ngclearn.utils.density package

Submodules

ngclearn.utils.density.bernoulliMixture module

class ngclearn.utils.density.bernoulliMixture.BernoulliMixture(K, max_iter=50, init_kmeans=False, key=None, **kwargs)

Bases: Mixture

Implements a Bernoulli mixture model (BMM) – or mixture of Bernoullis (MoB). Adaptation of parameters is conducted via the Expectation-Maximization (EM) learning algorithm. Note that this Bernoulli mixture assumes that each component is a factorizable mutlivariate Bernoulli distribution. (A Categorical distribution is assumed over the latent variables).

Parameters:

• K – the number of components/latent variables within this BMM

• max_iter – the maximum number of EM iterations to fit parameters to data (Default = 50)

• init_kmeans – <Unsupported>

calc_log_likelihood(X)

Calculates the multivariate Bernoulli log likelihood of a design matrix/dataset X, under the current parameters of this Bernoulli mixture.

Parameters:

X – the design matrix to estimate log likelihood values over under this BMM

Returns:

(column) vector of individual log likelihoods, scalar for the complete log likelihood p(X)

fit(X, tol=0.001, verbose=False)

Run full fitting process of this BMM.

Parameters:

• X – the dataset to fit this BMM to

• tol – the tolerance value for detecting convergence (via difference-of-means); will engage in early-stopping if tol >= 0. (Default: 1e-3)

• verbose – if True, this function will print out per-iteration measurements to I/O

init(X)

Initializes this BMM in accordance to a supplied design matrix.

Parameters:

X – the design matrix to initialize this BMM to

sample(n_samples, mode_j=-1)

Draw samples from the current underlying BMM model

Parameters:

• n_samples – the number of samples to draw from this BMM

• mode_j – if >= 0, will only draw samples from a specific component of this BMM (Default = -1), ignoring the Categorical prior over latent variables/components

Returns:

Design matrix of samples drawn under the distribution defined by this BMM

update(X)

Performs a single iterative update (E-step followed by M-step) of parameters (assuming model initialized)

Parameters:

X – the dataset / design matrix to fit this BMM to

ngclearn.utils.density.exponentialMixture module

class ngclearn.utils.density.exponentialMixture.ExponentialMixture(K, max_iter=50, init_kmeans=False, key=None, **kwargs)

Bases: Mixture

Implements an exponential mixture model (EMM) – or mixture of exponentials (MoExp). Adaptation of parameters is conducted via the Expectation-Maximization (EM) learning algorithm. Note that this exponential mixture assumes that each component is a factorizable mutlivariate exponential distribution. (A Categorical distribution is assumed over the latent variables).

The exponential distribution of each component (dimension d) is assumed to be:

pdf(x_d; lmbda_d) = lmbda_d * exp(-lmbda_d x_d) for x >= 0, else 0 for x < 0;

where lbmda is the rate parameter vector

Parameters:

• K – the number of components/latent variables within this EMM

• max_iter – the maximum number of EM iterations to fit parameters to data (Default = 50)

• init_kmeans – <Unsupported>

calc_log_likelihood(X)

Calculates the multivariate exponential log likelihood of a design matrix/dataset X, under the current parameters of this exponential mixture.

Parameters:

X – the design matrix to estimate log likelihood values over under this EMM

Returns:

(column) vector of individual log likelihoods, scalar for the complete log likelihood p(X)

fit(X, tol=0.001, verbose=False)

Run full fitting process of this EMM.

Parameters:

• X – the dataset to fit this EMM to

• tol – the tolerance value for detecting convergence (via difference-of-means); will engage in early-stopping if tol >= 0. (Default: 1e-3)

• verbose – if True, this function will print out per-iteration measurements to I/O

init(X)

Initializes this EMM in accordance to a supplied design matrix.

Parameters:

X – the design matrix to initialize this EMM to

sample(n_samples, mode_j=-1)

Draw samples from the current underlying EMM model

Parameters:

• n_samples – the number of samples to draw from this EMM

• mode_j – if >= 0, will only draw samples from a specific component of this EMM (Default = -1), ignoring the Categorical prior over latent variables/components

Returns:

Design matrix of samples drawn under the distribution defined by this EMM

update(X)

Performs a single iterative update (E-step followed by M-step) of parameters (assuming model initialized)

Parameters:

X – the dataset / design matrix to fit this BMM to

Returns:

responsibilities (gamma), priors (pi), rates (lambda), EMM log-likelihood

ngclearn.utils.density.gaussianMixture module

class ngclearn.utils.density.gaussianMixture.GaussianMixture(K, max_iter=50, assume_diag_cov=False, init_kmeans=False, key=None, **kwargs)

Bases: Mixture

Implements a Gaussian mixture model (GMM) – or mixture of Gaussians (MoG). Adaptation of parameters is conducted via the Expectation-Maximization (EM) learning algorithm and leverages full covariance matrices in the component multivariate Gaussians. (A Categorical distribution is assumed over the latent variables).

Parameters:

• K – the number of components/latent variables within this GMM

• max_iter – the maximum number of EM iterations to fit parameters to data (Default = 50)

• assume_diag_cov – if True, assumes a diagonal covariance for each component (Default = False)

• init_kmeans – <Unsupported>

calc_log_likelihood(X)

Calculates the multivariate Gaussian log likelihood of a design matrix/dataset X, under the current parameters of this Gaussian mixture model.

Parameters:

X – the design matrix to estimate log likelihood values over under this GMM

Returns:

(column) vector of individual log likelihoods, scalar for the complete log likelihood p(X)

fit(X, tol=0.001, verbose=False)

Run full fitting process of this GMM.

Parameters:

• X – the dataset to fit this GMM to

• tol – the tolerance value for detecting convergence (via difference-of-means); will engage in early-stopping if tol >= 0. (Default: 1e-3)

• verbose – if True, this function will print out per-iteration measurements to I/O

init(X)

Initializes this GMM in accordance to a supplied design matrix.

Parameters:

X – the design matrix to initialize this GMM to

sample(n_samples, mode_j=-1)

Draw samples from the current underlying GMM model

Parameters:

• n_samples – the number of samples to draw from this GMM

• mode_j – if >= 0, will only draw samples from a specific component of this GMM (Default = -1), ignoring the Categorical prior over latent variables/components

Returns:

Design matrix of samples drawn under the distribution defined by this GMM

update(X)

Performs a single iterative update (E-step followed by M-step) of parameters (assuming model initialized)

Parameters:

X – the dataset / design matrix to fit this GMM to

ngclearn.utils.density.mixture module

class ngclearn.utils.density.mixture.Mixture(K, max_iter=50, **kwargs)

Bases: object

Implements a general mixture model template/structure. Effectively, this is the parent class/template for mixtures of distributions.

Parameters:

• K – the number of components/latent variables within this mixture model

• max_iter – the maximum number of iterations to fit parameters to data (Default = 50)

calc_log_likelihood(X)

fit(X, tol=0.001, verbose=False)

init(X)

sample(n_samples, mode_j=-1)

update(X)

Module contents