reservoirpy.observables.nrmse#

reservoirpy.observables.nrmse(
y_true: ndarray,
y_pred: ndarray,
norm: Literal['minmax', 'var', 'mean', 'q1q3'] = 'minmax',
norm_value: float | None = None,
dimensionwise: bool = False,
) → float[source]#

Normalized root mean squared error metric:

\[\frac{1}{\lambda} * \sqrt{\frac{\sum_{i=0}^{N-1} (y_i - \hat{y}_i)^2}{N}}\]
where \(\lambda\) may be:

  • \(\max y - \min y\) (Peak-to-peak amplitude) if norm="minmax";

  • \(\mathrm{Var}(y)\) (variance over time) if norm="var";

  • \(\mathbb{E}[y]\) (mean over time) if norm="mean";

  • \(Q_{3}(y) - Q_{1}(y)\) (quartiles) if norm="q1q3";

  • or any value passed to norm_value.

Parameters:

  • y_true (array-like of shape (N, features)) – Ground truth values.

  • y_pred (array-like of shape (N, features)) – Predicted values.

  • norm ({"minmax", "var", "mean", "q1q3"}, default to "minmax") – Normalization method.

  • norm_value (float, optional) – A normalization factor. If set, will override the norm parameter.

  • dimensionwise (boolean, optional) – If True, return a mean squared error for each dimension of the timeseries

Returns:

  • float – Normalized root mean squared error.

  • If dimensionwise is True, returns a Numpy array of shape $(features, )$.

Return type:

float

Examples

>>> from reservoirpy.nodes import Reservoir, Ridge
>>> model = Reservoir(units=100, sr=1) >> Ridge(ridge=1e-8)

>>> from reservoirpy.datasets import mackey_glass, to_forecasting
>>> x_train, x_test, y_train, y_test = to_forecasting(mackey_glass(1000), test_size=0.2)
>>> y_pred = model.fit(x_train, y_train).run(x_test)

>>> from reservoirpy.observables import nrmse
>>> print(nrmse(y_true=y_test, y_pred=y_pred, norm="var"))
0.007854318015438394