MeanSquaredError#

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

Mean squared error (MSE) or root mean squared error (RMSE).

If square_root is False then calculates MSE and if square_root is True then RMSE is calculated. Both MSE and RMSE are both non-negative floating point. The best value is 0.0.

MSE is measured in squared units of the input data, and RMSE is on the same scale as the data. Because MSE and RMSE square the forecast error rather than taking the absolute value, they penalize large errors more than MAE.

Parameters:
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.

multilevel{‘raw_values’, ‘uniform_average’, ‘uniform_average_time’}

Defines how to aggregate metric for hierarchical data (with levels). If ‘uniform_average’ (default), errors are mean-averaged across levels. If ‘uniform_average_time’, metric is applied to all data, ignoring level index. If ‘raw_values’, does not average errors across levels, hierarchy is retained.

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 sktime.performance_metrics.forecasting import MeanSquaredError
>>> y_true = np.array([3, -0.5, 2, 7, 2])
>>> y_pred = np.array([2.5, 0.0, 2, 8, 1.25])
>>> mse = MeanSquaredError()
>>> mse(y_true, y_pred)
0.4125
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> mse(y_true, y_pred)
0.7083333333333334
>>> rmse = MeanSquaredError(square_root=True)
>>> rmse(y_true, y_pred)
0.8227486121839513
>>> rmse = MeanSquaredError(multioutput='raw_values')
>>> rmse(y_true, y_pred)
array([0.41666667, 1.        ])
>>> rmse = MeanSquaredError(multioutput='raw_values', square_root=True)
>>> rmse(y_true, y_pred)
array([0.64549722, 1.        ])
>>> rmse = MeanSquaredError(multioutput=[0.3, 0.7])
>>> rmse(y_true, y_pred)
0.825
>>> rmse = MeanSquaredError(multioutput=[0.3, 0.7], square_root=True)
>>> rmse(y_true, y_pred)
0.8936491673103708

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 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 error (MSE) or root mean squared error (RMSE).

get_class_tag(tag_name[, tag_value_default])

Get a class tag's value.

get_class_tags()

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

get_config()

Get config flags for self.

get_param_defaults()

Get object's parameter defaults.

get_param_names()

Get object's parameter names.

get_params([deep])

Get a dict of parameters values for this object.

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 composed of other BaseObjects.

load_from_path(serial)

Load object from file location.

load_from_serial(serial)

Load object from serialized memory container.

reset()

Reset the object to a clean post-init state.

save([path, serialization_format])

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

set_config(**config_dict)

Set config flags to given values.

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, **kwargs)[source]#

Mean squared error (MSE) or root mean squared error (RMSE).

If square_root is False then calculates MSE and if square_root is True then RMSE is calculated. Both MSE and RMSE are both non-negative floating point. The best value is 0.0.

MSE is measured in squared units of the input data, and RMSE is on the same scale as the data. Because MSE and RMSE square the forecast error rather than taking the absolute value, they penalize large errors more than MAE.

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 (RMSE) If False, returns mean squared error (MSE)

Returns:
lossfloat or ndarray of floats

MSE loss. If multioutput is ‘raw_values’, then MSE is returned for each output separately. If multioutput is ‘uniform_average’ or an ndarray of weights, then the weighted average MSE 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 sktime.performance_metrics.forecasting import mean_squared_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_error(y_true, y_pred)
0.4125
>>> y_true = np.array([[0.5, 1], [-1, 1], [7, -6]])
>>> y_pred = np.array([[0, 2], [-1, 2], [8, -5]])
>>> mean_squared_error(y_true, y_pred)
0.7083333333333334
>>> mean_squared_error(y_true, y_pred, square_root=True)
0.8227486121839513
>>> mean_squared_error(y_true, y_pred, multioutput='raw_values')
array([0.41666667, 1.        ])
>>> mean_squared_error(y_true, y_pred, multioutput='raw_values', square_root=True)
array([0.64549722, 1.        ])
>>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7])
0.825
>>> mean_squared_error(y_true, y_pred, multioutput=[0.3, 0.7], square_root=True)
0.8936491673103708
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

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

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_pred :time 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, 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.

Raises:
RuntimeError if the clone is non-conforming, due to faulty __init__.

Notes

If successful, equal in value to type(self)(**self.get_params(deep=False)).

clone_tags(estimator, tag_names=None)[source]#

Clone 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 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_pred :time 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, 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 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_pred :time 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)[source]#

Get a class tag’s value.

Does not return information from dynamic tags (set via set_tags or clone_tags) that are defined on instances.

Parameters:
tag_namestr

Name of tag value.

tag_value_defaultany

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()[source]#

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

Retrieves tag: value pairs from _tags class attribute. Does not return information from dynamic tags (set via set_tags or clone_tags) that are defined on instances.

Returns:
collected_tagsdict

Dictionary of class tag name: tag value pairs. Collected from _tags class attribute via nested inheritance.

get_config()[source]#

Get config flags for self.

Returns:
config_dictdict

Dictionary of config name : config value pairs. Collected from _config class attribute via nested inheritance and then any overrides and new tags from _onfig_dynamic object attribute.

classmethod get_param_defaults()[source]#

Get object’s parameter defaults.

Returns:
default_dict: dict[str, Any]

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 object’s parameter names.

Returns:
param_names: list[str]

Alphabetically sorted list of parameter names of cls.

get_params(deep=True)[source]#

Get a dict of parameters values for this object.

Parameters:
deepbool, default=True

Whether to return parameters of components.

  • If True, will return a dict of parameter name : value for this object, including parameters of components (= BaseObject-valued parameters).

  • If False, will return a dict of parameter name : value for this object, but not include parameters of components.

Returns:
paramsdict with str-valued keys

Dictionary of parameters, paramname : paramvalue keys-value pairs include:

  • always: all parameters of this object, as via get_param_names values are parameter value for that key, of this object values are always identical to values passed at construction

  • if deep=True, also contains keys/value pairs of component parameters parameters of components are indexed as [componentname]__[paramname] all parameters of componentname appear as paramname with its value

  • if deep=True, also contains arbitrary levels of component recursion, e.g., [componentname]__[componentcomponentname]__[paramname], etc

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

Default/fallback value if tag is not found

raise_errorbool

whether a ValueError is raised when the tag is not found

Returns:
tag_valueAny

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.

is_composite()[source]#

Check if the object is composed of other BaseObjects.

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 an object has any parameters whose values are BaseObjects.

classmethod load_from_path(serial)[source]#

Load object from file location.

Parameters:
serialresult of ZipFile(path).open(“object)
Returns:
deserialized self resulting in output at path, of cls.save(path)
classmethod load_from_serial(serial)[source]#

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.

Using reset, runs __init__ with current values of hyper-parameters (result of get_params). This Removes any object attributes, except:

  • hyper-parameters = arguments of __init__

  • object attributes containing double-underscores, i.e., the string “__”

Class and object methods, and class attributes are also unaffected.

Returns:
self

Instance of class reset to a clean post-init state but retaining the current hyper-parameter values.

Notes

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

save(path=None, serialization_format='pickle')[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/.

serialization_format: str, default = “pickle”

Module to use for serialization. The available options are “pickle” and “cloudpickle”. Note that non-default formats might require installation of other soft dependencies.

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

Set config flags to given values.

Parameters:
config_dictdict

Dictionary of config name : config value pairs. Valid configs, values, and their meaning is listed below:

displaystr, “diagram” (default), or “text”

how jupyter kernels display instances of self

  • “diagram” = html box diagram representation

  • “text” = string printout

print_changed_onlybool, default=True

whether printing of self lists only self-parameters that differ from defaults (False), or all parameter names and values (False). Does not nest, i.e., only affects self and not component estimators.

warningsstr, “on” (default), or “off”

whether to raise warnings, affects warnings from sktime only

  • “on” = will raise warnings from sktime

  • “off” = will not raise warnings from sktime

backend:parallelstr, optional, default=”None”

backend to use for parallelization when broadcasting/vectorizing, one of

  • “None”: executes loop sequentally, simple list comprehension

  • “loky”, “multiprocessing” and “threading”: uses joblib.Parallel

  • “joblib”: custom and 3rd party joblib backends, e.g., spark

  • “dask”: uses dask, requires dask package in environment

backend:parallel:paramsdict, optional, default={} (no parameters passed)

additional parameters passed to the parallelization backend as config. Valid keys depend on the value of backend:parallel:

  • “None”: no additional parameters, backend_params is ignored

  • “loky”, “multiprocessing” and “threading”: default joblib backends any valid keys for joblib.Parallel can be passed here, e.g., n_jobs, with the exception of backend which is directly controlled by backend. If n_jobs is not passed, it will default to -1, other parameters will default to joblib defaults.

  • “joblib”: custom and 3rd party joblib backends, e.g., spark. Any valid keys for joblib.Parallel can be passed here, e.g., n_jobs, backend must be passed as a key of backend_params in this case. If n_jobs is not passed, it will default to -1, other parameters will default to joblib defaults.

  • “dask”: any valid keys for dask.compute can be passed, e.g., scheduler

Returns:
selfreference to self.

Notes

Changes object state, copies configs in config_dict to self._config_dynamic.

set_params(**params)[source]#

Set the parameters of this object.

The method works on simple estimators as well as on composite objects. Parameter key strings <component>__<parameter> can be used for composites, i.e., objects that contain other objects, to access <parameter> in the component <component>. The string <parameter>, without <component>__, can also be used if this makes the reference unambiguous, e.g., there are no two parameters of components with the name <parameter>.

Parameters:
**paramsdict

BaseObject parameters, keys must be <component>__<parameter> strings. __ suffixes can alias full strings, if unique among get_params keys.

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 setting tag values in tag_dict as dynamic tags in self.