def test_genpareto_likelihood(xi: float, beta: float, hybridize: bool) -> None:
"""
Test to check that maximizing the likelihood recovers the parameters
"""
# generate samples
xis = mx.nd.zeros((NUM_SAMPLES, )) + xi
betas = mx.nd.zeros((NUM_SAMPLES, )) + beta
distr = GenPareto(xis, betas)
samples = distr.sample()
init_biases = [
inv_softplus(xi - START_TOL_MULTIPLE * TOL * xi),
inv_softplus(beta - START_TOL_MULTIPLE * TOL * beta),
]
xi_hat, beta_hat = maximum_likelihood_estimate_sgd(
GenParetoOutput(),
samples,
init_biases=init_biases,
hybridize=hybridize,
learning_rate=PositiveFloat(0.05),
num_epochs=PositiveInt(10),
)
print("XI:", xi_hat, "BETA:", beta_hat)
assert (np.abs(xi_hat - xi) <
TOL * xi), f"alpha did not match: xi = {xi}, xi_hat = {xi_hat}"
assert (np.abs(beta_hat - beta) < TOL *
beta), f"beta did not match: beta = {beta}, beta_hat = {beta_hat}"
MixtureDistribution(
mixture_probs=mx.nd.array([[0.6, 0.4]]),
components=[
Gaussian(mu=mx.nd.array([-1.0]), sigma=mx.nd.array([0.2])),
Gamma(alpha=mx.nd.array([2.0]), beta=mx.nd.array([0.5])),
],
),
MixtureDistributionOutput([GaussianOutput(), GammaOutput()]),
2_000,
),
(
MixtureDistribution(
mixture_probs=mx.nd.array([[0.7, 0.3]]),
components=[
Gaussian(mu=mx.nd.array([-1.0]), sigma=mx.nd.array([0.2])),
GenPareto(xi=mx.nd.array([0.6]), beta=mx.nd.array([1.0])),
],
),
MixtureDistributionOutput([GaussianOutput(), GenParetoOutput()]),
2_000,
),
],
)
@pytest.mark.parametrize("serialize_fn", serialize_fn_list)
@pytest.mark.skip("Skip test that takes long time to run")
def test_inference_mixture_different_families(
mixture_distribution: MixtureDistribution,
mixture_distribution_output: MixtureDistributionOutput,
epochs: int,
serialize_fn,
) -> None: