def test_shapes(batch_shape: Tuple, num_pieces: int, num_samples: int):
gamma = mx.nd.ones(shape=(*batch_shape,))
slopes = mx.nd.ones(shape=(*batch_shape, num_pieces)) # all positive
knot_spacings = (
mx.nd.ones(shape=(*batch_shape, num_pieces)) / num_pieces
) # positive and sum to 1
target = mx.nd.ones(shape=batch_shape) # shape of gamma
distr = PiecewiseLinear(
gamma=gamma, slopes=slopes, knot_spacings=knot_spacings
)
# assert that the parameters and target have proper shapes
assert gamma.shape == target.shape
assert knot_spacings.shape == slopes.shape
assert len(gamma.shape) + 1 == len(knot_spacings.shape)
# assert that batch_shape is computed properly
assert distr.batch_shape == batch_shape
# assert that shapes of original parameters are correct
assert distr.b.shape == slopes.shape
assert distr.knot_positions.shape == knot_spacings.shape
# assert that the shape of crps is correct
assert distr.crps(target).shape == batch_shape
# assert that the quantile shape is correct when computing the quantile values at knot positions - used for a_tilde
assert distr.quantile(knot_spacings, axis=-2).shape == (
*batch_shape,
num_pieces,
)
# assert that the samples and the quantile values shape when num_samples is None is correct
samples = distr.sample()
assert samples.shape == batch_shape
assert distr.quantile(samples).shape == batch_shape
# assert that the samples and the quantile values shape when num_samples is not None is correct
samples = distr.sample(num_samples)
assert samples.shape == (num_samples, *batch_shape)
assert distr.quantile(samples, axis=0).shape == (num_samples, *batch_shape)
def test_piecewise_linear(
gamma: float,
slopes: np.ndarray,
knot_spacings: np.ndarray,
hybridize: bool,
) -> None:
'''
Test to check that minimizing the CRPS recovers the quantile function
'''
num_samples = 500 # use a few samples for timeout failure
gammas = mx.nd.zeros((num_samples, )) + gamma
slopess = mx.nd.zeros((num_samples, len(slopes))) + mx.nd.array(slopes)
knot_spacingss = mx.nd.zeros(
(num_samples, len(knot_spacings))) + mx.nd.array(knot_spacings)
pwl_sqf = PiecewiseLinear(gammas, slopess, knot_spacingss)
samples = pwl_sqf.sample()
# Parameter initialization
gamma_init = gamma - START_TOL_MULTIPLE * TOL * gamma
slopes_init = slopes - START_TOL_MULTIPLE * TOL * slopes
knot_spacings_init = knot_spacings
# We perturb knot spacings such that even after the perturbation they sum to 1.
mid = len(slopes) // 2
knot_spacings_init[:mid] = (knot_spacings[:mid] -
START_TOL_MULTIPLE * TOL * knot_spacings[:mid])
knot_spacings_init[mid:] = (knot_spacings[mid:] +
START_TOL_MULTIPLE * TOL * knot_spacings[mid:])
init_biases = [gamma_init, slopes_init, knot_spacings_init]
# check if it returns original parameters of mapped
gamma_hat, slopes_hat, knot_spacings_hat = maximum_likelihood_estimate_sgd(
PiecewiseLinearOutput(len(slopes)),
samples,
init_biases=init_biases,
hybridize=hybridize,
learning_rate=PositiveFloat(0.01),
num_epochs=PositiveInt(20),
)
# Since the problem is highly non-convex we may not be able to recover the exact parameters
# Here we check if the estimated parameters yield similar function evaluations at different quantile levels.
quantile_levels = np.arange(0.1, 1.0, 0.1)
# create a LinearSplines instance with the estimated parameters to have access to .quantile
pwl_sqf_hat = PiecewiseLinear(
mx.nd.array(gamma_hat),
mx.nd.array(slopes_hat).expand_dims(axis=0),
mx.nd.array(knot_spacings_hat).expand_dims(axis=0),
)
# Compute quantiles with the estimated parameters
quantiles_hat = np.squeeze(
pwl_sqf_hat.quantile(mx.nd.array(quantile_levels).expand_dims(axis=0),
axis=1).asnumpy())
# Compute quantiles with the original parameters
# Since params is replicated across samples we take only the first entry
quantiles = np.squeeze(
pwl_sqf.quantile(
mx.nd.array(quantile_levels).expand_dims(axis=0).repeat(
axis=0, repeats=num_samples),
axis=1,
).asnumpy()[0, :])
for ix, (quantile, quantile_hat) in enumerate(zip(quantiles,
quantiles_hat)):
assert np.abs(quantile_hat - quantile) < TOL * quantile, (
f"quantile level {quantile_levels[ix]} didn't match:"
f" "
f"q = {quantile}, q_hat = {quantile_hat}")