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add examples of Hybrid FGs from HBNs as unit tests

release/4.3a0
Varun Agrawal 2024-08-25 00:48:32 -04:00
parent 3d8383089b
commit 1f373fd136
1 changed files with 229 additions and 4 deletions
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233
gtsam/hybrid/tests/testGaussianMixtureFactor.cpp
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@ -200,6 +200,228 @@ TEST(GaussianMixtureFactor, Error) {
4.0, mixtureFactor.error({continuousValues, discreteValues}), 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
@ -271,11 +493,12 @@ HybridGaussianFactorGraph GetFactorGraphFromBayesNet(
*
* 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.
*
* p(Z1 | X1, X2, M1) has 2 factors each for the binary mode m1, with only the
* means being different.
* 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, DifferentMeansHBN) {
TEST(GaussianMixtureFactor, DifferentMeans) {
DiscreteKey m1(M(1), 2);
Values values;
@ -355,6 +578,8 @@ TEST(GaussianMixtureFactor, DifferentMeansHBN) {
/**
* @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);