Stochastic Models

class cca_zoo.models._stochastic.IncrementalPLS(latent_dims: int = 1, scale: bool = True, centre=True, copy_data=True, random_state=None, accept_sparse=None, batch_size=1, shuffle=True, sampler=None, batch_sampler=None, num_workers=0, pin_memory=False, drop_last=True, timeout=0, worker_init_fn=None, epochs=1, simple=False)

Bases: _BaseStochastic

A class used to fit Incremental PLS

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• simple (bool, optional) – Whether to use the simple update, by default False

References

Arora, Raman, et al. “Stochastic optimization for PCA and PLS.” 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2012.

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

class cca_zoo.models._stochastic.PLSStochasticPower(latent_dims: int = 1, scale: bool = True, centre=True, copy_data=True, random_state=None, accept_sparse=None, batch_size=1, shuffle=True, sampler=None, batch_sampler=None, num_workers=0, pin_memory=False, drop_last=True, timeout=0, worker_init_fn=None, epochs=1, learning_rate=0.01)

Bases: _BaseStochastic

A class used to fit Stochastic PLS

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• learning_rate (float, optional) – Learning rate to use, by default 0.01

References

Arora, Raman, et al. “Stochastic optimization for PCA and PLS.” 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2012.

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

class cca_zoo.models._stochastic.PLSGHAGEP(*args, **kwargs)

Bases: RCCAGHAGEP

A class used to fit PLS by GHA-GEP

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• learning_rate (float, optional) – Learning rate to use, by default 0.01

References

Chapman, James, Ana Lawry Aguila, and Lennie Wells. “A Generalized EigenGame with Extensions to Multiview Representation Learning.” arXiv preprint arXiv:2211.11323 (2022).

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

class cca_zoo.models._stochastic.CCAGHAGEP(*args, **kwargs)

Bases: RCCAGHAGEP

A class used to fit CCA by GHA-GEP

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• learning_rate (float, optional) – Learning rate to use, by default 0.01

References

Chapman, James, Ana Lawry Aguila, and Lennie Wells. “A Generalized EigenGame with Extensions to Multiview Representation Learning.” arXiv preprint arXiv:2211.11323 (2022).

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

class cca_zoo.models._stochastic.RCCAGHAGEP(latent_dims: int = 1, scale: bool = True, centre=True, copy_data=True, random_state=None, accept_sparse=None, batch_size=1, shuffle=True, sampler=None, batch_sampler=None, num_workers=0, pin_memory=False, drop_last=True, timeout=0, worker_init_fn=None, epochs=1, learning_rate=0.01, c=0, **kwargs)

Bases: _BaseStochastic

A class used to fit Regularized CCA by GHA-GEP

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• learning_rate (float, optional) – Learning rate to use, by default 0.01

• c (float, optional) – Regularization parameter, by default 0

References

Chapman, James, Ana Lawry Aguila, and Lennie Wells. “A Generalized EigenGame with Extensions to Multiview Representation Learning.” arXiv preprint arXiv:2211.11323 (2022).

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

class cca_zoo.models._stochastic.PLSEigenGame(*args, **kwargs)

Bases: RCCAEigenGame

A class used to fit PLS by Delta-EigenGame

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• learning_rate (float, optional) – Learning rate to use, by default 0.01

References

Chapman, James, Ana Lawry Aguila, and Lennie Wells. “A Generalized EigenGame with Extensions to Multiview Representation Learning.” arXiv preprint arXiv:2211.11323 (2022).

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

class cca_zoo.models._stochastic.CCAEigenGame(*args, **kwargs)

Bases: RCCAEigenGame

A class used to fit CCA by Delta-EigenGame

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• learning_rate (float, optional) – Learning rate to use, by default 0.01

References

Chapman, James, Ana Lawry Aguila, and Lennie Wells. “A Generalized EigenGame with Extensions to Multiview Representation Learning.” arXiv preprint arXiv:2211.11323 (2022).

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

class cca_zoo.models._stochastic.RCCAEigenGame(latent_dims: int = 1, scale: bool = True, centre=True, copy_data=True, random_state=None, accept_sparse=None, batch_size=1, shuffle=True, sampler=None, batch_sampler=None, num_workers=0, pin_memory=False, drop_last=True, timeout=0, worker_init_fn=None, epochs=1, learning_rate=0.01, c=0, **kwargs)

Bases: _BaseStochastic

A class used to fit Regularized CCA by Delta-EigenGame

Parameters

• latent_dims (int, optional) – Number of latent dimensions to use, by default 1

• scale (bool, optional) – Whether to scale the data, by default True

• centre (bool, optional) – Whether to centre the data, by default True

• copy_data (bool, optional) – Whether to copy the data, by default True

• random_state (int, optional) – Random state to use, by default None

• accept_sparse (bool, optional) – Whether to accept sparse data, by default None

• batch_size (int, optional) – Batch size to use, by default 1

• shuffle (bool, optional) – Whether to shuffle the data, by default True

• sampler (torch.utils.data.Sampler, optional) – Sampler to use, by default None

• batch_sampler (torch.utils.data.Sampler, optional) – Batch sampler to use, by default None

• num_workers (int, optional) – Number of workers to use, by default 0

• pin_memory (bool, optional) – Whether to pin memory, by default False

• drop_last (bool, optional) – Whether to drop the last batch, by default True

• timeout (int, optional) – Timeout to use, by default 0

• worker_init_fn (function, optional) – Worker init function to use, by default None

• epochs (int, optional) – Number of epochs to use, by default 1

• learning_rate (float, optional) – Learning rate to use, by default 0.01

• c (float, optional) – Regularization parameter, by default 0

References

Chapman, James, Ana Lawry Aguila, and Lennie Wells. “A Generalized EigenGame with Extensions to Multiview Representation Learning.” arXiv preprint arXiv:2211.11323 (2022).

Parameters

• latent_dims (int, optional) – Number of latent dimensions to fit. Default is 1.

• scale (bool, optional) – Whether to scale the data to unit variance. Default is True.

• centre (bool, optional) – Whether to centre the data. Default is True.

• copy_data (bool, optional) – Whether to copy the data. Default is True.

• accept_sparse (bool, optional) – Whether to accept sparse data. Default is False.

• random_state (int, RandomState instance or None, optional (default=None)) – Pass an int for reproducible output across multiple function calls.

fit(views: Iterable[ndarray], y=None, **kwargs)

Fits the model to the given data

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

self

Return type

object

fit_transform(views: Iterable[ndarray], **kwargs)

Fits the model to the given data and returns the transformed views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays

get_factor_loadings(views: Iterable[ndarray], normalize=True, **kwargs)

Returns the factor loadings for each view

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• normalize (bool, optional) – Whether to normalize the factor loadings. Default is True.

• kwargs (any additional keyword arguments required by the given model) –

Returns

factor_loadings

Return type

list of numpy arrays

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

pairwise_correlations(views: Iterable[ndarray], **kwargs)

Returns the pairwise correlations between the views in each dimension

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

pairwise_correlations

Return type

numpy array of shape (n_views, n_views, latent_dims)

score(views: Iterable[ndarray], y=None, **kwargs)

Returns the average pairwise correlation between the views

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• y (None) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

score

Return type

float

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(views: Iterable[ndarray], **kwargs)

Parameters

• views (list/tuple of numpy arrays or array likes with the same number of rows (samples)) –

• kwargs (any additional keyword arguments required by the given model) –

Returns

transformed_views

Return type

list of numpy arrays