HMM

class HMM(emission_funcs: list, transition_prob_mat: ndarray, initial_probs: ndarray = None)

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 initial 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 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 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.
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.
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, 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_random_state([random_state, deep, ...])	Set random_state pseudo-random seed parameters for self.
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')

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()

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.

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)

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')

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__}

fit(X, Y=None)

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)

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)

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()

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()

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)

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 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()

Get object’s parameter names.

Returns:

param_names: list[str]

Alphabetically sorted list of parameter names of cls.

get_params(deep=True)

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)

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()

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()

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

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)

predict(X)

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)

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()

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')

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)

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)

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_random_state(random_state=None, deep=True, self_policy='copy')

Set random_state pseudo-random seed parameters for self.

Finds random_state named parameters via estimator.get_params, and sets them to integers derived from random_state via set_params. These integers are sampled from chain hashing via sample_dependent_seed, and guarantee pseudo-random independence of seeded random generators.

Applies to random_state parameters in estimator depending on self_policy, and remaining component estimators if and only if deep=True.

Note: calls set_params even if self does not have a random_state, or none of the components have a random_state parameter. Therefore, set_random_state will reset any scikit-base estimator, even those without a random_state parameter.

Parameters:

random_stateint, RandomState instance or None, default=None

Pseudo-random number generator to control the generation of the random integers. Pass int for reproducible output across multiple function calls.

deepbool, default=True

Whether to set the random state in sub-estimators. If False, will set only self’s random_state parameter, if exists. If True, will set random_state parameters in sub-estimators as well.

self_policystr, one of {“copy”, “keep”, “new”}, default=”copy”

• “copy” : estimator.random_state is set to input random_state

• “keep” : estimator.random_state is kept as is

• “new” : estimator.random_state is set to a new random state,

derived from input random_state, and in general different from it

Returns:

selfreference to self

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 setting tag values in tag_dict as dynamic tags in self.

update(X, Y=None)

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)

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 “_”.