# MeanSquaredPercentageError#

class MeanSquaredPercentageError(multioutput='uniform_average', multilevel='uniform_average', symmetric=False, square_root=False)[source]#

Mean squared percentage error (MSPE) or square root version.

If square_root is False then calculates MSPE and if square_root is True then calculates root mean squared percentage error (RMSPE). If symmetric is True then calculates sMSPE or sRMSPE. Output is non-negative floating point. The best value is 0.0.

MSPE is measured in squared percentage error relative to the test data and RMSPE is measured in percentage error relative to the test data. Because the calculation takes the square rather than absolute value of the percentage forecast error, large errors are penalized more than MAPE, sMAPE, MdAPE or sMdAPE.

There is no limit on how large the error can be, particulalrly when y_true values are close to zero. In such cases the function returns a large value instead of inf.

Parameters:
symmetricbool, default = False

Whether to calculate the symmetric version of the percentage metric

square_rootbool, default = False

Whether to take the square root of the metric

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.

References

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

Examples

```>>> import numpy as np
>>> from aeon.performance_metrics.forecasting import     MeanSquaredPercentageError
>>> y_true = np.array([3, -0.5, 2, 7, 2])
>>> y_pred = np.array([2.5, 0.0, 2, 8, 1.25])
>>> mspe = MeanSquaredPercentageError(symmetric=False)
>>> mspe(y_true, y_pred)
0.23776218820861678
>>> smspe = MeanSquaredPercentageError(square_root=True, symmetric=False)
>>> smspe(y_true, y_pred)
0.48760864246710883
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> mspe(y_true, y_pred)
0.5080309901738473
>>> smspe(y_true, y_pred)
0.7026794936195895
>>> mspe = MeanSquaredPercentageError(multioutput='raw_values', symmetric=False)
>>> mspe(y_true, y_pred)
array([0.34013605, 0.67592593])
>>> smspe = MeanSquaredPercentageError(multioutput='raw_values',     symmetric=False, square_root=True)
>>> smspe(y_true, y_pred)
array([0.58321184, 0.82214714])
>>> mspe = MeanSquaredPercentageError(multioutput=[0.3, 0.7], symmetric=False)
>>> mspe(y_true, y_pred)
0.5751889644746787
>>> smspe = MeanSquaredPercentageError(multioutput=[0.3, 0.7],     symmetric=False, square_root=True)
>>> smspe(y_true, y_pred)
0.7504665536595034
```

Methods

 `__call__`(y_true, y_pred, **kwargs) Calculate metric value using underlying metric function. 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[, horizon_weight, multioutput, ...]) Mean squared percentage error (MSPE) or square root version. `get_class_tag`(tag_name[, tag_value_default]) Get tag value from estimator class (only class tags). Get class tags from estimator class and all its parent classes. Get parameter defaults for the object. Get parameter names for the object. `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 from estimator class and dynamic tag overrides. `get_test_params`([parameter_set]) Return testing parameter settings for the estimator. Check if the object is composite. `load_from_path`(serial) Load object from file location. `load_from_serial`(serial) Load object from serialized memory container. Reset the object to a clean post-init state. `save`([path]) Save serialized self to bytes-like object or to (.zip) file. `set_params`(**params) Set the parameters of this object. `set_tags`(**tag_dict) Set dynamic tags to given values.
func(y_pred, horizon_weight=None, multioutput='uniform_average', square_root=False, symmetric=False, **kwargs)[source]#

Mean squared percentage error (MSPE) or square root version.

If square_root is False then calculates MSPE and if square_root is True then calculates root mean squared percentage error (RMSPE). If symmetric is True then calculates sMSPE or sRMSPE. Output is non-negative floating point. The best value is 0.0.

MSPE is measured in squared percentage error relative to the test data and RMSPE is measured in percentage error relative to the test data. Because the calculation takes the square rather than absolute value of the percentage forecast error, large errors are penalized more than MAPE, sMAPE, MdAPE or sMdAPE.

There is no limit on how large the error can be, particulalrly when y_true values are close to zero. In such cases the function returns a large value instead of inf.

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.

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.

square_rootbool, default=False

Whether to take the square root of the mean squared error. If True, returns root mean squared error (RMSPE) If False, returns mean squared error (MSPE)

symmetricbool, default=False

Calculates symmetric version of metric if True.

Returns:
lossfloat

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

References

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

Examples

```>>> from aeon.performance_metrics.forecasting import mean_squared_percentage_error
>>> y_true = np.array([3, -0.5, 2, 7, 2])
>>> y_pred = np.array([2.5, 0.0, 2, 8, 1.25])
>>> mean_squared_percentage_error(y_true, y_pred, symmetric=False)
0.23776218820861678
>>> mean_squared_percentage_error(y_true, y_pred, square_root=True,     symmetric=False)
0.48760864246710883
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> mean_squared_percentage_error(y_true, y_pred, symmetric=False)
0.5080309901738473
>>> mean_squared_percentage_error(y_true, y_pred, square_root=True,     symmetric=False)
0.7026794936195895
>>> mean_squared_percentage_error(y_true, y_pred, multioutput='raw_values',     symmetric=False)
array([0.34013605, 0.67592593])
>>> mean_squared_percentage_error(y_true, y_pred, multioutput='raw_values',     square_root=True, symmetric=False)
array([0.58321184, 0.82214714])
>>> mean_squared_percentage_error(y_true, y_pred, multioutput=[0.3, 0.7],     symmetric=False)
0.5751889644746787
>>> mean_squared_percentage_error(y_true, y_pred, multioutput=[0.3, 0.7],     square_root=True, symmetric=False)
0.7504665536595034
```
__call__(y_true, y_pred, **kwargs)[source]#

Calculate metric value using underlying metric function.

Parameters:
y_truetime series in aeon 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_pred :time series in aeon compatible data container format

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

Returns:
lossfloat, np.ndarray, or pd.DataFrame

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

and self.multilevel=”uniform_average” or “uniform_average_time” value is metric averaged over variables and levels (see class docstring)

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

and self.multilevel=”uniform_average” or “uniform_average_time” i-th entry is metric calculated for i-th variable

pd.DataFrame if self.multilevel=raw.values

of shape (n_levels, ) if self.multioutput = “uniform_average” or array of shape (n_levels, y_true.columns) if self.multioutput=”raw_values” metric is applied per level, row averaging (yes/no) as in multioutput

clone()[source]#

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)).

Returns:
instance of type(self), clone of self (see above)
clone_tags(estimator, tag_names=None)[source]#

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')[source]#

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')[source]#

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)[source]#

Evaluate the desired metric on given inputs.

Parameters:
y_truetime series in aeon 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_pred :time series in aeon compatible data container format

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

Returns:
lossfloat, np.ndarray, or pd.DataFrame

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

and self.multilevel=”uniform_average” or “uniform_average_time” value is metric averaged over variables and levels (see class docstring)

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

and self.multilevel=”uniform_average” or “uniform_average_time” i-th entry is metric calculated for i-th variable

pd.DataFrame if self.multilevel=raw.values

of shape (n_levels, ) if self.multioutput = “uniform_average” or array of shape (n_levels, y_true.columns) if self.multioutput=”raw_values” metric is applied per level, row averaging (yes/no) as in multioutput

evaluate_by_index(y_true, y_pred, **kwargs)[source]#

Return the metric evaluated at each time point.

Parameters:
y_truetime series in aeon 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_pred :time series in aeon 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)[source]#

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

Parameters:
tag_namestr

Name of tag value.

tag_value_defaultany type

Returns:
tag_value

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

classmethod get_class_tags()[source]#

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.

classmethod get_param_defaults()[source]#

Get parameter defaults for the object.

Returns:
default_dict: dict with str keys

keys are all parameters of cls that have a default defined in __init__ values are the defaults, as defined in __init__

classmethod get_param_names()[source]#

Get parameter names for the object.

Returns:
param_names: list of str, alphabetically sorted list of parameter names of cls
get_params(deep=True)[source]#

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)[source]#

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

raise_errorbool

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()[source]#

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')[source]#

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

is_composite()[source]#

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

Parameters:
serialresult of ZipFile(path).open(“object)
Returns:
deserialized self resulting in output at path, of cls.save(path)

Load object from serialized memory container.

Parameters:
serial1st element of output of cls.save(None)
Returns:
deserialized self resulting in output serial, of cls.save(None)
reset()[source]#

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

save(path=None)[source]#

Save serialized self to bytes-like object or to (.zip) file.

Behaviour: if path is None, returns an in-memory serialized self if path is a file location, stores self at that location as a zip file

saved files are zip files with following contents: _metadata - contains class of self, i.e., type(self) _obj - serialized self. This class uses the default serialization (pickle).

Parameters:
pathNone or file location (str or Path)

if None, self is saved to an in-memory object if file location, self is saved to that file location. If:

path=”estimator” then a zip file estimator.zip will be made at cwd. path=”/home/stored/estimator” then a zip file estimator.zip will be stored in /home/stored/.

Returns:
if path is None - in-memory serialized self
if path is file location - ZipFile with reference to the file
set_params(**params)[source]#

Set the parameters of this object.

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

Parameters:
**paramsdict

BaseObject parameters

Returns:
selfreference to self (after parameters have been set)
set_tags(**tag_dict)[source]#

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.