KalmanFilterTransformerPK#

class KalmanFilterTransformerPK(state_dim, state_transition=None, transition_offsets=None, measurement_offsets=None, process_noise=None, measurement_noise=None, measurement_function=None, initial_state=None, initial_state_covariance=None, estimate_matrices=None, denoising=False)[source]#

Kalman Filter is used for denoising data, or inferring the hidden state of data.

The Kalman Filter is an unsupervised algorithm, consisting of several mathematical equations which are used to create an estimate of the state of a process.

This class is the adapter for the pykalman package into sktime. KalmanFilterTransformerPK implements hidden inferred states and denoising, depending on the boolean input parameter denoising. In addition, KalmanFilterTransformerPK provides parameter optimization via Expectation-Maximization (EM) algorithm [2], implemented by pykalman.

Parameters

state_dimint

System state feature dimension.

state_transitionnp.ndarray, optional (default=None)

of shape (state_dim, state_dim) or (time_steps, state_dim, state_dim). State transition matrix, also referred to as F, is a matrix which describes the way the underlying series moves through successive time periods.

process_noisenp.ndarray, optional (default=None)

of shape (state_dim, state_dim) or (time_steps, state_dim, state_dim). Process noise matrix, also referred to as Q, the uncertainty of the dynamic model.

measurement_noisenp.ndarray, optional (default=None)

of shape (measurement_dim, measurement_dim) or (time_steps, measurement_dim, measurement_dim). Measurement noise matrix, also referred to as R, represents the uncertainty of the measurements.

measurement_functionnp.ndarray, optional (default=None)

of shape (measurement_dim, state_dim) or (time_steps, measurement_dim, state_dim). Measurement equation matrix, also referred to as H, adjusts dimensions of measurements to match dimensions of state.

initial_statenp.ndarray, optional (default=None)

of shape (state_dim,). Initial estimated system state, also referred to as X0.

initial_state_covariancenp.ndarray, optional (default=None)

of shape (state_dim, state_dim). Initial estimated system state covariance, also referred to as P0.

transition_offsetsnp.ndarray, optional (default=None)

of shape (state_dim,) or (time_steps, state_dim). State offsets, also referred to as b, as described in pykalman.

measurement_offsetsnp.ndarray, optional (default=None)

of shape (measurement_dim,) or (time_steps, measurement_dim). Observation (measurement) offsets, also referred to as d, as described in pykalman.

denoisingbool, optional (default=False).

This parameter affects transform. If False, then transform will be inferring hidden state. If True, uses pykalman smooth for denoising.

estimate_matricesstr or list of str, optional (default=None).

Subset of [state_transition, measurement_function, process_noise, measurement_noise, initial_state, initial_state_covariance, transition_offsets, measurement_offsets] or - all. If estimate_matrices is an iterable of strings, only matrices in estimate_matrices will be estimated using EM algorithm, like described in pykalman. If estimate_matrices is all, then all matrices will be estimated using EM algorithm.

Note - parameters estimated by EM algorithm assumed to be constant.

Attributes

is_fitted: Whether fit has been called.

See also

KalmanFilterTransformerFP: Kalman Filter transformer, adapter for the FilterPy package into sktime.

Notes

pykalman KalmanFilter documentation :: https://pykalman.github.io/#kalmanfilter

References

1: Greg Welch and Gary Bishop, “An Introduction to the Kalman Filter”, 2006 https://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf
2: R.H.Shumway and D.S.Stoffer “An Approach to time Series Smoothing and Forecasting Using the EM Algorithm”, 1982 https://www.stat.pitt.edu/stoffer/dss_files/em.pdf

>>> import numpy as np  
>>> import sktime.transformations.series.kalman_filter as kf
>>> time_steps, state_dim, measurement_dim = 10, 2, 3
>>>
>>> X = np.random.rand(time_steps, measurement_dim) * 10
>>> transformer = kf.KalmanFilterTransformerPK(state_dim=state_dim) 
>>> X_transformed = transformer.fit_transform(X=X)  

Example of - denoising, matrix estimation and missing values:

>>> import numpy as np  
>>> import sktime.transformations.series.kalman_filter as kf
>>> time_steps, state_dim, measurement_dim = 10, 2, 2
>>>
>>> X = np.random.rand(time_steps, measurement_dim)
>>> # missing value
>>> X[0][0] = np.nan
>>>
>>> # If matrices estimation is required, elements of `estimate_matrices`
>>> # are assumed to be constants.
>>> transformer = kf.KalmanFilterTransformerPK(  
...     state_dim=state_dim,
...     measurement_noise=np.eye(measurement_dim),
...     denoising=True,
...     estimate_matrices=['measurement_noise']
...     )
>>>
>>> X_transformed = transformer.fit_transform(X=X)  

Example of - dynamic inputs (matrix per time-step) and missing values:

>>> import numpy as np  
>>> import sktime.transformations.series.kalman_filter as kf
>>> time_steps, state_dim, measurement_dim = 10, 4, 4
>>>
>>> X = np.random.rand(time_steps, measurement_dim)
>>> # missing values
>>> X[0] = [np.NaN for i in range(measurement_dim)]
>>>
>>> # Dynamic input -
>>> # `state_transition` provide different matrix for each time step.
>>> transformer = kf.KalmanFilterTransformerPK(  
...     state_dim=state_dim,
...     state_transition=np.random.rand(time_steps, state_dim, state_dim),
...     estimate_matrices=['initial_state', 'initial_state_covariance']
...     )
>>>
>>> X_transformed = transformer.fit_transform(X=X)  

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 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 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_fitted_params`([deep])	Get fitted parameters.
`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.
`inverse_transform`(X[, y])	Inverse transform X and return an inverse transformed version.
`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])	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.
`transform`(X[, y])	Transform X and return a transformed version.
`update`(X[, y, update_params])	Update transformer with X, optionally y.

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. There are currently no reserved values for transformers.

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

check_is_fitted()[source]#

Check if the estimator has been fitted.

Raises

NotFittedError: If the estimator has not been fitted yet.

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.

fit(X, y=None)[source]#

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

Xtime series in sktime compatible data container format

Data to fit transform to, of sktime type as follows: Series: interpreted as single time series

pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) if np.ndarray, of shape (n_timepoints) or (n_variables, n_timepoints)

Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,: pd.DataFrame in long/wide format, or 3D np.ndarray if pd.DataFrame with 2-level MultiIndex, index is (instance, time) if 3D np.ndarray, of shape (n_instances, n_variables, n_timepoints)
Hierarchical: pd.DataFrame with 3- or more-level MultiIndex: highest (rightmost) level of MultiIndex is time

for more details on sktime mtype format specifications, and additional valid type specifications, refer to

examples/AA_datatypes_and_datasets.ipynb

yoptional, time series in sktime compatible data format, default=None

Additional data, e.g., labels for transformation some transformers require this, see class docstring for details

Returns

selfa fitted instance of the estimator

fit_transform(X, y=None)[source]#

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

Xtime series in sktime compatible data container format

Data to transform, of sktime type as follows: Series: interpreted as single time series

pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) if np.ndarray, of shape (n_timepoints) or (n_variables, n_timepoints)

Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,: pd.DataFrame in long/wide format, or 3D np.ndarray if pd.DataFrame with 2-level MultiIndex, index is (instance, time) if 3D np.ndarray, of shape (n_instances, n_variables, n_timepoints)
Hierarchical: pd.DataFrame with 3- or more-level MultiIndex: highest (rightmost) level of MultiIndex is time

for more details on sktime mtype format specifications, and additional valid type specifications, refer to

examples/AA_datatypes_and_datasets.ipynb

yoptional, time series in sktime compatible data format, default=None

Additional data, e.g., labels for transformation some transformers require this, see class docstring for details

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)[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.

get_fitted_params(deep=True)[source]#

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()[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.

inverse_transform(X, y=None)[source]#

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

Xtime series in sktime compatible data container format

Data to inverse transform, of sktime type as follows: Series: interpreted as single time series

pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) if np.ndarray, of shape (n_timepoints) or (n_variables, n_timepoints)

Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,: pd.DataFrame in long/wide format, or 3D np.ndarray if pd.DataFrame with 2-level MultiIndex, index is (instance, time) if 3D np.ndarray, of shape (n_instances, n_variables, n_timepoints)
Hierarchical: pd.DataFrame with 3- or more-level MultiIndex: highest (rightmost) level of MultiIndex is time

for more details on sktime mtype format specifications, and additional valid type specifications, refer to

examples/AA_datatypes_and_datasets.ipynb

yoptional, time series in sktime compatible data format, default=None

Additional data, e.g., labels for transformation some transformers require this, see class docstring for details

Returns

inverse transformed version of X: of the same type as X, and conforming to mtype format specifications

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.

property is_fitted[source]#: Whether fit has been called.

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)[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_config(**config_dict)[source]#

Set config flags to given values.

Parameters

config_dictdict: Dictionary of config name : config value pairs.

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 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

self: Reference 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.

transform(X, y=None)[source]#

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

Xtime series in sktime compatible data container format

Data to fit transform to, of sktime type as follows: Series: interpreted as single time series

pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) if np.ndarray, of shape (n_timepoints) or (n_variables, n_timepoints)

Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,: pd.DataFrame in long/wide format, or 3D np.ndarray if pd.DataFrame with 2-level MultiIndex, index is (instance, time) if 3D np.ndarray, of shape (n_instances, n_variables, n_timepoints)
Hierarchical: pd.DataFrame with 3- or more-level MultiIndex: highest (rightmost) level of MultiIndex is time

for more details on sktime mtype format specifications, and additional valid type specifications, refer to

examples/AA_datatypes_and_datasets.ipynb

yoptional, time series in sktime compatible data format, default=None

Additional data, e.g., labels for transformation some transformers require this, see class docstring for details

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)[source]#

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

Xtime series in sktime compatible data container format

Data to update transform with, of sktime type as follows: Series: interpreted as single time series

pd.Series, pd.DataFrame, or np.ndarray (1D or 2D) if np.ndarray, of shape (n_timepoints) or (n_variables, n_timepoints)

Panel: pd.DataFrame with 2-level MultiIndex, list of pd.DataFrame,: pd.DataFrame in long/wide format, or 3D np.ndarray if pd.DataFrame with 2-level MultiIndex, index is (instance, time) if 3D np.ndarray, of shape (n_instances, n_variables, n_timepoints)
Hierarchical: pd.DataFrame with 3- or more-level MultiIndex: highest (rightmost) level of MultiIndex is time

for more details on sktime mtype format specifications, and additional valid type specifications, refer to

examples/AA_datatypes_and_datasets.ipynb

yoptional, time series in sktime compatible data format, default=None

Additional data, e.g., labels for transformation some transformers require this, see class docstring for details

Returns

selfa fitted instance of the estimator