def test_neg_binomial(mu_alpha: Tuple[float, float], hybridize: bool) -> None:
'''
Test to check that maximizing the likelihood recovers the parameters
'''
# test instance
mu, alpha = mu_alpha
# generate samples
mus = mx.nd.zeros((NUM_SAMPLES, )) + mu
alphas = mx.nd.zeros((NUM_SAMPLES, )) + alpha
neg_bin_distr = NegativeBinomial(mu=mus, alpha=alphas)
samples = neg_bin_distr.sample()
init_biases = [
inv_softplus(mu - START_TOL_MULTIPLE * TOL * mu),
inv_softplus(alpha + START_TOL_MULTIPLE * TOL * alpha),
]
mu_hat, alpha_hat = maximum_likelihood_estimate_sgd(
NegativeBinomialOutput(),
samples,
hybridize=hybridize,
init_biases=init_biases,
num_epochs=PositiveInt(15),
)
assert (np.abs(mu_hat - mu) <
TOL * mu), f"mu did not match: mu = {mu}, mu_hat = {mu_hat}"
assert (np.abs(alpha_hat - alpha) < TOL * alpha
), f"alpha did not match: alpha = {alpha}, alpha_hat = {alpha_hat}"
(Dirichlet(alpha=mx.nd.ones(shape=(3, 4, 5))), (3, 4), (5, )),
(
DirichletMultinomial(
dim=5, n_trials=9, alpha=mx.nd.ones(shape=(3, 4, 5))),
(3, 4),
(5, ),
),
(
Laplace(mu=mx.nd.zeros(shape=(3, 4, 5)),
b=mx.nd.ones(shape=(3, 4, 5))),
(3, 4, 5),
(),
),
(
NegativeBinomial(
mu=mx.nd.zeros(shape=(3, 4, 5)),
alpha=mx.nd.ones(shape=(3, 4, 5)),
),
(3, 4, 5),
(),
),
(
Uniform(
low=-mx.nd.ones(shape=(3, 4, 5)),
high=mx.nd.ones(shape=(3, 4, 5)),
),
(3, 4, 5),
(),
),
(
PiecewiseLinear(
gamma=mx.nd.ones(shape=(3, 4, 5)),
),
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(
mu=mx.nd.zeros(shape=BATCH_SHAPE),
alpha=mx.nd.ones(shape=BATCH_SHAPE),
),
Poisson(rate=mx.nd.ones(shape=BATCH_SHAPE)),
Uniform(
low=-mx.nd.ones(shape=BATCH_SHAPE),
high=mx.nd.ones(shape=BATCH_SHAPE),
),
PiecewiseLinear(
gamma=mx.nd.ones(shape=BATCH_SHAPE),
slopes=mx.nd.ones(shape=(3, 4, 5, 10)),
knot_spacings=mx.nd.ones(shape=(3, 4, 5, 10)) / 10,
),
MixtureDistribution(
mixture_probs=mx.nd.stack(
0.2 * mx.nd.ones(shape=BATCH_SHAPE),
0.8 * mx.nd.ones(shape=BATCH_SHAPE),