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)

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/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()	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.
reset()	Reset the object to a clean post-init state.
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')

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()

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 sktime 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 sktime 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()

Get fitted parameters.

Overrides BaseEstimator default in case of vectorization.

State required:

Requires state to be “fitted”.

Returns

fitted_paramsdict of fitted parameters, keys are str names of parameters

parameters of components are indexed as [componentname]__[paramname]

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.

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 sktime 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.

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 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 sktime 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 sktime 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