API Reference#

`alpha_stable`	A Distribution continuous random variable.
`multivariate_alpha_stable`	Multivariate alpha stable distribution generator.
`random`	Random number generation for Alpha Stable Distributions
`statistics`	Statistics for Alpha Stable Distributions
`machine_learning`	Machine Learning for Alpha Stable Distributions.

class aub_htp.AlphaStableKMeans(n_clusters: int = 8, alpha: float = 1.0, *, max_iter: int = 100, tol: float = 1e-06)#

Bases: ClusterMixin, BaseEstimator

fit(X, y=None)#

predict(X)#

score(X, y=None, sample_weight=None)#

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → AlphaStableKMeans#

Configure whether metadata should be requested to be passed to the score method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config()). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters#

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sample_weight parameter in score.

Returns#

selfobject: The updated object.

class aub_htp.AlphaStableLinearRegressor(alpha: float = 1.0, *, max_iter: int = 5000, tol: float = 1e-06, optimizer: str = 'Powell')#

Bases: RegressorMixin, BaseEstimator

Scikit-learn compatible Alpha-stable linear regression.

Given $\textbf{x}$ and $\textbf{y}$ as training data, where $\textbf{x}$ is a matrix of shape (n_samples, n_features) and $\textbf{y}$ is a matrix of shape (n_samples, n_targets), the objective is to find the weights $\textbf{w}$ and bias $b$ that minimizes the loss function:

\[\mathrm{arg\,min}_{\mathbf{w}, b} P_\alpha(y - (\mathbf{x}\mathbf{w}^T + b))^\alpha\]

fit(X, y)#

predict(X)#

score(X, y, sample_weight=None)#

Return coefficient of determination on test data.

The coefficient of determination, $R^2$, is defined as $(1 - \frac{u}{v})$, where $u$ is the residual sum of squares ((y_true - y_pred)** 2).sum() and $v$ is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a $R^2$ score of 0.0.

Parameters#

Xarray-like of shape (n_samples, n_features): Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs): True values for X.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns#

scorefloat: $R^2$ of self.predict(X) w.r.t. y.

Notes#

The $R^2$ score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score(). This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → AlphaStableLinearRegressor#

Configure whether metadata should be requested to be passed to the score method.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters#

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sample_weight parameter in score.

Returns#

selfobject: The updated object.

class aub_htp.AlphaStablePCA(n_components: int = None, alpha: float = 1.0, *, shape_estimation_method: Literal['method1', 'method2', 'method3'] = 'method1')#

Bases: TransformerMixin, BaseEstimator

components_: ndarray#

fit(X, y=None)#

fit_transform(X, y=None)#

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters#

Xarray-like of shape (n_samples, n_features): Input samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None: Target values (None for unsupervised transformations).
**fit_paramsdict: Additional fit parameters. Pass only if the estimator accepts additional params in its fit method.

Returns#

X_newndarray array of shape (n_samples, n_features_new): Transformed array.

location_: ndarray#

power_: ndarray#

score(X, y=None)#

shape_: ndarray#

transform(X)#

class aub_htp.AlphaStableShape(alpha: float = 1.0, alpha_kernel: float = None, alpha_data: float = None, method: Literal['method1', 'method2', 'method3'] = 'method1')#

Bases: BaseEstimator

fit(X, y=None)#

score(X, y=None)#

class aub_htp.BaseSpectralMeasureSampler#

Bases: ABC

Spectral Measure Sampler is an interface to define the sampling algorithm for a spectral measure. The underlying mathematical spectral measure $\Lambda$ has to uphold the following property:

\[\int_{\mathbb{S}^{d-1}}s\Lambda(ds)=0\]

To create a custom spectral measure sampler, you need to inherit from this class and implement the following methods:

Example:

class CustomSpectralMeasureSampler(BaseSpectralMeasureSampler):
    def sample(self, number_of_samples: int, random_state: None | int | np.random.RandomState | np.random.Generator = None) -> np.ndarray:
        random_state = get_random_state_generator(random_state)
        return random_state.rand(number_of_samples, self.dimensions())
    def dimensions(self) -> int:
        return 2
    def mass(self) -> float:
        return 1.0

abstractmethod dimensions() → int#: Number of dimensions of the vector space of the spectral measure.

Returns#

dimensions : int

abstractmethod mass() → float#: Mass of the spectral measure.

Returns#

mass : float

abstractmethod sample(number_of_samples: int, random_state: None | int | RandomState | Generator = None) → ndarray#

Sampling algorithm for the spectral measure sampler.

Parameters#

number_of_samplesint: The number of samples to draw from the spectral measure.
random_stateNone | int | np.random.RandomState | np.random.Generator, optional: The random state to use for the sampling. You are encouraged to use aub_htp.random.get_random_state_generator() to get a random state generator as such: random_state = get_random_state_generator(random_state)

Returns#

samplesnp.ndarray: The samples from the spectral measure.

class aub_htp.DiscreteSampler(alpha: float, positions: ndarray, weights: ndarray)#

Bases: BaseSpectralMeasureSampler

dimensions() → int#: Number of dimensions of the vector space of the spectral measure.

Returns#

dimensions : int

mass() → float#: Mass of the spectral measure.

Returns#

mass : float

sample(number_of_samples: int, random_state: None | int | RandomState | Generator = None) → ndarray#

Sampling algorithm for the spectral measure sampler.

Parameters#

number_of_samplesint: The number of samples to draw from the spectral measure.
random_stateNone | int | np.random.RandomState | np.random.Generator, optional: The random state to use for the sampling. You are encouraged to use aub_htp.random.get_random_state_generator() to get a random state generator as such: random_state = get_random_state_generator(random_state)

Returns#

samplesnp.ndarray: The samples from the spectral measure.

class aub_htp.EllipticSampler(number_of_dimensions: int, alpha: float, sigma: ndarray, mass: float | None = None)#

Bases: BaseSpectralMeasureSampler

dimensions() → int#: Number of dimensions of the vector space of the spectral measure.

Returns#

dimensions : int

mass() → float#: Mass of the spectral measure.

Returns#

mass : float

sample(number_of_samples: int, random_state: None | int | RandomState | Generator = None) → ndarray#

Sampling algorithm for the spectral measure sampler.

Parameters#

number_of_samplesint: The number of samples to draw from the spectral measure.
random_stateNone | int | np.random.RandomState | np.random.Generator, optional: The random state to use for the sampling. You are encouraged to use aub_htp.random.get_random_state_generator() to get a random state generator as such: random_state = get_random_state_generator(random_state)

Returns#

samplesnp.ndarray: The samples from the spectral measure.

class aub_htp.IsotropicSampler(number_of_dimensions: int, alpha: float, gamma: float)#

Bases: BaseSpectralMeasureSampler

dimensions() → int#: Number of dimensions of the vector space of the spectral measure.

Returns#

dimensions : int

mass() → float#: Mass of the spectral measure.

Returns#

mass : float

sample(number_of_samples: int, random_state: None | int | RandomState | Generator = None) → ndarray#

Sampling algorithm for the spectral measure sampler.

Parameters#

number_of_samplesint: The number of samples to draw from the spectral measure.
random_stateNone | int | np.random.RandomState | np.random.Generator, optional: The random state to use for the sampling. You are encouraged to use aub_htp.random.get_random_state_generator() to get a random state generator as such: random_state = get_random_state_generator(random_state)

Returns#

samplesnp.ndarray: The samples from the spectral measure.

class aub_htp.MixedSampler(spectral_measures: list[BaseSpectralMeasureSampler], weights: ndarray)#

Bases: BaseSpectralMeasureSampler

dimensions() → int#: Number of dimensions of the vector space of the spectral measure.

Returns#

dimensions : int

mass() → float#: Mass of the spectral measure.

Returns#

mass : float

sample(number_of_samples: int, random_state: None | int | RandomState | Generator = None) → ndarray#

Sampling algorithm for the spectral measure sampler.

Parameters#

number_of_samplesint: The number of samples to draw from the spectral measure.
random_stateNone | int | np.random.RandomState | np.random.Generator, optional: The random state to use for the sampling. You are encouraged to use aub_htp.random.get_random_state_generator() to get a random state generator as such: random_state = get_random_state_generator(random_state)

Returns#

samplesnp.ndarray: The samples from the spectral measure.

class aub_htp.UnivariateSampler(alpha: float, beta: float, gamma: float)#

Bases: BaseSpectralMeasureSampler

dimensions() → int#: Number of dimensions of the vector space of the spectral measure.

Returns#

dimensions : int

mass() → float#: Mass of the spectral measure.

Returns#

mass : float

sample(number_of_samples: int, random_state: None | int | RandomState | Generator = None) → ndarray#

Sampling algorithm for the spectral measure sampler.

Parameters#

number_of_samplesint: The number of samples to draw from the spectral measure.
random_stateNone | int | np.random.RandomState | np.random.Generator, optional: The random state to use for the sampling. You are encouraged to use aub_htp.random.get_random_state_generator() to get a random state generator as such: random_state = get_random_state_generator(random_state)

Returns#

samplesnp.ndarray: The samples from the spectral measure.

aub_htp.alpha_location(data: ndarray, alpha: float) → ndarray#

aub_htp.alpha_power(data: ndarray, alpha: float) → float#

class aub_htp.alpha_stable_gen(momtype=1, a=None, b=None, xtol=1e-14, badvalue=None, name=None, longname=None, shapes=None, seed=None)#

Bases: rv_continuous

property parameterization#

pdf(x, *args, **kwds)#

Probability density function at x of the given RV.

Parameters#

xarray_like: quantiles
arg1, arg2, arg3,…array_like: The shape parameter(s) for the distribution (see docstring of the instance object for more information)
locarray_like, optional: location parameter (default=0)
scalearray_like, optional: scale parameter (default=1)

Returns#

pdfndarray: Probability density function evaluated at x

rvs(*args, **kwds)#

Random variates of given type.

Parameters#

arg1, arg2, arg3,…array_like: The shape parameter(s) for the distribution (see docstring of the instance object for more information).
locarray_like, optional: Location parameter (default=0).
scalearray_like, optional: Scale parameter (default=1).
sizeint or tuple of ints, optional: Defining number of random variates (default is 1).
random_state{None, int, numpy.random.Generator,: numpy.random.RandomState}, optional

If random_state is None (or np.random), the numpy.random.RandomState singleton is used. If random_state is an int, a new RandomState instance is used, seeded with random_state. If random_state is already a Generator or RandomState instance, that instance is used.

Returns#

rvsndarray or scalar: Random variates of given size.

with_parametrization(parametrization: Literal['S1', 'S0'])#

aub_htp.get_random_state_generator(random_state: None | int | RandomState | Generator = None) → Generator#

A scipy-compatible random state generator factory. This function is used to get a random state generator from a random state.

Parameters#

random_stateNone | int | np.random.RandomState | np.random.Generator, optional: The random state to use for the sampling.

Returns#

random_state_generatornp.random.Generator: The random state generator.

aub_htp.l_alpha_loss(y, y_pred, *, alpha: float)#

class aub_htp.multivariate_alpha_stable_gen(seed=None)#

Bases: multi_rv_generic

Multivariate alpha stable distribution generator.

rvs(alpha: float, spectral_measure_sampler: BaseSpectralMeasureSampler | Literal['standard_isotropic_2d', 'standard_isotropic_3d', '1x2_elliptic_2d', '1x2x4_elliptic_3d', 'coin_flip_discrete'] = 'standard_isotropic_2d', shift: ndarray = 0, size: int | None = None, random_state: None | int | RandomState | Generator = None)#

Sample from a multivariate alpha stable distribution.

Parameters#

alphafloat: The alpha parameter of the alpha stable distribution.
spectral_measure_samplerBaseSpectralMeasureSampler or str: The spectral measure sampler to use.
shiftnp.ndarray: The shift vector to apply to the samples.
sizeint or tuple of ints, optional: Defines the shape of the returned array. Default is 1.
random_stateint or None, optional: Random state to use for the random number generator.

Returns#

samplesndarray: Samples from the multivariate alpha stable distribution.

Raises#

ValueError: If the spectral measure sampler is not supported.

aub_htp.r_alpha_score(y, y_pred, *, alpha: float) → float#

aub_htp.sample_alpha_stable_vector(alpha: float, spectral_measure: BaseSpectralMeasureSampler, number_of_samples: int = 1, shift_vector: ndarray = 0, max_number_of_convergence_terms: int = 50000, error: float = 0.01, random_state: None | int | RandomState | Generator = None)#