues actual = bn->optimize();
+
+  HybridValues expected(
+      VectorValues{
+          {X(1), Vector1(0.0)}, {X(2), Vector1(0.25)}, {X(3), Vector1(-0.6)}},
+      DiscreteValues{{M(1), 1}, {M(2), 0}});
+
+  EXPECT(assert_equal(expected, actual));
+
+  {
+    DiscreteValues dv{{M(1), 0}, {M(2), 0}};
+    VectorValues cont = bn->optimize(dv);
+    double error = bn->error(HybridValues(cont, dv));
+    // regression
+    EXPECT_DOUBLES_EQUAL(1.77418393408, error, 1e-9);
+  }
+  {
+    DiscreteValues dv{{M(1), 0}, {M(2), 1}};
+    VectorValues cont = bn->optimize(dv);
+    double error = bn->error(HybridValues(cont, dv));
+    // regression
+    EXPECT_DOUBLES_EQUAL(1.77418393408, error, 1e-9);
+  }
+  {
+    DiscreteValues dv{{M(1), 1}, {M(2), 0}};
+    VectorValues cont = bn->optimize(dv);
+    double error = bn->error(HybridValues(cont, dv));
+    // regression
+    EXPECT_DOUBLES_EQUAL(1.10751726741, error, 1e-9);
+  }
+  {
+    DiscreteValues dv{{M(1), 1}, {M(2), 1}};
+    VectorValues cont = bn->optimize(dv);
+    double error = bn->error(HybridValues(cont, dv));
+    // regression
+    EXPECT_DOUBLES_EQUAL(1.10751726741, error, 1e-9);
+  }
+}
+
+/* ************************************************************************* */
+// Test components with differing covariances
+TEST(MixtureFactor, DifferentCovariances) {
+  DiscreteKey m1(M(1), 2);
+
+  Values values;
+  double x1 = 1.0, x2 = 1.0;
+  values.insert(X(1), x1);
+  values.insert(X(2), x2);
+
+  double between = 0.0;
+
+  auto model0 = noiseModel::Isotropic::Sigma(1, 1e2);
+  auto model1 = noiseModel::Isotropic::Sigma(1, 1e-2);
+  auto prior_noise = noiseModel::Isotropic::Sigma(1, 1e-3);
+
+  auto f0 =
+      std::make_shared<BetweenFactor<double>>(X(1), X(2), between, model0);
+  auto f1 =
+      std::make_shared<BetweenFactor<double>>(X(1), X(2), between, model1);
+  std::vector<NonlinearFactor::shared_ptr> factors{f0, f1};
+
+  // Create via toFactorGraph
+  using symbol_shorthand::Z;
+  Matrix H0_1, H0_2, H1_1, H1_2;
+  Vector d0 = f0->evaluateError(x1, x2, &H0_1, &H0_2);
+  std::vector<std::pair<Key, Matrix>> terms0 = {{Z(1), gtsam::I_1x1 /*Rx*/},
+                                                //
+                                                {X(1), H0_1 /*Sp1*/},
+                                                {X(2), H0_2 /*Tp2*/}};
+
+  Vector d1 = f1->evaluateError(x1, x2, &H1_1, &H1_2);
+  std::vector<std::pair<Key, Matrix>> terms1 = {{Z(1), gtsam::I_1x1 /*Rx*/},
+                                                //
+                                                {X(1), H1_1 /*Sp1*/},
+                                                {X(2), H1_2 /*Tp2*/}};
+  auto gm = new gtsam::GaussianMixture(
+      {Z(1)}, {X(1), X(2)}, {m1},
+      {std::make_shared<GaussianConditional>(terms0, 1, -d0, model0),
+       std::make_shared<GaussianConditional>(terms1, 1, -d1, model1)});
+  gtsam::HybridBayesNet bn;
+  bn.emplace_back(gm);
+
+  gtsam::VectorValues measurements;
+  measurements.insert(Z(1), gtsam::Z_1x1);
+  // Create FG with single GaussianMixtureFactor
+  HybridGaussianFactorGraph mixture_fg = bn.toFactorGraph(measurements);
+
+  // Linearized prior factor on X1
+  auto prior = PriorFactor<double>(X(1), x1, prior_noise).linearize(values);
+  mixture_fg.push_back(prior);
+
+  auto hbn = mixture_fg.eliminateSequential();
+
+  VectorValues cv;
+  cv.insert(X(1), Vector1(0.0));
+  cv.insert(X(2), Vector1(0.0));
+  // P(m1) = [0.5, 0.5], so we should pick 0
+  DiscreteValues dv;
+  dv.insert({M(1), 0});
+  HybridValues expected_values(cv, dv);
+
+  HybridValues actual_values = hbn->optimize();
+  EXPECT(assert_equal(expected_values, actual_values));
+
+  // Check that we get different error values at the MLE point μ.
+  AlgebraicDecisionTree<Key> errorTree = hbn->errorTree(cv);
+
+  HybridValues hv0(cv, DiscreteValues{{M(1), 0}});
+  HybridValues hv1(cv, DiscreteValues{{M(1), 1}});
+
+  AlgebraicDecisionTree<Key> expectedErrorTree(m1, 9.90348755254,
+                                               0.69314718056);
+  EXPECT(assert_equal(expectedErrorTree, errorTree));
+}
+
 /* ************************************************************************* */
 int main() {
   TestResult tr;

gtsam/linear/VectorValues.h

@@ -263,11 +263,6 @@ namespace gtsam {
     /** equals required by Testable for unit testing */
     bool equals(const VectorValues& x, double tol = 1e-9) const;
 
-    /// Check equality.
-    friend bool operator==(const VectorValues& lhs, const VectorValues& rhs) {
-      return lhs.equals(rhs);
-    }
-
     /// @{
     /// @name Advanced Interface
     /// @{