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improve the gaussian mixture model tests

release/4.3a0
Varun Agrawal 2024-08-28 13:18:55 -04:00
parent 3dab868ef0
commit 088f1f04bb
1 changed files with 85 additions and 28 deletions
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113
gtsam/hybrid/tests/testGaussianMixtureFactor.cpp
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@ -200,6 +200,42 @@ TEST(GaussianMixtureFactor, Error) {
4.0, mixtureFactor.error({continuousValues, discreteValues}), 1e-9);
}
namespace test_gmm {
/**
* Function to compute P(m=1|z). For P(m=0|z), swap `mus and sigmas.
* Follows equation 7.108 since it is more generic.
*/
double sigmoid(double mu0, double mu1, double sigma0, double sigma1, double z) {
double x1 = ((z - mu0) / sigma0), x2 = ((z - mu1) / sigma1);
double d = std::sqrt(sigma0 * sigma0) / std::sqrt(sigma1 * sigma1);
double e = d * std::exp(-0.5 * (x1 * x1 - x2 * x2));
return 1 / (1 + e);
};
HybridBayesNet GetGaussianMixtureModel(double mu0, double mu1, double sigma0,
double sigma1) {
DiscreteKey m(M(0), 2);
Key z = Z(0);
auto model0 = noiseModel::Isotropic::Sigma(1, sigma0);
auto model1 = noiseModel::Isotropic::Sigma(1, sigma1);
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);
return hbn;
}
} // namespace test_gmm
/* ************************************************************************* */
/**
* Test a simple Gaussian Mixture Model represented as P(m)P(z|m)
@ -211,6 +247,8 @@ TEST(GaussianMixtureFactor, Error) {
* which represents a sigmoid function.
*/
TEST(GaussianMixtureFactor, GaussianMixtureModel) {
using namespace test_gmm;
double mu0 = 1.0, mu1 = 3.0;
double sigma = 2.0;
auto model = noiseModel::Isotropic::Sigma(1, sigma);
@ -218,28 +256,52 @@ TEST(GaussianMixtureFactor, GaussianMixtureModel) {
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);
auto hbn = GetGaussianMixtureModel(mu0, mu1, sigma, sigma);
// 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));
// So should be P(m=1|z) = 0.5 at z=3.0 - 1.0=2.0
double midway = mu1 - mu0, lambda = 4;
{
VectorValues given;
given.insert(z, Vector1(midway));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
HybridBayesNet expected;
expected.emplace_back(new DiscreteConditional(m, "0.5/0.5"));
EXPECT_DOUBLES_EQUAL(
sigmoid(mu0, mu1, sigma, sigma, midway),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{M(0), 1}}), 1e-8);
EXPECT(assert_equal(expected, *bn));
// At the halfway point between the means, we should get P(m|z)=0.5
HybridBayesNet expected;
expected.emplace_back(new DiscreteConditional(m, "0.5/0.5"));
EXPECT(assert_equal(expected, *bn));
}
{
// Shift by -lambda
VectorValues given;
given.insert(z, Vector1(midway - lambda));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
EXPECT_DOUBLES_EQUAL(
sigmoid(mu0, mu1, sigma, sigma, midway - lambda),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{M(0), 1}}), 1e-8);
}
{
// Shift by lambda
VectorValues given;
given.insert(z, Vector1(midway + lambda));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
EXPECT_DOUBLES_EQUAL(
sigmoid(mu0, mu1, sigma, sigma, midway + lambda),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{M(0), 1}}), 1e-8);
}
}
/* ************************************************************************* */
@ -255,30 +317,25 @@ TEST(GaussianMixtureFactor, GaussianMixtureModel) {
* where m1>m0 close to 3.1333.
*/
TEST(GaussianMixtureFactor, GaussianMixtureModel2) {
using namespace test_gmm;
double mu0 = 1.0, mu1 = 3.0;
auto model0 = noiseModel::Isotropic::Sigma(1, 8.0);
auto model1 = noiseModel::Isotropic::Sigma(1, 4.0);
double sigma0 = 8.0, sigma1 = 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);
auto hbn = GetGaussianMixtureModel(mu0, mu1, sigma0, sigma1);
// The result should be a bell curve like function
// with m1 > m0 close to 3.1333.
// We get 3.1333 by finding the maximum value of the function.
VectorValues given;
given.insert(z, Vector1(3.133));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
// regression
HybridBayesNet expected;
expected.emplace_back(
new DiscreteConditional(m, "0.325603277954/0.674396722046"));