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}"
(
GaussianOutput(),
mx.nd.random.normal(shape=(3, 4, 5, 6)),
[None, mx.nd.ones(shape=(3, 4, 5))],
(3, 4, 5),
(),
),
(
StudentTOutput(),
mx.nd.random.normal(shape=(3, 4, 5, 6)),
[None, mx.nd.ones(shape=(3, 4, 5))],
(3, 4, 5),
(),
),
(
GammaOutput(),
mx.nd.random.gamma(shape=(3, 4, 5, 6)),
[None, mx.nd.ones(shape=(3, 4, 5))],
(3, 4, 5),
(),
),
(
MultivariateGaussianOutput(dim=5),
mx.nd.random.normal(shape=(3, 4, 10)),
[None, mx.nd.ones(shape=(3, 4, 5))],
(3, 4),
(5, ),
),
(
LowrankMultivariateGaussianOutput(dim=5, rank=4),
mx.nd.random.normal(shape=(3, 4, 10)),