def test_gamma_likelihood(alpha: float, beta: float, hybridize: bool) -> None:
"""
Test to check that maximizing the likelihood recovers the parameters
"""
# generate samples
alphas = mx.nd.zeros((NUM_SAMPLES, )) + alpha
betas = mx.nd.zeros((NUM_SAMPLES, )) + beta
distr = Gamma(alphas, betas)
samples = distr.sample()
init_biases = [
inv_softplus(alpha - START_TOL_MULTIPLE * TOL * alpha),
inv_softplus(beta - START_TOL_MULTIPLE * TOL * beta),
]
alpha_hat, beta_hat = maximum_likelihood_estimate_sgd(
GammaOutput(),
samples,
init_biases=init_biases,
hybridize=hybridize,
learning_rate=PositiveFloat(0.05),
num_epochs=PositiveInt(5),
)
assert (np.abs(alpha_hat - alpha) < TOL * alpha
), f"alpha did not match: alpha = {alpha}, alpha = {alpha_hat}"
assert (np.abs(beta_hat - beta) < TOL *
beta), f"beta did not match: beta = {beta}, beta_hat = {beta_hat}"
@pytest.mark.parametrize(
"distr, expected_batch_shape, expected_event_shape",
[
(
Gaussian(
mu=mx.nd.zeros(shape=(3, 4, 5)),
sigma=mx.nd.ones(shape=(3, 4, 5)),
),
(3, 4, 5),
(),
),
(
Gamma(
alpha=mx.nd.ones(shape=(3, 4, 5)),
beta=mx.nd.ones(shape=(3, 4, 5)),
),
(3, 4, 5),
(),
),
(
Beta(
alpha=mx.nd.ones(shape=(3, 4, 5)),
beta=mx.nd.ones(shape=(3, 4, 5)),
),
(3, 4, 5),
(),
),
(
StudentT(
mu=mx.nd.zeros(shape=(3, 4, 5)),
bin_centers=mx.nd.array(np.logspace(-1, 1, 23))
+ mx.nd.zeros(BATCH_SHAPE + (23,)),
),
[
bij.AffineTransformation(
scale=1e-1 + mx.nd.random.uniform(shape=BATCH_SHAPE)
),
bij.softrelu,
],
),
Gaussian(
mu=mx.nd.zeros(shape=BATCH_SHAPE),
sigma=mx.nd.ones(shape=BATCH_SHAPE),
),
Gamma(
alpha=mx.nd.ones(shape=BATCH_SHAPE),
beta=mx.nd.ones(shape=BATCH_SHAPE),
),
Beta(
alpha=0.5 * mx.nd.ones(shape=BATCH_SHAPE),
beta=0.5 * mx.nd.ones(shape=BATCH_SHAPE),
),
StudentT(
mu=mx.nd.zeros(shape=BATCH_SHAPE),
sigma=mx.nd.ones(shape=BATCH_SHAPE),
nu=mx.nd.ones(shape=BATCH_SHAPE),
),
Dirichlet(alpha=mx.nd.ones(shape=BATCH_SHAPE)),
Laplace(
mu=mx.nd.zeros(shape=BATCH_SHAPE), b=mx.nd.ones(shape=BATCH_SHAPE)
),
NegativeBinomial(