MedianAbsoluteScaledError

class MedianAbsoluteScaledError(multioutput='uniform_average', multilevel='uniform_average', sp=1)

Median absolute scaled error (MdASE).

MdASE output is non-negative floating point. The best value is 0.0.

Taking the median instead of the mean of the test and train absolute errors makes this metric more robust to error outliers since the median tends to be a more robust measure of central tendency in the presence of outliers.

Like MASE and other scaled performance metrics this scale-free metric can be used to compare forecast methods on a single series or between series.

Also like MASE, this metric is well suited to intermittent-demand series because it will not give infinite or undefined values unless the training data is a flat timeseries. In this case the function returns a large value instead of inf.

Works with multioutput (multivariate) timeseries data with homogeneous seasonal periodicity.

Parameters

spint, default = 1

Seasonal periodicity of data.

multioutput{‘raw_values’, ‘uniform_average’} or array-like of shape (n_outputs,), default=’uniform_average’

Defines how to aggregate metric for multivariate (multioutput) data. If array-like, values used as weights to average the errors. If ‘raw_values’, returns a full set of errors in case of multioutput input. If ‘uniform_average’, errors of all outputs are averaged with uniform weight.

Attributes

greater_is_better

Whether greater is better for the metric.

See also

MeanAbsoluteScaledError

MeanSquaredScaledError

MedianSquaredScaledError

References

Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4.

Hyndman, R. J. (2006). “Another look at forecast accuracy metrics for intermittent demand”, Foresight, Issue 4.

Makridakis, S., Spiliotis, E. and Assimakopoulos, V. (2020) “The M4 Competition: 100,000 time series and 61 forecasting methods”, International Journal of Forecasting, Volume 3.

Examples

>>> import numpy as np
>>> from sktime.performance_metrics.forecasting import MedianAbsoluteScaledError
>>> y_train = np.array([5, 0.5, 4, 6, 3, 5, 2])
>>> y_true = np.array([3, -0.5, 2, 7])
>>> y_pred = np.array([2.5, 0.0, 2, 8])
>>> mdase = MedianAbsoluteScaledError()
>>> mdase(y_true, y_pred, y_train=y_train)
0.16666666666666666
>>> y_train = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> mdase(y_true, y_pred, y_train=y_train)
0.18181818181818182
>>> mdase = MedianAbsoluteScaledError(multioutput='raw_values')
>>> mdase(y_true, y_pred, y_train=y_train)
array([0.10526316, 0.28571429])
>>> mdase = MedianAbsoluteScaledError(multioutput=[0.3, 0.7])
>>> mdase( y_true, y_pred, y_train=y_train)
0.21935483870967742

Methods

__call__(y_true, y_pred, **kwargs)	Calculate metric value using underlying metric function.
clone()	Obtain a clone of the object with same hyper-parameters.
clone_tags(estimator[, tag_names])	clone/mirror tags from another estimator as dynamic override.
create_test_instance([parameter_set])	Construct Estimator instance if possible.
create_test_instances_and_names([parameter_set])	Create list of all test instances and a list of names for them.
evaluate(y_true, y_pred, **kwargs)	Evaluate the desired metric on given inputs.
evaluate_by_index(y_true, y_pred, **kwargs)	Return the metric evaluated at each time point.
func(y_pred[, sp, horizon_weight, multioutput])	Median absolute scaled error (MdASE).
get_class_tag(tag_name[, tag_value_default])	Get tag value from estimator class (only class tags).
get_class_tags()	Get class tags from estimator class and all its parent classes.
get_params([deep])	Get parameters for this estimator.
get_tag(tag_name[, tag_value_default, …])	Get tag value from estimator class and dynamic tag overrides.
get_tags()	Get tags from estimator class and dynamic tag overrides.
get_test_params([parameter_set])	Return testing parameter settings for the estimator.
is_composite()	Check if the object is composite.
reset()	Reset the object to a clean post-init state.
set_params(**params)	Set the parameters of this estimator.
set_tags(**tag_dict)	Set dynamic tags to given values.

func(y_pred, sp=1, horizon_weight=None, multioutput='uniform_average', **kwargs)

Median absolute scaled error (MdASE).

MdASE output is non-negative floating point. The best value is 0.0.

Taking the median instead of the mean of the test and train absolute errors makes this metric more robust to error outliers since the median tends to be a more robust measure of central tendency in the presence of outliers.

Like MASE and other scaled performance metrics this scale-free metric can be used to compare forecast methods on a single series or between series.

Also like MASE, this metric is well suited to intermittent-demand series because it will not give infinite or undefined values unless the training data is a flat timeseries. In this case the function returns a large value instead of inf.

Works with multioutput (multivariate) timeseries data with homogeneous seasonal periodicity.

Parameters

y_truepd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Ground truth (correct) target values.

y_predpd.Series, pd.DataFrame or np.array of shape (fh,) or (fh, n_outputs) where fh is the forecasting horizon

Forecasted values.

y_trainpd.Series, pd.DataFrame or np.array of shape (n_timepoints,) or (n_timepoints, n_outputs), default = None

Observed training values.

spint

Seasonal periodicity of training data.

horizon_weightarray-like of shape (fh,), default=None

Forecast horizon weights.

multioutput{‘raw_values’, ‘uniform_average’} or array-like of shape (n_outputs,), default=’uniform_average’

Defines how to aggregate metric for multivariate (multioutput) data. If array-like, values used as weights to average the errors. If ‘raw_values’, returns a full set of errors in case of multioutput input. If ‘uniform_average’, errors of all outputs are averaged with uniform weight.

Returns

lossfloat or ndarray of floats

MdASE loss. If multioutput is ‘raw_values’, then MdASE is returned for each output separately. If multioutput is ‘uniform_average’ or an ndarray of weights, then the weighted average MdASE of all output errors is returned.

See also

mean_absolute_scaled_error

mean_squared_scaled_error

median_squared_scaled_error

References

Hyndman, R. J and Koehler, A. B. (2006). “Another look at measures of forecast accuracy”, International Journal of Forecasting, Volume 22, Issue 4.

Hyndman, R. J. (2006). “Another look at forecast accuracy metrics for intermittent demand”, Foresight, Issue 4.

Makridakis, S., Spiliotis, E. and Assimakopoulos, V. (2020) “The M4 Competition: 100,000 time series and 61 forecasting methods”, International Journal of Forecasting, Volume 3.

Examples

>>> from sktime.performance_metrics.forecasting import median_absolute_scaled_error
>>> y_train = np.array([5, 0.5, 4, 6, 3, 5, 2])
>>> y_true = [3, -0.5, 2, 7]
>>> y_pred = [2.5, 0.0, 2, 8]
>>> median_absolute_scaled_error(y_true, y_pred, y_train=y_train)
0.16666666666666666
>>> y_train = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> median_absolute_scaled_error(y_true, y_pred, y_train=y_train)
0.18181818181818182
>>> median_absolute_scaled_error(y_true, y_pred, y_train=y_train,     multioutput='raw_values')
array([0.10526316, 0.28571429])
>>> median_absolute_scaled_error( y_true, y_pred, y_train=y_train,     multioutput=[0.3, 0.7])
0.21935483870967742

__call__(y_true, y_pred, **kwargs)

Calculate metric value using underlying metric function.

Parameters

y_truetime series in sktime compatible data container format

Ground truth (correct) target values y can be in one of the following formats: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

y_predtime series in sktime compatible data container format

Forecasted values to evaluate must be of same format as y_true, same indices and columns if indexed

Returns

lossfloat or np.ndarray

Calculated metric, averaged or by variable. float if self.multioutput=”uniform_average” or array-like

value is metric averaged over variables (see class docstring)

np.ndarray of shape (y_true.columns,) if self.multioutput=”raw_values”

i-th entry is metric calculated for i-th variable

clone()

Obtain a clone of the object with same hyper-parameters.

A clone is a different object without shared references, in post-init state. This function is equivalent to returning sklearn.clone of self. Equal in value to type(self)(**self.get_params(deep=False)).

clone_tags(estimator, tag_names=None)

clone/mirror tags from another estimator as dynamic override.

Parameters

estimatorestimator inheriting from :class:BaseEstimator

tag_namesstr or list of str, default = None

Names of tags to clone. If None then all tags in estimator are used as tag_names.

Returns

Self

Reference to self.

Notes

Changes object state by setting tag values in tag_set from estimator as dynamic tags in self.

classmethod create_test_instance(parameter_set='default')

Construct Estimator instance if possible.

Parameters

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns

instanceinstance of the class with default parameters

Notes

get_test_params can return dict or list of dict. This function takes first or single dict that get_test_params returns, and constructs the object with that.

classmethod create_test_instances_and_names(parameter_set='default')

Create list of all test instances and a list of names for them.

Parameters

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns

objslist of instances of cls

i-th instance is cls(**cls.get_test_params()[i])

nameslist of str, same length as objs

i-th element is name of i-th instance of obj in tests convention is {cls.__name__}-{i} if more than one instance otherwise {cls.__name__}

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

evaluate(y_true, y_pred, **kwargs)

Evaluate the desired metric on given inputs.

Parameters

y_truetime series in sktime compatible data container format

Ground truth (correct) target values y can be in one of the following formats: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

y_predtime series in sktime compatible data container format

Forecasted values to evaluate must be of same format as y_true, same indices and columns if indexed

Returns

lossfloat or np.ndarray

Calculated metric, averaged or by variable. float if self.multioutput=”uniform_average” or array-like

value is metric averaged over variables (see class docstring)

np.ndarray of shape (y_true.columns,) if self.multioutput=”raw_values”

i-th entry is metric calculated for i-th variable

evaluate_by_index(y_true, y_pred, **kwargs)

Return the metric evaluated at each time point.

Parameters

y_truetime series in sktime compatible data container format

Ground truth (correct) target values y can be in one of the following formats: Series scitype: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel scitype: pd.DataFrame with 2-level row MultiIndex,

3D np.ndarray, list of Series pd.DataFrame, or nested pd.DataFrame

Hierarchical scitype: pd.DataFrame with 3 or more level row MultiIndex

y_predtime series in sktime compatible data container format

Forecasted values to evaluate must be of same format as y_true, same indices and columns if indexed

Returns

losspd.Series or pd.DataFrame

Calculated metric, by time point (default=jackknife pseudo-values). pd.Series if self.multioutput=”uniform_average” or array-like

index is equal to index of y_true entry at index i is metric at time i, averaged over variables

pd.DataFrame if self.multioutput=”raw_values”

index and columns equal to those of y_true i,j-th entry is metric at time i, at variable j

classmethod get_class_tag(tag_name, tag_value_default=None)

Get tag value from estimator class (only class tags).

Parameters

tag_namestr

Name of tag value.

tag_value_defaultany type

Default/fallback value if tag is not found.

Returns

tag_value

Value of the tag_name tag in self. If not found, returns tag_value_default.

classmethod get_class_tags()

Get class tags from estimator class and all its parent classes.

Returns

collected_tagsdict

Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance. NOT overridden by dynamic tags set by set_tags or mirror_tags.

get_params(deep=True)

Get parameters for this estimator.

Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsdict

Parameter names mapped to their values.

get_tag(tag_name, tag_value_default=None, raise_error=True)

Get tag value from estimator class and dynamic tag overrides.

Parameters

tag_namestr

Name of tag to be retrieved

tag_value_defaultany type, optional; default=None

Default/fallback value if tag is not found

raise_errorbool

whether a ValueError is raised when the tag is not found

Returns

tag_value

Value of the tag_name tag in self. If not found, returns an error if raise_error is True, otherwise it returns tag_value_default.

Raises

ValueError if raise_error is True i.e. if tag_name is not in self.get_tags(

).keys()

get_tags()

Get tags from estimator class and dynamic tag overrides.

Returns

collected_tagsdict

Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance and then any overrides and new tags from _tags_dynamic object attribute.

classmethod get_test_params(parameter_set='default')

Return testing parameter settings for the estimator.

Parameters

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns

paramsdict or list of dict, default = {}

Parameters to create testing instances of the class Each dict are parameters to construct an “interesting” test instance, i.e., MyClass(**params) or MyClass(**params[i]) creates a valid test instance. create_test_instance uses the first (or only) dictionary in params

property greater_is_better

Whether greater is better for the metric.

is_composite()

Check if the object is composite.

A composite object is an object which contains objects, as parameters. Called on an instance, since this may differ by instance.

Returns

composite: bool, whether self contains a parameter which is BaseObject

reset()

Reset the object to a clean post-init state.

Equivalent to sklearn.clone but overwrites self. After self.reset() call, self is equal in value to type(self)(**self.get_params(deep=False))

Detail behaviour: removes any object attributes, except:

hyper-parameters = arguments of __init__ object attributes containing double-underscores, i.e., the string “__”

runs __init__ with current values of hyper-parameters (result of get_params)

Not affected by the reset are: object attributes containing double-underscores class and object methods, class attributes

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**paramsdict

Estimator parameters.

Returns

selfestimator instance

Estimator instance.

set_tags(**tag_dict)

Set dynamic tags to given values.

Parameters

tag_dictdict

Dictionary of tag name : tag value pairs.

Returns

Self

Reference to self.

Notes

Changes object state by settting tag values in tag_dict as dynamic tags in self.