def calculate_crps(y_pred):
module = get_array_module(y_pred)
quantiles = to_array(module, self.quantiles, like=y_pred)
return qq.crps(y_pred,
y_true,
quantiles,
quantile_axis=self.quantile_axis)
def crps(y_pred, y_true, quantiles):
r"""
Compute the Continuous Ranked Probability Score (CRPS) for given quantile
predictions.
This function uses a piece-wise linear fit to the approximate posterior
CDF obtained from the predicted quantiles in :code:`y_pred` to
approximate the continuous ranked probability score (CRPS):
.. math::
CRPS(\mathbf{y}, x) = \int_{-\infty}^\infty (F_{x | \mathbf{y}}(x')
- \mathrm{1}_{x < x'})^2 \: dx'
Arguments:
y_pred(numpy.array): Array of shape `(n, k)` containing the `k`
estimated quantiles for each of the `n`
predictions.
y_test(numpy.array): Array containing the `n` true values, i.e.
samples of the true conditional distribution
estimated by the QRNN.
quantiles: 1D array containing the `k` quantile fractions :math:`\tau`
that correspond to the columns in `y_pred`.
Returns:
`n`-element array containing the CRPS values for each of the
predictions in `y_pred`.
"""
y_pred = self.predict(x)
return qq.crps(y_pred, self.quantiles, y_true, quantile_axis=1)
def test_crps(xp):
"""
Tests the calculation of the CRPS for different shapes of input
arrays.
"""
#
# 1D predictions
#
quantiles = arange(xp, 0.1, 0.91, 0.1)
y_pred = arange(xp, 1.0, 9.1, 1.0)
scores = crps(y_pred, 4.9, quantiles,)
assert np.all(np.isclose(scores, 0.86 * xp.ones_like(scores)))
#
# 2D predictions
#
quantiles = arange(xp, 0.1, 0.91, 0.1)
y_pred = eo.repeat(arange(xp, 1.0, 9.1, 1.0), 'q -> w q', w=2)
y_true = 4.9 * xp.ones(2)
scores = crps(y_pred, y_true, quantiles)
assert np.all(np.isclose(scores, 0.86 * xp.ones_like(scores)))
##
## 3D predictions, quantiles along last axis
##
quantiles = arange(xp, 0.1, 0.91, 0.1)
y_pred = eo.repeat(arange(xp, 1.0, 9.1, 1.0), 'q -> h w q', w=10, h=10)
y_true = 4.9 * xp.ones((10, 10))
scores = crps(y_pred, y_true, quantiles, quantile_axis=2)
assert np.all(np.isclose(scores, 0.86 * xp.ones_like(scores)))
##
## 3D predictions, quantiles along first axis
##
quantiles = arange(xp, 0.1, 0.91, 0.1)
y_pred = eo.repeat(arange(xp, 1.0, 9.1, 1.0), 'q -> h q w', w=10, h=10)
y_true = 4.9 * xp.ones((10, 10))
scores = crps(y_pred, y_true, quantiles, quantile_axis=1)
assert np.all(np.isclose(scores, 0.86 * xp.ones_like(scores)))
def crps(self, y_pred, y_true):
"""
Calculate the CRPS score from predicted quantiles.
Args:
y_pred: Tensor containing the quantiles predicted by the NN
model.
y_true: Tensor containing the true values.
"""
module = get_array_module(y_pred)
quantiles = to_array(module, self.quantiles, like=y_pred)
return qq.crps(
y_pred, y_true, quantiles, quantile_axis=self.quantile_axis
)