ThetaLinesTransformer

class ThetaLinesTransformer(theta=(0, 2))

Decompose the original data into two or more Theta-lines.

Implementation of decomposition for Theta-method [1] as described in [2].

Overview: Input univariate series of length “n” and ThetaLinesTransformer modifies the local curvature of the time series using Theta-coefficient values passed through the parameter theta.

Each Theta-coefficient is applied directly to the second differences of the input series. The resulting transformed series (Theta-lines) are returned as a pd.DataFrame of shape len(input series) * len(theta).

Parameters:

thetasequence of float, default=(0,2)

Theta-coefficients to use in transformation.

Attributes:

is_fitted

Whether fit has been called.

Notes

Depending on the value of the Theta-coefficient, Theta-lines either augment the long-term trend (0 < Theta < 1) or the the short-term behaviour (Theta > 1).

Special cases:

• Theta == 0 : deflates input data to linear trend

• Theta == 1 : returns data unchanged

• Theta < 0 : transforms time series and mirrors it along the linear trend.

References

[1]

V.Assimakopoulos et al., “The theta model: a decomposition approach to forecasting”, International Journal of Forecasting, vol. 16, pp. 521-530, 2000.

[2]

E.Spiliotis et al., “Generalizing the Theta method for automatic forecasting “, European Journal of Operational Research, vol. 284, pp. 550-558, 2020.

Examples

>>> from aeon.transformations.series.theta import ThetaLinesTransformer
>>> from aeon.datasets import load_airline
>>> y = load_airline()
>>> transformer = ThetaLinesTransformer([0, 0.25, 0.5, 0.75])
>>> y_thetas = transformer.fit_transform(y)

Methods

check_is_fitted()	Check if the estimator has been fitted.
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.
fit(X[, y])	Fit transformer to X, optionally to y.
fit_transform(X[, y])	Fit to data, then transform it.
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_fitted_params([deep])	Get fitted parameters.
get_param_defaults()	Get parameter defaults for the object.
get_param_names()	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()	Get tags from estimator class and dynamic tag overrides.
get_test_params([parameter_set])	Return testing parameter settings for the estimator.
inverse_transform(X[, y])	Inverse transform X and return an inverse transformed version.
is_composite()	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()	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.
transform(X[, y])	Transform X and return a transformed version.
update(X[, y, update_params])	Update transformer with X, optionally y.

check_is_fitted()

Check if the estimator has been fitted.

Raises:

NotFittedError

If the estimator has not been fitted yet.

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)).

Returns:

instance of type(self), clone of self (see above)

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.

fit(X, y=None)

Fit transformer to X, optionally to y.

State change:

Changes state to “fitted”.

Writes to self: _is_fitted : flag is set to True. _X : X, coerced copy of X, if remember_data tag is True

possibly coerced to inner type or update_data compatible type by reference, when possible

model attributes (ending in “_”) : dependent on estimator

Parameters:

XSeries or Panel, any supported mtype

Data to fit transform to, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to aeon mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns:

selfa fitted instance of the estimator

fit_transform(X, y=None)

Fit to data, then transform it.

Fits the transformer to X and y and returns a transformed version of X.

State change:

Changes state to “fitted”.

Writes to self: _is_fitted : flag is set to True. _X : X, coerced copy of X, if remember_data tag is True

possibly coerced to inner type or update_data compatible type by reference, when possible

model attributes (ending in “_”) : dependent on estimator

Parameters:

XSeries or Panel, any supported mtype

Data to be transformed, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to aeon mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns:

transformed version of X

type depends on type of X and scitype:transform-output tag:

X | tf-output | type of return |

|----------|————–|------------------------| | Series | Primitives | pd.DataFrame (1-row) | | Panel | Primitives | pd.DataFrame | | Series | Series | Series | | Panel | Series | Panel | | Series | Panel | Panel |

instances in return correspond to instances in X

combinations not in the table are currently not supported

Explicitly, with examples:

if X is Series (e.g., pd.DataFrame) and transform-output is Series

then the return is a single Series of the same mtype Example: detrending a single series

if X is Panel (e.g., pd-multiindex) and transform-output is Series

then the return is Panel with same number of instances as X

(the transformer is applied to each input Series instance)

Example: all series in the panel are detrended individually

if X is Series or Panel and transform-output is Primitives

then the return is pd.DataFrame with as many rows as instances in X Example: i-th row of the return has mean and variance of the i-th series

if X is Series and transform-output is Panel

then the return is a Panel object of type pd-multiindex Example: i-th instance of the output is the i-th window running over X

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_fitted_params(deep=True)

Get fitted parameters.

State required:

Requires state to be “fitted”.

Parameters:

deepbool, default=True

Whether to return fitted parameters of components.

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

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

Returns:

fitted_paramsdict with str-valued keys

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

• always: all fitted parameters of this object, as via get_param_names values are fitted parameter value for that key, of this object

• 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

classmethod get_param_defaults()

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()

Get parameter names for the object.

Returns:

param_names: list of str, alphabetically sorted list of parameter names of cls

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

inverse_transform(X, y=None)

Inverse transform X and return an inverse transformed version.

Currently it is assumed that only transformers with tags

“scitype:transform-input”=”Series”, “scitype:transform-output”=”Series”,

have an inverse_transform.

State required:

Requires state to be “fitted”.

Accesses in self: _is_fitted : must be True _X : optionally accessed, only available if remember_data tag is True fitted model attributes (ending in “_”) : accessed by _inverse_transform

Parameters:

XSeries or Panel, any supported mtype

Data to be inverse transformed, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to aeon mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns:

inverse transformed version of X

of the same type as X, and conforming to mtype format specifications

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

property is_fitted

Whether fit has been called.

classmethod load_from_path(serial)

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)

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()

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)

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)

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)

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.

transform(X, y=None)

Transform X and return a transformed version.

State required:

Requires state to be “fitted”.

Accesses in self: _is_fitted : must be True _X : optionally accessed, only available if remember_data tag is True fitted model attributes (ending in “_”) : must be set, accessed by _transform

Parameters:

XSeries or Panel, any supported mtype

Data to be transformed, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to aeon mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

Returns:

transformed version of X

type depends on type of X and scitype:transform-output tag:

| transform | |

X | -output | type of return |

|----------|————–|------------------------| | Series | Primitives | pd.DataFrame (1-row) | | Panel | Primitives | pd.DataFrame | | Series | Series | Series | | Panel | Series | Panel | | Series | Panel | Panel |

instances in return correspond to instances in X

combinations not in the table are currently not supported

Explicitly, with examples:

if X is Series (e.g., pd.DataFrame) and transform-output is Series

then the return is a single Series of the same mtype Example: detrending a single series

if X is Panel (e.g., pd-multiindex) and transform-output is Series

then the return is Panel with same number of instances as X

(the transformer is applied to each input Series instance)

Example: all series in the panel are detrended individually

if X is Series or Panel and transform-output is Primitives

then the return is pd.DataFrame with as many rows as instances in X Example: i-th row of the return has mean and variance of the i-th series

if X is Series and transform-output is Panel

then the return is a Panel object of type pd-multiindex Example: i-th instance of the output is the i-th window running over X

update(X, y=None, update_params=True)

Update transformer with X, optionally y.

State required:

Requires state to be “fitted”.

Accesses in self: _is_fitted : must be True _X : accessed by _update and by update_data, if remember_data tag is True fitted model attributes (ending in “_”) : must be set, accessed by _update

Writes to self: _X : updated by values in X, via update_data, if remember_data tag is True fitted model attributes (ending in “_”) : only if update_params=True

type and nature of update are dependent on estimator

Parameters:

XSeries or Panel, any supported mtype

Data to fit transform to, of python type as follows:

Series: pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,

nested pd.DataFrame, or pd.DataFrame in long/wide format

subject to aeon mtype format specifications, for further details see

examples/AA_datatypes_and_datasets.ipynb

ySeries or Panel, default=None

Additional data, e.g., labels for transformation

update_paramsbool, default=True

whether the model is updated. Yes if true, if false, simply skips call. argument exists for compatibility with forecasting module.

Returns:

selfa fitted instance of the estimator