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Simplify tests

release/4.3a0
Frank Dellaert 2024-09-25 16:55:12 -07:00
parent 06887b702a
commit 314a8310cf
1 changed files with 53 additions and 139 deletions
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192
gtsam/hybrid/tests/testGaussianMixture.cpp
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@ -44,39 +44,39 @@ using symbol_shorthand::M;
using symbol_shorthand::X;
using symbol_shorthand::Z;
namespace test_gmm {
/**
* Function to compute P(m=1|z). For P(m=0|z), swap mus and sigmas.
* Closed form computation of P(m=1|z).
* If sigma0 == sigma1, it simplifies to a sigmoid function.
*
* Follows equation 7.108 since it is more generic.
*/
double prob_m_z(double mu0, double mu1, double sigma0, double sigma1,
double z) {
static double prob_m_z(double mu0, double mu1, double sigma0, double sigma1,
double z) {
double x1 = ((z - mu0) / sigma0), x2 = ((z - mu1) / sigma1);
double d = sigma1 / sigma0;
double e = d * std::exp(-0.5 * (x1 * x1 - x2 * x2));
return 1 / (1 + e);
};
// Define mode key and an assignment m==1
static const DiscreteKey m(M(0), 2);
static const DiscreteValues m1Assignment{{M(0), 1}};
/**
* 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).
*/
static 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 c0 = make_shared<GaussianConditional>(Z(0), Vector1(mu0), I_1x1, model0),
c1 = make_shared<GaussianConditional>(Z(0), Vector1(mu1), I_1x1, model1);
HybridBayesNet hbn;
DiscreteKeys discreteParents{m};
hbn.emplace_shared<HybridGaussianConditional>(
KeyVector{z}, KeyVector{}, discreteParents,
HybridGaussianConditional::Conditionals(discreteParents,
std::vector{c0, c1}));
hbn.emplace_shared<HybridGaussianConditional>(KeyVector{Z(0)}, KeyVector{}, m,
std::vector{c0, c1});
auto mixing = make_shared<DiscreteConditional>(m, "50/50");
hbn.push_back(mixing);
@ -84,150 +84,64 @@ static HybridBayesNet GetGaussianMixtureModel(double mu0, double mu1,
return hbn;
}
} // namespace test_gmm
/// Given p(z,m) and z, use eliminate to obtain P(m|z).
static DiscreteConditional solveForMeasurement(const HybridBayesNet &hbn,
double z) {
VectorValues given;
given.insert(Z(0), Vector1(z));
/* ************************************************************************* */
/**
* 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.
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
return *gfg.eliminateSequential()->at(0)->asDiscrete();
}
/*
* 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(HybridGaussianFactor, GaussianMixtureModel) {
using namespace test_gmm;
double mu0 = 1.0, mu1 = 3.0;
double sigma = 2.0;
DiscreteKey m(M(0), 2);
Key z = Z(0);
auto hbn = GetGaussianMixtureModel(mu0, mu1, sigma, sigma);
// The result should be a sigmoid.
// 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));
// At the halfway point between the means, we should get P(m|z)=0.5
double midway = mu1 - mu0;
auto pMid = solveForMeasurement(hbn, midway);
EXPECT(assert_equal(DiscreteConditional(m, "50/50"), pMid));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
// 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);
EXPECT_DOUBLES_EQUAL(
prob_m_z(mu0, mu1, sigma, sigma, midway),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{m.first, 1}}),
1e-8);
// At the halfway point between the means, we should get P(m|z)=0.5
HybridBayesNet expected;
expected.emplace_shared<DiscreteConditional>(m, "50/50");
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(
prob_m_z(mu0, mu1, sigma, sigma, midway - lambda),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{m.first, 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(
prob_m_z(mu0, mu1, sigma, sigma, midway + lambda),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{m.first, 1}}),
1e-8);
auto posterior = solveForMeasurement(hbn, z);
EXPECT_DOUBLES_EQUAL(expected, posterior(m1Assignment), 1e-8);
}
}
/* ************************************************************************* */
/**
* 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 Gaussian-like function
* where m1>m0 close to 3.1333.
/*
* 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(HybridGaussianFactor, GaussianMixtureModel2) {
using namespace test_gmm;
double mu0 = 1.0, mu1 = 3.0;
double sigma0 = 8.0, sigma1 = 4.0;
DiscreteKey m(M(0), 2);
Key z = Z(0);
auto hbn = GetGaussianMixtureModel(mu0, mu1, sigma0, sigma1);
double m1_high = 3.133, lambda = 4;
{
// 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));
// 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 = solveForMeasurement(hbn, zMax);
EXPECT(assert_equal(DiscreteConditional(m, "32.56/67.44"), pMax, 1e-5));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
// 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);
EXPECT_DOUBLES_EQUAL(
prob_m_z(mu0, mu1, sigma0, sigma1, m1_high),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{M(0), 1}}), 1e-8);
// At the halfway point between the means
HybridBayesNet expected;
expected.emplace_shared<DiscreteConditional>(
m, DiscreteKeys{},
vector<double>{prob_m_z(mu1, mu0, sigma1, sigma0, m1_high),
prob_m_z(mu0, mu1, sigma0, sigma1, m1_high)});
EXPECT(assert_equal(expected, *bn));
}
{
// Shift by -lambda
VectorValues given;
given.insert(z, Vector1(m1_high - lambda));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
EXPECT_DOUBLES_EQUAL(
prob_m_z(mu0, mu1, sigma0, sigma1, m1_high - lambda),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{m.first, 1}}),
1e-8);
}
{
// Shift by lambda
VectorValues given;
given.insert(z, Vector1(m1_high + lambda));
HybridGaussianFactorGraph gfg = hbn.toFactorGraph(given);
HybridBayesNet::shared_ptr bn = gfg.eliminateSequential();
EXPECT_DOUBLES_EQUAL(
prob_m_z(mu0, mu1, sigma0, sigma1, m1_high + lambda),
bn->at(0)->asDiscrete()->operator()(DiscreteValues{{m.first, 1}}),
1e-8);
auto posterior = solveForMeasurement(hbn, z);
EXPECT_DOUBLES_EQUAL(expected, posterior(m1Assignment), 1e-8);
}
}