def test_values(
distr: PiecewiseLinear,
target: List[float],
expected_target_cdf: List[float],
expected_target_crps: List[float],
):
target = mx.nd.array(target).reshape(shape=(len(target),))
expected_target_cdf = np.array(expected_target_cdf).reshape(
(len(expected_target_cdf),)
)
expected_target_crps = np.array(expected_target_crps).reshape(
(len(expected_target_crps),)
)
assert all(np.isclose(distr.cdf(target).asnumpy(), expected_target_cdf))
assert all(np.isclose(distr.crps(target).asnumpy(), expected_target_crps))
# compare with empirical cdf from samples
num_samples = 100_000
samples = distr.sample(num_samples).asnumpy()
assert np.isfinite(samples).all()
emp_cdf, edges = empirical_cdf(samples)
calc_cdf = distr.cdf(mx.nd.array(edges)).asnumpy()
assert np.allclose(calc_cdf[1:, :], emp_cdf, atol=1e-2)
def test_values(
distr: PiecewiseLinear,
target: List[float],
expected_target_cdf: List[float],
expected_target_crps: List[float],
):
target = mx.nd.array(target).reshape(shape=(len(target), ))
expected_target_cdf = np.array(expected_target_cdf).reshape(
(len(expected_target_cdf), ))
expected_target_crps = np.array(expected_target_crps).reshape(
(len(expected_target_crps), ))
assert all(np.isclose(distr._cdf(target).asnumpy(), expected_target_cdf))
assert all(np.isclose(distr.crps(target).asnumpy(), expected_target_crps))
def test_simple_symmetric():
gamma = mx.nd.array([-1.0])
slopes = mx.nd.array([[2.0, 2.0]])
knot_spacings = mx.nd.array([[0.5, 0.5]])
distr = PiecewiseLinear(gamma=gamma,
slopes=slopes,
knot_spacings=knot_spacings)
assert distr.cdf(mx.nd.array([-2.0])).asnumpy().item() == 0.0
assert distr.cdf(mx.nd.array([+2.0])).asnumpy().item() == 1.0
expected_crps = np.array([1.0 + 2.0 / 3.0])
assert np.allclose(
distr.crps(mx.nd.array([-2.0])).asnumpy(), expected_crps)
assert np.allclose(distr.crps(mx.nd.array([2.0])).asnumpy(), expected_crps)
def test_shapes(batch_shape: Tuple, num_pieces: int, num_samples: int,
serialize_fn):
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)
distr = serialize_fn(distr)
# 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_internal(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_internal(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_internal(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}")
import pytest
import mxnet as mx
import numpy as np
from gluonts.distribution import PiecewiseLinear
from gluonts.testutil import empirical_cdf
@pytest.mark.parametrize(
"distr, target, expected_target_cdf, expected_target_crps",
[
(
PiecewiseLinear(
gamma=mx.nd.ones(shape=(1, )),
slopes=mx.nd.array([2, 3, 1]).reshape(shape=(1, 3)),
knot_spacings=mx.nd.array([0.3, 0.4, 0.3
]).reshape(shape=(1, 3)),
),
[2.2],
[0.5],
[0.223000],
),
(
PiecewiseLinear(
gamma=mx.nd.ones(shape=(2, )),
slopes=mx.nd.array([[1, 1], [1, 2]]).reshape(shape=(2, 2)),
knot_spacings=mx.nd.array([[0.4, 0.6], [0.4, 0.6]
]).reshape(shape=(2, 2)),
),
[1.5, 1.6],
[0.5, 0.5],
),
(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)),
slopes=mx.nd.ones(shape=(3, 4, 5, 10)),
knot_spacings=mx.nd.ones(shape=(3, 4, 5, 10)) / 10,
),
(3, 4, 5),
(),
),
(
MixtureDistribution(
mixture_probs=mx.nd.stack(
0.2 * mx.nd.ones(shape=(3, 1, 5)),
0.8 * mx.nd.ones(shape=(3, 1, 5)),
axis=-1,
),
components=[
Gaussian(
mu=mx.nd.zeros(shape=(3, 4, 5)),