def cdf(self, x):
r"""
Approximate the posterior CDF for given inputs `x`.
Propagates the inputs in `x` forward through the network and
approximates the posterior CDF by a piecewise linear function.
The piecewise linear function is given by its values at approximate
quantiles :math:`x_\tau`` for :math:`\tau = \{0.0, \tau_1, \ldots,
\tau_k, 1.0\}` where :math:`\tau_k` are the quantiles to be estimated
by the network. The values for :math:`x_{0.0}` and :math:`x_{1.0}` are
computed using
.. math::
x_{0.0} = 2.0 x_{\tau_1} - x_{\tau_2}
x_{1.0} = 2.0 x_{\tau_k} - x_{\tau_{k-1}}
Arguments:
x(np.array): Array of shape `(n, m)` containing `n` inputs for which
to predict the conditional quantiles.
Returns:
Tuple (xs, fs) containing the :math:`x`-values in `xs` and corresponding
values of the posterior CDF :math:`F(x)` in `fs`.
"""
y_pred = self.predict(x)
return qq.cdf(y_pred, self.quantiles, quantile_axis=1)
def test_cdf(xp):
"""
Tests the calculation of the pdf 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)
x_cdf, y_cdf = cdf(y_pred, quantiles)
assert np.all(np.isclose(x_cdf[0], -xp.ones_like(x_cdf[0])))
assert np.all(np.isclose(x_cdf[-1], 11.0 * xp.ones_like(x_cdf[-1])))
#
# 2D predictions
#
y_pred = eo.repeat(arange(xp, 1.0, 9.1, 1.0), 'q -> w q', w=10)
x_cdf, y_cdf = cdf(y_pred, quantiles)
assert np.all(np.isclose(x_cdf[:, 0], -xp.ones_like(x_cdf[:, 0])))
assert np.all(np.isclose(x_cdf[:, -1], 11.0 * xp.ones_like(x_cdf[:, -1])))
#
# 3D predictions, quantiles along last axis
#
y_pred = eo.repeat(arange(xp, 1.0, 9.1, 1.0), 'q -> h w q', h=10, w=10)
x_cdf, y_cdf = cdf(y_pred, quantiles, quantile_axis=-1)
assert np.all(np.isclose(x_cdf[:, :, 0], -xp.ones_like(x_cdf[:, :, 0])))
assert np.all(
np.isclose(x_cdf[:, :, -1], 11.0 * xp.ones_like(x_cdf[:, :, -1])))
#
# 3D predictions, quantiles along first axis
#
y_pred = eo.repeat(arange(xp, 1.0, 9.1, 1.0), 'q -> h q w', h=10, w=10)
x_cdf, y_cdf = cdf(y_pred, quantiles, quantile_axis=1)
assert np.all(np.isclose(x_cdf[:, 0, :], -xp.ones_like(x_cdf[:, 0, :])))
assert np.all(
np.isclose(x_cdf[:, -1, :], 11.0 * xp.ones_like(x_cdf[:, -1, :])))
def cdf(self, y_pred):
"""
Calculate CDF from predicted quantiles.
Args:
y_pred: Tensor containing the quantiles predicted by the NN
model.
"""
module = get_array_module(y_pred)
quantiles = to_array(module, self.quantiles, like=y_pred)
return qq.cdf(y_pred,
quantiles,
quantile_axis=self.quantile_axis)
def calculate_cdf(y_pred):
module = get_array_module(y_pred)
quantiles = to_array(module, self.quantiles, like=y_pred)
return qq.cdf(y_pred, quantiles, quantile_axis=self.quantile_axis)