HMM Classifier¶

Multiple HMMs can be combined to form a multi-class classifier.

The HMMClassifier can be used to classify:

Univariate/multivariate numerical observation sequences, by using GaussianMixtureHMM models.
Univariate categorical observation sequences, by using CategoricalHMM models.

To classify a new observation sequence \(O'\), the HMMClassifier works by:

Creating HMMs \(\lambda_1, \lambda_2, \ldots, \lambda_C\) and training each model using the Baum—Welch algorithm on the subset of training observation sequences with the same class label as the model.
Calculating the likelihoods \(\mathbb{P}(O'\ |\ \lambda_1), \mathbb{P}(O'\ |\ \lambda_2), \ldots, \mathbb{P}(O'\ |\ \lambda_C)\) of each model generating \(O'\) using the Forward algorithm.
Scaling the likelihoods by priors \(p(\lambda_1), p(\lambda_2), \ldots, p(\lambda_C)\), producing un-normalized posteriors

\(\mathbb{P}(O'\ |\ \lambda_c)p(\lambda_c)\) for each class.
Choosing the class represented by the HMM with the highest posterior probability for \(O'\).

\[\begin{split}c' = \operatorname*{\arg\max}_{c\in\{1,\ldots,C\}}\ p(\lambda_c\ |\ O') = \operatorname*{\arg\\max}_{c\in\{1,\ldots,C\}}\ \mathbb{P}(O'\ |\ \lambda_c)p(\lambda_c)\end{split}\]

These steps are summarized in the diagram below.

API reference¶

Class¶

HMMClassifier

A classifier consisting of HMMs, each trained independently to recognize sequences of a single class.

Methods¶

`__init__`(*[, prior, classes, n_jobs])	Initializes a `HMMClassifier`.
`add_model`(model, label)	Adds a single HMM to the classifier.
`add_models`(models)	Adds HMMs to the classifier.
`fit`([X, y, lengths])	Fits the HMMs to the sequence(s) in `X`.
`predict`(X[, lengths])	Predicts classes for the sequence(s) in `X`.
`predict_proba`(X[, lengths])	Predicts class probabilities for the sequence(s) in `X`.
`predict_scores`(X[, lengths])	Predicts class scores for the sequence(s) in `X`.
`score`(X, y, lengths[, normalize, sample_weight])	Calculates accuracy for the sequence(s) in `X`.

class sequentia.models.hmm.classifier.HMMClassifier[source]¶

A classifier consisting of HMMs, each trained independently to recognize sequences of a single class.

The predicted class for a given observation sequence is the class represented by the HMM which produces the maximum posterior probability for the observation sequence.

Examples

Using a HMMClassifier (with GaussianMixtureHMM models) to classify spoken digits.

import numpy as np
from sequentia.datasets import load_digits
from sequentia.models.hmm import GaussianMixtureHMM, HMMClassifier

# Seed for reproducible pseudo-randomness
random_state = np.random.RandomState(1)

# Fetch MFCCs of spoken digits
data = load_digits()
train_data, test_data = data.split(test_size=0.2, random_state=random_state)

# Create a HMMClassifier using a class frequency prior
clf = HMMClassifier(prior='frequency')

# Add an untrained HMM for each class
for label in data.classes:
    model = GaussianMixtureHMM(random_state=random_state)
    clf.add_model(model, label)

# Fit the HMMs by providing training observation sequences for all classes
X_train, y_train, lengths_train = train_data.X_y_lengths
clf.fit(X_train, y_train, lengths_train)

# Predict classes for the test observation sequences
X_test, lengths_test = test_data.X_lengths
y_pred = clf.predict(X_test, lengths_test)

As done in the above example, we can provide unfitted HMMs using add_model() or add_models(), then provide training observation sequences for all classes to fit(), which will automatically train each HMM on the appropriate subset of data.

Alternatively, we may provide pre-fitted HMMs and call fit() with no arguments.

 # Create a HMMClassifier using a class frequency prior
 clf = HMMClassifier(prior='frequency')

# Manually fit each HMM on its own subset of data
 for X_train, lengths_train, label for train_data.iter_by_class():
     model = GaussianMixtureHMM(random_state=random_state)
     model.fit(X_train, lengths_train)
     clf.add_model(model, label)

 # Fit the classifier
 clf.fit()

__init__(*, prior=None, classes=None, n_jobs=1)[source]¶

Initializes a HMMClassifier.

Parameters:

prior (Optional[Union[Literal['frequency'], dict]]) –
Type of prior probability to assign to each HMM.
- If None, a uniform prior will be used, making each HMM equally likely.
- If "frequency", the prior probability of each HMM is equal to the fraction of total observation sequences that the HMM was fitted with.
- If a dict, custom prior probabilities can be assigned to each HMM. The keys should be the label of the class represented by the HMM, and the value should be the prior probability for the HMM.
classes (Optional[Array]) –
Set of possible class labels.
- If not provided, these will be determined from the training data labels.
- If provided, output from methods such as predict_proba() and predict_scores() will follow the ordering of the class labels provided here.
n_jobs (Union[NegativeInt, PositiveInt]) –
Maximum number of concurrently running workers.
- If 1, no parallelism is used at all (useful for debugging).
- If -1, all CPUs are used.
- If < -1, (n_cpus + 1 + n_jobs) are used — e.g. n_jobs=-2 uses all but one.

Return type:

HMMClassifier

add_model(model, label)[source]¶

Adds a single HMM to the classifier.

Parameters:

model (_HMM) – HMM to add to the classifier.
label (int) – Class represented by the HMM.

Note:

All models added to the classifier must be of the same type — either GaussianMixtureHMM or CategoricalHMM.

add_models(models)[source]¶

Adds HMMs to the classifier.

Parameters:: models (Dict[int, _HMM]) – HMMs to add to the classifier. The key for each HMM should be the label of the class represented by the HMM.
Note:: All models added to the classifier must be of the same type — either GaussianMixtureHMM or CategoricalHMM.

fit(X=None, y=None, lengths=None)[source]¶

Fits the HMMs to the sequence(s) in X.

If fitted models were provided with add_model() or add_models(), no arguments should be passed to fit().
If unfitted models were provided with add_model() or add_models(), training data X, y and lengths must be provided to fit().

Parameters:

X (Optional[Array]) –
Univariate or multivariate observation sequence(s).
- Should be a single 1D array if CategoricalHMM is being used, or either a 1D or 2D array if GaussianMixtureHMM is being used.
- Should have length as the 1st dimension and features as the 2nd dimension.
- Should be a concatenated sequence if multiple sequences are provided, with respective sequence lengths being provided in the lengths argument for decoding the original sequences.
y (Optional[Array]) – Classes corresponding to sequence(s) provided in X.
lengths (Optional[Array]) –
Lengths of the observation sequence(s) provided in X.
- If None, then X is assumed to be a single observation sequence.
- len(X) should be equal to sum(lengths).

Returns:

The fitted classifier.

Return type:

HMMClassifier

classmethod load(path)[source]¶

Loads and deserializes a fitted HMM classifier.

Parameters:: path (Union[str, Path, IO]) – Location to load the serialized classifier from.
Returns:: Fitted HMM classifier.
Return type:: HMMClassifier

HMM Classifier¶

API reference¶

Class¶

Methods¶

Table of Contents

Previous topic

Next topic

This Page