HMM#

class HMM(emission_funcs: list, transition_prob_mat: numpy.ndarray, initial_probs: Optional[numpy.ndarray] = None)[source]#

Implements a simple HMM fitted with Viterbi algorithm.

The HMM annotation estimator uses the the Viterbi algorithm to fit a sequence of ‘hidden state’ class annotations (represented by an array of integers the same size as the observation) to a sequence of observations.

This is done by finding the most likely path given the emission probabilities - (ie the probability that a particular observation would be generated by a given hidden state), the transition prob (ie the probability of transitioning from one state to another or staying in the same state) and the initial probabilities - ie the belief of the probability distribution of hidden states at the start of the observation sequence).

Current assumptions/limitations of this implementation:
  • the spacing of time series points is assumed to be equivalent.

  • it only works on univariate data.

  • the emission parameters and transition probabilities are

    assumed to be known.

  • if no initial probs are passed, uniform probabilities are

    assigned (ie rather than the stationary distribution.)

  • requires and returns np.ndarrays.

_fit is currently empty as the parameters of the probability distribution are required to be passed to the algorithm.

_predict - first the transition_probability and transition_id matrices are calculated - these are both nxm matrices, where n is the number of hidden states and m is the number of observations. The transition probability matrices record the probability of the most likely sequence which has observation m being assigned to hidden state n. The transition_id matrix records the step before hidden state n that proceeds it in the most likely path. This logic is mostly carried out by helper function _calculate_trans_mats. Next, these matrices are used to calculate the most likely path (by backtracing from the final mostly likely state and the id’s that proceeded it.) This logic is done via a helper func hmm_viterbi_label.

Parameters
emission_funcslist, shape = [num hidden states]

List should be of length n (the number of hidden states) Either a list of callables [fx_1, fx_2] with signature fx_1(X) -> float or a list of callables and matched keyword arguments for those callables [(fx_1, kwarg_1), (fx_2, kwarg_2)] with signature fx_1(X, **kwargs) -> float (or a list with some mixture of the two). The callables should take a value and return a probability when passed a single observation. All functions should be properly normalized PDFs over the same space as the observed data.

transition_prob_mat: 2D np.ndarry, shape = [num_states, num_states]

Each row should sum to 1 in order to be properly normalized (ie the j’th column in the i’th row represents the probability of transitioning from state i to state j.)

initial_probs: 1D np.ndarray, shape = [num hidden states], optional

A array of probabilities that the sequence of hidden states starts in each of the hidden states. If passed, should be of length n the number of hidden states and should match the length of both the emission funcs list and the transition_prob_mat. The initial probs should be reflective of prior beliefs. If none is passed will each hidden state will be assigned an equal inital prob.

Attributes
emission_funcslist, shape = [num_hidden_states]

The functions to use in calculating the emission probabilities. Taken from the __init__ param of same name.

transition_prob_mat: 2D np.ndarry, shape = [num_states, num_states]

Matrix of transition probabilities from hidden state to hidden state. Taken from the __init__ param of same name.

initial_probs1D np.ndarray, shape = [num_hidden_states]

Probability over the hidden state identity of the first state. If the __init__ param of same name was passed it will take on that value. Otherwise it is set to be uniform over all hidden states.

num_statesint

The number of hidden states. Set to be the length of the emission_funcs parameter which was passed.

stateslist

A list of integers from 0 to num_states-1. Integer labels for the hidden states.

num_obsint

The length of the observations data. Extracted from data.

trans_prob2D np.ndarray, shape = [num_observations, num_hidden_states]

Shape [num observations, num hidden states]. The max probability that that observation is assigned to that hidden state. Calculated in _calculate_trans_mat and assigned in _predict.

trans_id2D np.ndarray, shape = [num_observations, num_hidden_states]

Shape [num observations, num hidden states]. The state id of the state proceeding the observation is assigned to that hidden state in the most likely path where that occurs. Calculated in _calculate_trans_mat and assigned in _predict.

Examples

>>> from sktime.annotation.hmm import HMM
>>> from scipy.stats import norm
>>> from numpy import asarray
>>> # define the emission probs for our HMM model:
>>> centers = [3.5,-5]
>>> sd = [.25 for i in centers]
>>> emi_funcs = [(norm.pdf, {'loc': mean,
...  'scale': sd[ind]}) for ind, mean in enumerate(centers)]
>>> hmm_est = HMM(emi_funcs, asarray([[0.25,0.75], [0.666, 0.333]]))
>>> # generate synthetic data (or of course use your own!)
>>> obs = asarray([3.7,3.2,3.4,3.6,-5.1,-5.2,-4.9])
>>> hmm_est = hmm_est.fit(obs)
>>> labels = hmm_est.predict(obs)

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 to training data.

fit_predict(X[, Y])

Fit to data, then predict 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.

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.

predict(X)

Create annotations on test/deployment data.

predict_scores(X)

Return scores for predicted annotations on test/deployment data.

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.

update(X[, Y])

Update model with new data and optional ground truth annotations.

update_predict(X)

Update model with new data and create annotations for it.

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
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. Equal in value to type(self)(**self.get_params(deep=False)).

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

clone/mirror tags from another estimator as dynamic override.

Parameters
estimatorestimator inheriting from :class:BaseEstimator
tag_namesstr or list of str, default = None

Names of tags to clone. If None then all tags in estimator are used as tag_names.

Returns
Self

Reference to self.

Notes

Changes object state by setting tag values in tag_set from estimator as dynamic tags in self.

classmethod create_test_instance(parameter_set='default')[source]#

Construct Estimator instance if possible.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns
instanceinstance of the class with default parameters

Notes

get_test_params can return dict or list of dict. This function takes first or single dict that get_test_params returns, and constructs the object with that.

classmethod create_test_instances_and_names(parameter_set='default')[source]#

Create list of all test instances and a list of names for them.

Parameters
parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns
objslist of instances of cls

i-th instance is cls(**cls.get_test_params()[i])

nameslist of str, same length as objs

i-th element is name of i-th instance of obj in tests convention is {cls.__name__}-{i} if more than one instance otherwise {cls.__name__}

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

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

Fit to training data.

Parameters
Xpd.DataFrame

Training data to fit model to (time series).

Ypd.Series, optional

Ground truth annotations for training if annotator is supervised.

Returns
self

Reference to self.

Notes

Creates fitted model that updates attributes ending in “_”. Sets _is_fitted flag to True.

fit_predict(X, Y=None)[source]#

Fit to data, then predict it.

Fits model to X and Y with given annotation parameters and returns the annotations made by the model.

Parameters
Xpd.DataFrame, pd.Series or np.ndarray

Data to be transformed

Ypd.Series or np.ndarray, optional (default=None)

Target values of data to be predicted.

Returns
selfpd.Series

Annotations for sequence X exact format depends on annotation type.

classmethod get_class_tag(tag_name, tag_value_default=None)[source]#

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

Parameters
tag_namestr

Name of tag value.

tag_value_defaultany type

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 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()[source]#

Get fitted parameters.

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()[source]#

Get parameter defaults for the object.

Returns
default_dict: dict with str keys

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

classmethod get_param_names()[source]#

Get parameter names for the object.

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

Get parameters for this estimator.

Parameters
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsdict

Parameter names mapped to their values.

get_tag(tag_name, tag_value_default=None, raise_error=True)[source]#

Get tag value from estimator class and dynamic tag overrides.

Parameters
tag_namestr

Name of tag to be retrieved

tag_value_defaultany type, optional; default=None

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()[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 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[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)
predict(X)[source]#

Create annotations on test/deployment data.

Parameters
Xpd.DataFrame

Data to annotate (time series).

Returns
Ypd.Series

Annotations for sequence X exact format depends on annotation type.

predict_scores(X)[source]#

Return scores for predicted annotations on test/deployment data.

Parameters
Xpd.DataFrame

Data to annotate (time series).

Returns
Ypd.Series

Scores for sequence X exact format depends on annotation type.

reset()[source]#

Reset the object to a clean post-init state.

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

Detail behaviour: removes any object attributes, except:

hyper-parameters = arguments of __init__ object attributes containing double-underscores, i.e., the string “__”

runs __init__ with current values of hyper-parameters (result of get_params)

Not affected by the reset are: object attributes containing double-underscores class and object methods, class attributes

save(path=None)[source]#

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

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

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

Parameters
pathNone or file location (str or Path)

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

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

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

Set the parameters of this object.

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

Parameters
**paramsdict

BaseObject parameters

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

Set dynamic tags to given values.

Parameters
tag_dictdict

Dictionary of tag name : tag value pairs.

Returns
Self

Reference to self.

Notes

Changes object state by settting tag values in tag_dict as dynamic tags in self.

update(X, Y=None)[source]#

Update model with new data and optional ground truth annotations.

Parameters
Xpd.DataFrame

Training data to update model with (time series).

Ypd.Series, optional

Ground truth annotations for training if annotator is supervised.

Returns
self

Reference to self.

Notes

Updates fitted model that updates attributes ending in “_”.

update_predict(X)[source]#

Update model with new data and create annotations for it.

Parameters
Xpd.DataFrame

Training data to update model with, time series.

Returns
Ypd.Series

Annotations for sequence X exact format depends on annotation type.

Notes

Updates fitted model that updates attributes ending in “_”.