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| /* ---------------------------------------------------------------------------- | ||
| * GTSAM Copyright 2010, Georgia Tech Research Corporation, | ||
| * Atlanta, Georgia 30332-0415 | ||
| * All Rights Reserved | ||
| * Authors: Frank Dellaert, et al. (see THANKS for the full author list) | ||
| * See LICENSE for the license information | ||
| * -------------------------------------------------------------------------- */ | ||
|
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| /** | ||
| * @file testGaussianMixture.cpp | ||
| * @brief Test hybrid elimination with a simple mixture model | ||
| * @author Varun Agrawal | ||
| * @author Frank Dellaert | ||
| * @date September 2024 | ||
| */ | ||
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| #include <gtsam/discrete/DecisionTreeFactor.h> | ||
| #include <gtsam/discrete/DiscreteConditional.h> | ||
| #include <gtsam/discrete/DiscreteKey.h> | ||
| #include <gtsam/hybrid/HybridBayesNet.h> | ||
| #include <gtsam/hybrid/HybridGaussianConditional.h> | ||
| #include <gtsam/hybrid/HybridGaussianFactorGraph.h> | ||
| #include <gtsam/inference/Key.h> | ||
| #include <gtsam/inference/Symbol.h> | ||
| #include <gtsam/linear/GaussianConditional.h> | ||
| #include <gtsam/linear/NoiseModel.h> | ||
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| // Include for test suite | ||
| #include <CppUnitLite/TestHarness.h> | ||
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| using namespace gtsam; | ||
| using symbol_shorthand::M; | ||
| using symbol_shorthand::Z; | ||
|
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| // Define mode key and an assignment m==1 | ||
| const DiscreteKey m(M(0), 2); | ||
| const DiscreteValues m1Assignment{{M(0), 1}}; | ||
|
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| // Define a 50/50 prior on the mode | ||
| DiscreteConditional::shared_ptr mixing = | ||
| std::make_shared<DiscreteConditional>(m, "60/40"); | ||
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| // define Continuous keys | ||
| const KeyVector continuousKeys{Z(0)}; | ||
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| /** | ||
| * Create a simple Gaussian Mixture Model represented as p(z|m)P(m) | ||
| * where m is a discrete variable and z is a continuous variable. | ||
| * The "mode" m is binary and depending on m, we have 2 different means | ||
| * μ1 and μ2 for the Gaussian density p(z|m). | ||
| */ | ||
| HybridBayesNet GaussianMixtureModel(double mu0, double mu1, double sigma0, | ||
| double sigma1) { | ||
| HybridBayesNet hbn; | ||
| auto model0 = noiseModel::Isotropic::Sigma(1, sigma0); | ||
| auto model1 = noiseModel::Isotropic::Sigma(1, sigma1); | ||
| auto c0 = std::make_shared<GaussianConditional>(Z(0), Vector1(mu0), I_1x1, | ||
| model0), | ||
| c1 = std::make_shared<GaussianConditional>(Z(0), Vector1(mu1), I_1x1, | ||
| model1); | ||
| hbn.emplace_shared<HybridGaussianConditional>(continuousKeys, KeyVector{}, m, | ||
| std::vector{c0, c1}); | ||
| hbn.push_back(mixing); | ||
| return hbn; | ||
| } | ||
|
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||
| /// Gaussian density function | ||
| double Gaussian(double mu, double sigma, double z) { | ||
| return exp(-0.5 * pow((z - mu) / sigma, 2)) / sqrt(2 * M_PI * sigma * sigma); | ||
| }; | ||
|
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||
| /** | ||
| * Closed form computation of P(m=1|z). | ||
| * If sigma0 == sigma1, it simplifies to a sigmoid function. | ||
| * Hardcodes 60/40 prior on mode. | ||
| */ | ||
| double prob_m_z(double mu0, double mu1, double sigma0, double sigma1, | ||
| double z) { | ||
| const double p0 = 0.6 * Gaussian(mu0, sigma0, z); | ||
| const double p1 = 0.4 * Gaussian(mu1, sigma1, z); | ||
| return p1 / (p0 + p1); | ||
| }; | ||
|
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| /// Given \phi(m;z)\phi(m) use eliminate to obtain P(m|z). | ||
| DiscreteConditional SolveHFG(const HybridGaussianFactorGraph &hfg) { | ||
| return *hfg.eliminateSequential()->at(0)->asDiscrete(); | ||
| } | ||
|
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| /// Given p(z,m) and z, convert to HFG and solve. | ||
| DiscreteConditional SolveHBN(const HybridBayesNet &hbn, double z) { | ||
| VectorValues given{{Z(0), Vector1(z)}}; | ||
| return SolveHFG(hbn.toFactorGraph(given)); | ||
| } | ||
|
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||
| /* | ||
| * Test a Gaussian Mixture Model P(m)p(z|m) with same sigma. | ||
| * The posterior, as a function of z, should be a sigmoid function. | ||
| */ | ||
| TEST(GaussianMixture, GaussianMixtureModel) { | ||
| double mu0 = 1.0, mu1 = 3.0; | ||
| double sigma = 2.0; | ||
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| auto hbn = GaussianMixtureModel(mu0, mu1, sigma, sigma); | ||
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| // At the halfway point between the means, we should get P(m|z)=0.5 | ||
| double midway = mu1 - mu0; | ||
| auto pMid = SolveHBN(hbn, midway); | ||
| EXPECT(assert_equal(DiscreteConditional(m, "60/40"), pMid)); | ||
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| // Everywhere else, the result should be a sigmoid. | ||
| for (const double shift : {-4, -2, 0, 2, 4}) { | ||
| const double z = midway + shift; | ||
| const double expected = prob_m_z(mu0, mu1, sigma, sigma, z); | ||
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| // Workflow 1: convert HBN to HFG and solve | ||
| auto posterior1 = SolveHBN(hbn, z); | ||
| EXPECT_DOUBLES_EQUAL(expected, posterior1(m1Assignment), 1e-8); | ||
|
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| // Workflow 2: directly specify HFG and solve | ||
| HybridGaussianFactorGraph hfg1; | ||
| hfg1.emplace_shared<DecisionTreeFactor>( | ||
| m, std::vector{Gaussian(mu0, sigma, z), Gaussian(mu1, sigma, z)}); | ||
| hfg1.push_back(mixing); | ||
| auto posterior2 = SolveHFG(hfg1); | ||
| EXPECT_DOUBLES_EQUAL(expected, posterior2(m1Assignment), 1e-8); | ||
| } | ||
| } | ||
|
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||
| /* | ||
| * Test a Gaussian Mixture Model P(m)p(z|m) with different sigmas. | ||
| * The posterior, as a function of z, should be a unimodal function. | ||
| */ | ||
| TEST(GaussianMixture, GaussianMixtureModel2) { | ||
| double mu0 = 1.0, mu1 = 3.0; | ||
| double sigma0 = 8.0, sigma1 = 4.0; | ||
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| auto hbn = GaussianMixtureModel(mu0, mu1, sigma0, sigma1); | ||
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| // We get zMax=3.1333 by finding the maximum value of the function, at which | ||
| // point the mode m==1 is about twice as probable as m==0. | ||
| double zMax = 3.133; | ||
| auto pMax = SolveHBN(hbn, zMax); | ||
| EXPECT(assert_equal(DiscreteConditional(m, "42/58"), pMax, 1e-4)); | ||
|
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| // Everywhere else, the result should be a bell curve like function. | ||
| for (const double shift : {-4, -2, 0, 2, 4}) { | ||
| const double z = zMax + shift; | ||
| const double expected = prob_m_z(mu0, mu1, sigma0, sigma1, z); | ||
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| // Workflow 1: convert HBN to HFG and solve | ||
| auto posterior1 = SolveHBN(hbn, z); | ||
| EXPECT_DOUBLES_EQUAL(expected, posterior1(m1Assignment), 1e-8); | ||
|
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| // Workflow 2: directly specify HFG and solve | ||
| HybridGaussianFactorGraph hfg; | ||
| hfg.emplace_shared<DecisionTreeFactor>( | ||
| m, std::vector{Gaussian(mu0, sigma0, z), Gaussian(mu1, sigma1, z)}); | ||
| hfg.push_back(mixing); | ||
| auto posterior2 = SolveHFG(hfg); | ||
| EXPECT_DOUBLES_EQUAL(expected, posterior2(m1Assignment), 1e-8); | ||
| } | ||
| } | ||
|
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| /* ************************************************************************* */ | ||
| int main() { | ||
| TestResult tr; | ||
| return TestRegistry::runAllTests(tr); | ||
| } | ||
| /* ************************************************************************* */ |
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