diff --git a/gtsam/hybrid/tests/testGaussianMixture.cpp b/gtsam/hybrid/tests/testGaussianMixture.cpp index 4da61912e1..7c241acb9c 100644 --- a/gtsam/hybrid/tests/testGaussianMixture.cpp +++ b/gtsam/hybrid/tests/testGaussianMixture.cpp @@ -31,7 +31,6 @@ #include using namespace gtsam; -using noiseModel::Isotropic; using symbol_shorthand::M; using symbol_shorthand::X; using symbol_shorthand::Z; diff --git a/gtsam/hybrid/tests/testGaussianMixtureFactor.cpp b/gtsam/hybrid/tests/testGaussianMixtureFactor.cpp index fcd9dd08f8..dab11039f1 100644 --- a/gtsam/hybrid/tests/testGaussianMixtureFactor.cpp +++ b/gtsam/hybrid/tests/testGaussianMixtureFactor.cpp @@ -18,7 +18,9 @@ * @date December 2021 */ +#include #include +#include #include #include #include @@ -27,16 +29,17 @@ #include #include #include +#include #include #include // Include for test suite #include +#include + using namespace std; using namespace gtsam; -using noiseModel::Isotropic; -using symbol_shorthand::F; using symbol_shorthand::M; using symbol_shorthand::X; using symbol_shorthand::Z; @@ -232,7 +235,7 @@ static HybridBayesNet GetGaussianMixtureModel(double mu0, double mu1, hbn.emplace_shared(KeyVector{z}, KeyVector{}, DiscreteKeys{m}, std::vector{c0, c1}); - auto mixing = make_shared(m, "0.5/0.5"); + auto mixing = make_shared(m, "50/50"); hbn.push_back(mixing); return hbn; @@ -278,7 +281,7 @@ TEST(GaussianMixtureFactor, GaussianMixtureModel) { // At the halfway point between the means, we should get P(m|z)=0.5 HybridBayesNet expected; - expected.emplace_shared(m, "0.5/0.5"); + expected.emplace_shared(m, "50/50"); EXPECT(assert_equal(expected, *bn)); } @@ -387,103 +390,134 @@ TEST(GaussianMixtureFactor, GaussianMixtureModel2) { namespace test_two_state_estimation { -/// Create Two State Bayes Network with measurements -static HybridBayesNet CreateBayesNet(double mu0, double mu1, double sigma0, - double sigma1, - bool add_second_measurement = false, - double prior_sigma = 1e-3, - double measurement_sigma = 3.0) { - DiscreteKey m1(M(1), 2); - Key z0 = Z(0), z1 = Z(1); - Key x0 = X(0), x1 = X(1); - - HybridBayesNet hbn; +DiscreteKey m1(M(1), 2); - auto measurement_model = noiseModel::Isotropic::Sigma(1, measurement_sigma); - // Add measurement P(z0 | x0) - auto p_z0 = std::make_shared( - z0, Vector1(0.0), -I_1x1, x0, I_1x1, measurement_model); - hbn.push_back(p_z0); +void addMeasurement(HybridBayesNet& hbn, Key z_key, Key x_key, double sigma) { + auto measurement_model = noiseModel::Isotropic::Sigma(1, sigma); + hbn.emplace_shared(z_key, Vector1(0.0), I_1x1, x_key, + -I_1x1, measurement_model); +} - // Add hybrid motion model +/// Create hybrid motion model p(x1 | x0, m1) +static GaussianMixture::shared_ptr CreateHybridMotionModel(double mu0, + double mu1, + double sigma0, + double sigma1) { auto model0 = noiseModel::Isotropic::Sigma(1, sigma0); auto model1 = noiseModel::Isotropic::Sigma(1, sigma1); - auto c0 = make_shared(x1, Vector1(mu0), I_1x1, x0, + auto c0 = make_shared(X(1), Vector1(mu0), I_1x1, X(0), -I_1x1, model0), - c1 = make_shared(x1, Vector1(mu1), I_1x1, x0, + c1 = make_shared(X(1), Vector1(mu1), I_1x1, X(0), -I_1x1, model1); + return std::make_shared( + KeyVector{X(1)}, KeyVector{X(0)}, DiscreteKeys{m1}, std::vector{c0, c1}); +} - auto motion = std::make_shared( - KeyVector{x1}, KeyVector{x0}, DiscreteKeys{m1}, std::vector{c0, c1}); - hbn.push_back(motion); +/// Create two state Bayes network with 1 or two measurement models +HybridBayesNet CreateBayesNet( + const GaussianMixture::shared_ptr& hybridMotionModel, + bool add_second_measurement = false) { + HybridBayesNet hbn; + + // Add measurement model p(z0 | x0) + addMeasurement(hbn, Z(0), X(0), 3.0); + // Optionally add second measurement model p(z1 | x1) if (add_second_measurement) { - // Add second measurement - auto p_z1 = std::make_shared( - z1, Vector1(0.0), -I_1x1, x1, I_1x1, measurement_model); - hbn.push_back(p_z1); + addMeasurement(hbn, Z(1), X(1), 3.0); } + // Add hybrid motion model + hbn.push_back(hybridMotionModel); + // Discrete uniform prior. - auto p_m1 = std::make_shared(m1, "0.5/0.5"); - hbn.push_back(p_m1); + hbn.emplace_shared(m1, "50/50"); return hbn; } +/// Approximate the discrete marginal P(m1) using importance sampling +std::pair approximateDiscreteMarginal( + const HybridBayesNet& hbn, + const GaussianMixture::shared_ptr& hybridMotionModel, + const VectorValues& given, size_t N = 100000) { + /// Create importance sampling network q(x0,x1,m) = p(x1|x0,m1) q(x0) P(m1), + /// using q(x0) = N(z0, sigmaQ) to sample x0. + HybridBayesNet q; + q.push_back(hybridMotionModel); // Add hybrid motion model + q.emplace_shared(GaussianConditional::FromMeanAndStddev( + X(0), given.at(Z(0)), /* sigmaQ = */ 3.0)); // Add proposal q(x0) for x0 + q.emplace_shared(m1, "50/50"); // Discrete prior. + + // Do importance sampling + double w0 = 0.0, w1 = 0.0; + std::mt19937_64 rng(42); + for (int i = 0; i < N; i++) { + HybridValues sample = q.sample(&rng); + sample.insert(given); + double weight = hbn.evaluate(sample) / q.evaluate(sample); + (sample.atDiscrete(M(1)) == 0) ? w0 += weight : w1 += weight; + } + double pm1 = w1 / (w0 + w1); + std::cout << "p(m0) = " << 100 * (1.0 - pm1) << std::endl; + std::cout << "p(m1) = " << 100 * pm1 << std::endl; + return {1.0 - pm1, pm1}; +} + } // namespace test_two_state_estimation /* ************************************************************************* */ /** - * Test a model P(z0|x0)P(x1|x0,m1)P(z1|x1)P(m1). + * Test a model p(z0|x0)p(z1|x1)p(x1|x0,m1)P(m1). * - * P(f01|x1,x0,m1) has different means and same covariance. + * p(x1|x0,m1) has mode-dependent mean but same covariance. * - * Converting to a factor graph gives us - * ϕ(x0)ϕ(x1,x0,m1)ϕ(x1)P(m1) + * Converting to a factor graph gives us ϕ(x0;z0)ϕ(x1;z1)ϕ(x1,x0,m1)P(m1) * - * If we only have a measurement on z0, then - * the probability of m1 should be 0.5/0.5. + * If we only have a measurement on x0, then + * the posterior probability of m1 should be 0.5/0.5. * Getting a measurement on z1 gives use more information. */ TEST(GaussianMixtureFactor, TwoStateModel) { using namespace test_two_state_estimation; double mu0 = 1.0, mu1 = 3.0; - double sigma = 2.0; - - DiscreteKey m1(M(1), 2); - Key z0 = Z(0), z1 = Z(1); + double sigma = 0.5; + auto hybridMotionModel = CreateHybridMotionModel(mu0, mu1, sigma, sigma); // Start with no measurement on x1, only on x0 - HybridBayesNet hbn = CreateBayesNet(mu0, mu1, sigma, sigma, false); + const Vector1 z0(0.5); VectorValues given; - given.insert(z0, Vector1(0.5)); + given.insert(Z(0), z0); { + HybridBayesNet hbn = CreateBayesNet(hybridMotionModel); 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"); + // Importance sampling run with 100k samples gives 50.051/49.949 + // approximateDiscreteMarginal(hbn, hybridMotionModel, given); + DiscreteConditional expected(m1, "50/50"); EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()))); } { - // Now we add a measurement z1 on x1 - hbn = CreateBayesNet(mu0, mu1, sigma, sigma, true); + // If we set z1=4.5 (>> 2.5 which is the halfway point), + // probability of discrete mode should be leaning to m1==1. + const Vector1 z1(4.5); + given.insert(Z(1), z1); - // If we see z1=2.6 (> 2.5 which is the halfway point), - // discrete mode should say m1=1 - given.insert(z1, Vector1(2.6)); + HybridBayesNet hbn = CreateBayesNet(hybridMotionModel, true); 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, "0.49772729/0.50227271"); - // regression - EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 1e-6)); + // Since we have a measurement on x1, we get a definite result + // Values taken from an importance sampling run with 100k samples: + // approximateDiscreteMarginal(hbn, hybridMotionModel, given); + DiscreteConditional expected(m1, "44.3854/55.6146"); + EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 0.002)); } } @@ -504,87 +538,110 @@ TEST(GaussianMixtureFactor, TwoStateModel2) { using namespace test_two_state_estimation; double mu0 = 1.0, mu1 = 3.0; - double sigma0 = 6.0, sigma1 = 4.0; - auto model0 = noiseModel::Isotropic::Sigma(1, sigma0); - auto model1 = noiseModel::Isotropic::Sigma(1, sigma1); - - DiscreteKey m1(M(1), 2); - Key z0 = Z(0), z1 = Z(1); + double sigma0 = 0.5, sigma1 = 2.0; + auto hybridMotionModel = CreateHybridMotionModel(mu0, mu1, sigma0, sigma1); // Start with no measurement on x1, only on x0 - HybridBayesNet hbn = CreateBayesNet(mu0, mu1, sigma0, sigma1, false); - + const Vector1 z0(0.5); VectorValues given; - given.insert(z0, Vector1(0.5)); + given.insert(Z(0), z0); { - // Start with no measurement on x1, only on x0 + HybridBayesNet hbn = CreateBayesNet(hybridMotionModel); HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given); - { - VectorValues vv{ - {X(0), Vector1(0.0)}, {X(1), Vector1(1.0)}, {Z(0), Vector1(0.5)}}; - HybridValues hv0(vv, DiscreteValues{{M(1), 0}}), - hv1(vv, DiscreteValues{{M(1), 1}}); - EXPECT_DOUBLES_EQUAL(gfg.error(hv0) / hbn.error(hv0), - gfg.error(hv1) / hbn.error(hv1), 1e-9); - } - { - VectorValues vv{ - {X(0), Vector1(0.5)}, {X(1), Vector1(3.0)}, {Z(0), Vector1(0.5)}}; - HybridValues hv0(vv, DiscreteValues{{M(1), 0}}), - hv1(vv, DiscreteValues{{M(1), 1}}); + // Check that ratio of Bayes net and factor graph for different modes is + // equal for several values of {x0,x1}. + for (VectorValues vv : + {VectorValues{{X(0), Vector1(0.0)}, {X(1), Vector1(1.0)}}, + VectorValues{{X(0), Vector1(0.5)}, {X(1), Vector1(3.0)}}}) { + vv.insert(given); // add measurements for HBN + HybridValues hv0(vv, {{M(1), 0}}), hv1(vv, {{M(1), 1}}); EXPECT_DOUBLES_EQUAL(gfg.error(hv0) / hbn.error(hv0), gfg.error(hv1) / hbn.error(hv1), 1e-9); } HybridBayesNet::shared_ptr bn = gfg.eliminateSequential(); + // Importance sampling run with 100k samples gives 50.095/49.905 + // approximateDiscreteMarginal(hbn, hybridMotionModel, given); + // Since no measurement on x1, we a 50/50 probability auto p_m = bn->at(2)->asDiscrete(); - EXPECT_DOUBLES_EQUAL(0.5, p_m->operator()(DiscreteValues{{m1.first, 0}}), - 1e-9); - EXPECT_DOUBLES_EQUAL(0.5, p_m->operator()(DiscreteValues{{m1.first, 1}}), - 1e-9); + EXPECT_DOUBLES_EQUAL(0.5, p_m->operator()({{M(1), 0}}), 1e-9); + EXPECT_DOUBLES_EQUAL(0.5, p_m->operator()({{M(1), 1}}), 1e-9); } { // Now we add a measurement z1 on x1 - hbn = CreateBayesNet(mu0, mu1, sigma0, sigma1, true); + const Vector1 z1(4.0); // favors m==1 + given.insert(Z(1), z1); - given.insert(z1, Vector1(2.2)); + HybridBayesNet hbn = CreateBayesNet(hybridMotionModel, true); HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given); - { - VectorValues vv{{X(0), Vector1(0.0)}, - {X(1), Vector1(1.0)}, - {Z(0), Vector1(0.5)}, - {Z(1), Vector1(2.2)}}; - HybridValues hv0(vv, DiscreteValues{{M(1), 0}}), - hv1(vv, DiscreteValues{{M(1), 1}}); - EXPECT_DOUBLES_EQUAL(gfg.error(hv0) / hbn.error(hv0), - gfg.error(hv1) / hbn.error(hv1), 1e-9); - } - { - VectorValues vv{{X(0), Vector1(0.5)}, - {X(1), Vector1(3.0)}, - {Z(0), Vector1(0.5)}, - {Z(1), Vector1(2.2)}}; - HybridValues hv0(vv, DiscreteValues{{M(1), 0}}), - hv1(vv, DiscreteValues{{M(1), 1}}); + // Check that ratio of Bayes net and factor graph for different modes is + // equal for several values of {x0,x1}. + for (VectorValues vv : + {VectorValues{{X(0), Vector1(0.0)}, {X(1), Vector1(1.0)}}, + VectorValues{{X(0), Vector1(0.5)}, {X(1), Vector1(3.0)}}}) { + vv.insert(given); // add measurements for HBN + HybridValues hv0(vv, {{M(1), 0}}), hv1(vv, {{M(1), 1}}); EXPECT_DOUBLES_EQUAL(gfg.error(hv0) / hbn.error(hv0), gfg.error(hv1) / hbn.error(hv1), 1e-9); } HybridBayesNet::shared_ptr bn = gfg.eliminateSequential(); - // Since we have a measurement on z2, we get a definite result - DiscreteConditional expected(m1, "0.44744586/0.55255414"); - // regression - EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 1e-6)); + // Values taken from an importance sampling run with 100k samples: + // approximateDiscreteMarginal(hbn, hybridMotionModel, given); + DiscreteConditional expected(m1, "48.3158/51.6842"); + EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 0.002)); + } + + { + // Add a different measurement z1 on x1 that favors m==0 + const Vector1 z1(1.1); + given.insert_or_assign(Z(1), z1); + + HybridBayesNet hbn = CreateBayesNet(hybridMotionModel, true); + HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given); + HybridBayesNet::shared_ptr bn = gfg.eliminateSequential(); + + // Values taken from an importance sampling run with 100k samples: + // approximateDiscreteMarginal(hbn, hybridMotionModel, given); + DiscreteConditional expected(m1, "55.396/44.604"); + EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 0.002)); } } +/* ************************************************************************* */ +/** + * Same model, P(z0|x0)P(x1|x0,m1)P(z1|x1)P(m1), but now with very informative + * measurements and vastly different motion model: either stand still or move + * far. This yields a very informative posterior. + */ +TEST(GaussianMixtureFactor, TwoStateModel3) { + using namespace test_two_state_estimation; + + double mu0 = 0.0, mu1 = 10.0; + double sigma0 = 0.2, sigma1 = 5.0; + auto hybridMotionModel = CreateHybridMotionModel(mu0, mu1, sigma0, sigma1); + + // We only check the 2-measurement case + const Vector1 z0(0.0), z1(10.0); + VectorValues given{{Z(0), z0}, {Z(1), z1}}; + + HybridBayesNet hbn = CreateBayesNet(hybridMotionModel, true); + HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given); + HybridBayesNet::shared_ptr bn = gfg.eliminateSequential(); + + // Values taken from an importance sampling run with 100k samples: + // approximateDiscreteMarginal(hbn, hybridMotionModel, given); + DiscreteConditional expected(m1, "8.91527/91.0847"); + EXPECT(assert_equal(expected, *(bn->at(2)->asDiscrete()), 0.002)); +} + /* ************************************************************************* */ int main() { TestResult tr;