queens.distributions package#

Distributions.

Modules for probability distributions.

Submodules#

queens.distributions.bernoulli module#

Bernoulli distribution.

class Bernoulli[source]#

Bases: Particle

Bernoulli distribution.

__init__(success_probability)[source]#

Initialize Bernoulli distribution.

Parameters:: success_probability (float) – Probability of sampling 1
Return type:: None

queens.distributions.beta module#

Beta Distribution.

class Beta[source]#

Bases: Continuous

Beta distribution.

A generalized one-dimensional beta distribution based on scipy stats. The generalized beta distribution has a lower bound and an upper bound. The parameters a and b determine the shape of the distribution within these bounds.

lower_bound#: Lower bound of the beta distribution.

upper_bound#: Upper bound of the beta distribution.

a#: Shape parameter of the beta distribution, must be greater than 0.

b#: Shape parameter of the beta distribution, must be greater than 0.

scipy_beta#: Scipy beta distribution object.

__init__(lower_bound, upper_bound, a, b)[source]#

Initialize Beta distribution.

Parameters:

lower_bound (float | ndarray) – Lower bound of the beta distribution.
upper_bound (float | ndarray) – Upper bound of the beta distribution.
a (float) – Shape parameter of the beta distribution, must be > 0.
b (float) – Shape parameter of the beta distribution, must be > 0.

Return type:

None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF at positions
Return type:: ndarray

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples from the distribution
Return type:: ndarray

grad_logpdf(x)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: x (ndarray) – Positions at which the gradient of the log-PDF is evaluated
Return type:: ndarray

logpdf(x)[source]#

Log of the probability density function.

Parameters:: x (ndarray) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

pdf(x)[source]#

Probability density function.

Parameters:: x (ndarray) – Positions at which the PDF is evaluated
Returns:: PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of CDF — quantiles).

Parameters:: quantiles (ndarray) – Quantiles at which the PPF is evaluated
Returns:: Positions which correspond to given quantiles
Return type:: ndarray

queens.distributions.categorical module#

General categorical distribution.

Disclaimer: Most of our iterators are not able to handle categorical distributions.

class Categorical[source]#

Bases: Distribution

General categorical distribution.

probabilities#: Probabilities associated with the categories

categories#: Categories

__init__(probabilities, categories)[source]#

Initialize categorical distribution.

Parameters:

probabilities (ndarray) – Probabilities associated with the categories
categories (ndarray) – Categories

Return type:

None

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Samples of the categorical distribution
Return type:: ndarray

logpdf(x)[source]#

Log of the probability mass function.

Parameters:: x (ndarray) – Positions at which the log-PMF is evaluated
Returns:: Log-PMF at positions
Return type:: ndarray

pdf(x)[source]#

Probability mass function.

Parameters:: x (ndarray) – Positions at which the PMF is evaluated
Returns:: PMF at positions
Return type:: ndarray

queens.distributions.exponential module#

Exponential distribution.

class Exponential[source]#

Bases: Continuous

Exponential distribution class.

For a multivariate distribution the components are assumed to be independent.

rate#: Rate parameter(s) of the distribution.

scale#: Scale parameters(s) of the distribution (\(scale = \frac{1}{rate}\)) .

pdf_const#: Constant for the evaluation of the PDF.

logpdf_const#: Constant for the evaluation of the log-PDF.

__init__(rate)[source]#

Initialize exponential distribution.

Parameters:: rate (float | ndarray) – rate parameter(s) of the distribution
Return type:: None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF at positions
Return type:: ndarray

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples from the distribution
Return type:: ndarray

grad_logpdf(x)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: x (ndarray) – Positions at which the gradient of the log-PDF is evaluated
Returns:: Gradient of the log-PDF evaluated at positions
Return type:: ndarray

logpdf(x)[source]#

Log of the probability density function.

Parameters:: x (ndarray) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of CDF — quantiles).

Parameters:: quantiles (ndarray) – Quantiles at which the PPF is evaluated
Returns:: Positions which correspond to given quantiles
Return type:: ndarray

queens.distributions.free_variable module#

Free Variable.

class FreeVariable[source]#

Bases: Continuous

Free variable class.

This is not a proper distribution class. It is used for variables with no underlying distribution.

__init__(dimension)[source]#

Initialize FreeVariable object.

Parameters:: dimension (int) – Dimensionality of the variable
Return type:: None

cdf(_)[source]#

Cumulative distribution function.

Parameters:: _ (Any)
Return type:: ndarray

draw(_=1)[source]#

Draw samples.

Parameters:: _ (int)
Return type:: ndarray

grad_logpdf(_)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: _ (Any)
Return type:: ndarray

logpdf(_)[source]#

Log of the probability density function.

Parameters:: _ (Any)
Return type:: ndarray

pdf(_)[source]#

Probability density function.

Parameters:: _ (Any)
Return type:: ndarray

ppf(_)[source]#

Percent point function (inverse of CDF — quantiles).

Parameters:: _ (Any)
Return type:: ndarray

queens.distributions.lognormal module#

LogNormal Distribution.

class LogNormal[source]#

Bases: Continuous

LogNormal distribution.

Support in (0, +inf).

normal_distribution#: Underlying normal distribution.

__init__(normal_mean, normal_covariance)[source]#

Initialize lognormal distribution.

Parameters:

normal_mean (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – mean of the normal distribution
normal_covariance (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – covariance of the normal distribution

Return type:

None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF at positions
Return type:: ndarray

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples from the distribution
Return type:: ndarray

grad_logpdf(x)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: x (ndarray) – Positions at which the gradient of log-PDF is evaluated
Returns:: Gradient of the log-PDF evaluated at positions
Return type:: ndarray

logpdf(x)[source]#

Log of the probability density function.

Parameters:: x (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

pdf(x)[source]#

Probability density function.

Parameters:: x (ndarray) – Positions at which the PDF is evaluated
Returns:: PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of CDF — quantiles).

Parameters:: quantiles (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Quantiles at which the PPF is evaluated
Returns:: Positions which correspond to given quantiles
Return type:: ndarray

queens.distributions.mean_field_normal module#

Mean-field normal distribution.

class MeanFieldNormal[source]#

Bases: Continuous

Mean-field normal distribution.

standard_deviation#: Standard deviation vector

__init__(mean, variance, dimension)[source]#

Initialize mean-field normal distribution.

Parameters:

mean (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Mean of the distribution
variance (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Variance of the distribution
dimension (int) – Dimensionality of the distribution

Return type:

None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF at positions
Return type:: ndarray

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples from the distribution
Return type:: ndarray

static get_check_array_dimension_and_reshape(input_array, dimension)[source]#

Check dimensions and potentially reshape array.

Parameters:

input_array (ndarray) – Input array
dimension (int) – Dimension of the array

Returns:

Input array with correct dimension

Return type:

ndarray

grad_logpdf(x)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: x (ndarray) – Positions at which the gradient of log-PDF is evaluated
Returns:: Gradient of the log-PDF evaluated at positions
Return type:: ndarray

grad_logpdf_var(x)[source]#

Gradient of the log-PDF with respect to the variance vector.

Parameters:: x (ndarray) – Positions at which the gradient of the log-PDF is evaluated
Returns:: Gradient of the log-PDF w.r.t. the variance at given variance vector and position x
Return type:: ndarray

logpdf(x)[source]#

Log of the probability density function.

Parameters:: x (ndarray) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of cdf — quantiles).

Parameters:: quantiles (ndarray) – Quantiles at which the PPF is evaluated
Return type:: ndarray

update_mean(mean)[source]#

Update the mean of the mean-field normal distribution.

Parameters:: mean (ndarray) – New mean vector
Return type:: None

update_variance(variance)[source]#

Update the variance of the mean-field normal distribution.

Parameters:: variance (ndarray) – New variance vector
Return type:: None

queens.distributions.mixture module#

Mixture distribution.

class Mixture[source]#

Bases: Continuous

Mixture models.

__init__(weights, component_distributions)[source]#

Initialize mixture model.

Parameters:

weights (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Weights of the mixtures
component_distributions (Sequence[Continuous]) – Component distributions of the mixture

Return type:

None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF of the mixture model
Return type:: ndarray

draw(num_draws=1)[source]#

Draw num_draw samples from the variational distribution.

Uses a two step process:

From a multinomial distribution, based on the weights, select a component
Sample from the selected component

Parameters:: num_draws (int) – Number of samples to draw
Returns:: Row-wise samples of the variational distribution
Return type:: ndarray

export_dict()[source]#

Create a dict of the distribution.

Returns:: Dictionary containing distribution information
Return type:: dict

grad_logpdf(x)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: x (ndarray) – Positions at which the gradient of log-PDF is evaluated
Returns:: Gradient of the log-PDF evaluated at positions
Return type:: ndarray

logpdf(x)[source]#

Log of the probability density function.

Parameters:: x (ndarray) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

pdf(x)[source]#

Probability density function.

Parameters:: x (ndarray) – Positions at which the PDF is evaluated
Returns:: PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of CDF — quantiles).

Parameters:: quantiles (ndarray) – Quantiles at which the PPF is evaluated
Return type:: ndarray

responsibilities(x)[source]#

Compute the responsibilities.

The responsibilities are defined as [1]:

Math:: gamma_j(x)=frac{w_j p_j(x)}{sum_{i=0}^{n_{components}-1}w_i p_i(x)}
Parameters:: x (ndarray)
Return type:: ndarray

[1]: Bishop, C. M. (2006). Pattern recognition and machine learning. Springer.

Parameters:: x (ndarray) – Positions at which the responsibilities are evaluated
Returns:: Responsibilities (number of samples x number of component)
Return type:: ndarray

queens.distributions.multinomial module#

Multinomial distribution.

class Multinomial[source]#

Bases: Discrete

Multinomial distribution.

__init__(n_trials, probabilities)[source]#

Initialize discrete uniform distribution.

Parameters:

n_trials (int) – Number of trials, i.e., the value to which every multivariate sample adds up to.
probabilities (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Probabilities associated with all the events in the sample space.

Return type:

None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Return type:: None

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples
Return type:: ndarray

logpdf(x)[source]#

Log of the probability mass function.

Parameters:: x (ndarray) – Positions at which the log-PMF is evaluated
Returns:: Log-PMF at positions
Return type:: ndarray

pdf(x)[source]#

Probability mass function.

Parameters:: x (ndarray) – Positions at which the PMF is evaluated
Returns:: PMF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of CDF - quantiles).

Parameters:: quantiles (ndarray) – Quantiles at which the PPF is evaluated
Return type:: None

queens.distributions.normal module#

Normal distribution.

class Normal[source]#

Bases: Continuous

Normal distribution.

low_chol#: Lower-triangular Cholesky factor of covariance matrix.

precision#: Precision matrix corresponding to covariance matrix.

logpdf_const#: Constant for evaluation of log-PDF.

__init__(mean, covariance)[source]#

Initialize normal distribution.

Parameters:

mean (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Mean of the distribution
covariance (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Covariance of the distribution

Return type:

None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF at positions
Return type:: ndarray

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples from the distribution
Return type:: ndarray

grad_logpdf(x)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: x (ndarray) – Positions at which the gradient of log-PDF is evaluated
Returns:: Gradient of the log-PDF evaluated at positions
Return type:: ndarray

logpdf(x)[source]#

Log of the probability density function.

Parameters:: x (ndarray) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of CDF — quantiles).

Parameters:: quantiles (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Quantiles at which the PPF is evaluated
Returns:: Positions which correspond to given quantiles
Return type:: ndarray

update_covariance(covariance)[source]#

Update covariance and dependent distribution parameters.

Parameters:: covariance (ndarray) – Covariance matrix
Return type:: None

queens.distributions.particle module#

Discrete particle distribution.

class Particle[source]#

Bases: Discrete

Discrete probability distributions.

Similar to particles in SMC, we use the approach where a distribution is approximated as particles:

The particles are the events of the sample space

The weights are denoted by the probabilities of the events

This class can be used directly, but is also used as parent class for other 1d discrete distributions as the computation of expectations is done in the same fashion.

mean#: Mean of the distribution

covariance#: Covariance of the distribution

dimension#: Dimensionality of the distribution

probabilities#: Probabilities associated with all the events in the sample space

sample_space#: Samples, i.e. possible outcomes of sampling the distribution

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF value of the distribution
Return type:: ndarray

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples
Return type:: ndarray

logpdf(x)[source]#

Log of the probability mass function.

Parameters:: x (ndarray) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

pdf(x)[source]#

Probability mass function.

Parameters:: x (ndarray) – Positions at which the PDF is evaluated
Returns:: PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of CDF-quantiles).

Parameters:: quantiles (ndarray) – Quantiles at which the PPF is evaluated
Returns:: Event samples corresponding to the quantiles
Return type:: ndarray

queens.distributions.uniform module#

Uniform distribution.

class Uniform[source]#

Bases: Continuous

Uniform distribution class.

lower_bound#: Lower bound(s) of the distribution.

upper_bound#: Upper bound(s) of the distribution.

width#: Width(s) of the distribution.

pdf_const#: Constant for the evaluation of the PDF.

logpdf_const#: Constant for the evaluation of the log-PDF.

__init__(lower_bound, upper_bound)[source]#

Initialize uniform distribution.

Parameters:

lower_bound (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Lower bound(s) of the distribution
upper_bound (_SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]) – Upper bound(s) of the distribution

Return type:

None

cdf(x)[source]#

Cumulative distribution function.

Parameters:: x (ndarray) – Positions at which the CDF is evaluated
Returns:: CDF at positions
Return type:: ndarray

draw(num_draws=1)[source]#

Draw samples.

Parameters:: num_draws (int) – Number of draws
Returns:: Drawn samples from the distribution
Return type:: ndarray

grad_logpdf(x)[source]#

Gradient of the log-PDF with respect to x.

Parameters:: x (ndarray) – Positions at which the gradient of log-PDF is evaluated
Returns:: Gradient of the log-PDF evaluated at positions
Return type:: ndarray

logpdf(x)[source]#

Log of the probability density function.

Parameters:: x (ndarray) – Positions at which the log-PDF is evaluated
Returns:: Log-PDF at positions
Return type:: ndarray

pdf(x)[source]#

Probability density function.

Parameters:: x (ndarray) – Positions at which the PDF is evaluated
Returns:: PDF at positions
Return type:: ndarray

ppf(quantiles)[source]#

Percent point function (inverse of cdf — quantiles).

Parameters:: quantiles (ndarray) – Quantiles at which the PPF is evaluated
Returns:: Positions which correspond to given quantiles
Return type:: ndarray

queens.distributions.uniform_discrete module#

Discrete uniform distribution.

class UniformDiscrete[source]#

Bases: Particle

Discrete uniform distribution.

__init__(sample_space)[source]#

Initialize discrete uniform distribution.

Parameters:: sample_space (ndarray) – Samples, i.e., possible outcomes of sampling the distribution
Return type:: None