# Welcome to LassoNet’s documentation!¶

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## Installation¶

pip install lassonet


## API¶

class lassonet.LassoNetRegressor(*, hidden_dims=(100), lambda_start='auto', lambda_seq=None, gamma=0.0, gamma_skip=0.0, path_multiplier=1.02, M=10, groups=None, dropout=0, batch_size=None, optim=None, n_iters=(1000, 100), patience=(100, 10), tol=0.99, backtrack=False, val_size=None, device=None, verbose=1, random_state=None, torch_seed=None, class_weight=None, tie_approximation=None)

Use LassoNet as regressor

Parameters
• hidden_dims (tuple of int, default=(100,)) – Shape of the hidden layers.

• lambda_start (float, default='auto') – First value on the path. Leave ‘auto’ to estimate it automatically.

• lambda_seq (iterable of float) – If specified, the model will be trained on this sequence of values, until all coefficients are zero. The dense model will always be trained first. Note: lambda_start and path_multiplier will be ignored.

• gamma (float, default=0.0) – l2 penalization on the network

• gamma – l2 penalization on the skip connection

• path_multiplier (float, default=1.02) – Multiplicative factor ($$1 + \epsilon$$) to increase the penalty parameter over the path

• M (float, default=10.0) – Hierarchy parameter.

• groups (None or list of lists) – Use group LassoNet regularization. groups is a list of list such that groups[i] contains the indices of the features in the i-th group.

• dropout (float, default = None) –

• batch_size (int, default=None) – If None, does not use batches. Batches are shuffled at each epoch.

• optim (torch optimizer or tuple of 2 optimizers, default=None) – Optimizer for initial training and path computation. Default is Adam(lr=1e-3), SGD(lr=1e-3, momentum=0.9).

• n_iters (int or pair of int, default=(1000, 100)) – Maximum number of training epochs for initial training and path computation. This is an upper-bound on the effective number of epochs, since the model uses early stopping.

• patience (int or pair of int or None, default=10) – Number of epochs to wait without improvement during early stopping.

• tol (float, default=0.99) – Minimum improvement for early stopping: new objective < tol * old objective.

• backtrack (bool, default=False) – If true, ensures the objective function decreases.

• val_size (float, default=None) – Proportion of data to use for early stopping. 0 means that training data is used. To disable early stopping, set patience=None. Default is 0.1 for all models except Cox for which training data is used. If X_val and y_val are given during training, it will be ignored.

• device (torch device, default=None) – Device on which to train the model using PyTorch. Default: GPU if available else CPU

• verbose (int, default=1) –

• random_state – Random state for validation

• torch_seed – Torch state for model random initialization

• class_weight (iterable of float, default=None) – If specified, weights for different classes in training. There must be one number per class.

• tie_approximation (str) – Tie approximation for the Cox model, must be one of (“breslow”, “efron”).

fit(X, y, *, X_val=None, y_val=None)

Train the model. Note that if lambda_ is not given, the trained model will most likely not use any feature.

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

path(X, y, *, X_val=None, y_val=None, lambda_seq=None, lambda_max=inf, return_state_dicts=True, callback=None)List[lassonet.interfaces.HistoryItem]

Train LassoNet on a lambda_ path. The path is defined by the class parameters: start at lambda_start and increment according to path_multiplier. The path will stop when no feature is being used anymore. callback will be called at each step on (model, history)

score(X, y, sample_weight=None)

Return the coefficient of determination of the prediction.

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
• X (array-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.

• y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.

• sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns

score$$R^2$$ of self.predict(X) wrt. y.

Return type

float

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_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

class lassonet.LassoNetClassifier(*, hidden_dims=(100), lambda_start='auto', lambda_seq=None, gamma=0.0, gamma_skip=0.0, path_multiplier=1.02, M=10, groups=None, dropout=0, batch_size=None, optim=None, n_iters=(1000, 100), patience=(100, 10), tol=0.99, backtrack=False, val_size=None, device=None, verbose=1, random_state=None, torch_seed=None, class_weight=None, tie_approximation=None)

Use LassoNet as classifier

Parameters
• hidden_dims (tuple of int, default=(100,)) – Shape of the hidden layers.

• lambda_start (float, default='auto') – First value on the path. Leave ‘auto’ to estimate it automatically.

• lambda_seq (iterable of float) – If specified, the model will be trained on this sequence of values, until all coefficients are zero. The dense model will always be trained first. Note: lambda_start and path_multiplier will be ignored.

• gamma (float, default=0.0) – l2 penalization on the network

• gamma – l2 penalization on the skip connection

• path_multiplier (float, default=1.02) – Multiplicative factor ($$1 + \epsilon$$) to increase the penalty parameter over the path

• M (float, default=10.0) – Hierarchy parameter.

• groups (None or list of lists) – Use group LassoNet regularization. groups is a list of list such that groups[i] contains the indices of the features in the i-th group.

• dropout (float, default = None) –

• batch_size (int, default=None) – If None, does not use batches. Batches are shuffled at each epoch.

• optim (torch optimizer or tuple of 2 optimizers, default=None) – Optimizer for initial training and path computation. Default is Adam(lr=1e-3), SGD(lr=1e-3, momentum=0.9).

• n_iters (int or pair of int, default=(1000, 100)) – Maximum number of training epochs for initial training and path computation. This is an upper-bound on the effective number of epochs, since the model uses early stopping.

• patience (int or pair of int or None, default=10) – Number of epochs to wait without improvement during early stopping.

• tol (float, default=0.99) – Minimum improvement for early stopping: new objective < tol * old objective.

• backtrack (bool, default=False) – If true, ensures the objective function decreases.

• val_size (float, default=None) – Proportion of data to use for early stopping. 0 means that training data is used. To disable early stopping, set patience=None. Default is 0.1 for all models except Cox for which training data is used. If X_val and y_val are given during training, it will be ignored.

• device (torch device, default=None) – Device on which to train the model using PyTorch. Default: GPU if available else CPU

• verbose (int, default=1) –

• random_state – Random state for validation

• torch_seed – Torch state for model random initialization

• class_weight (iterable of float, default=None) – If specified, weights for different classes in training. There must be one number per class.

• tie_approximation (str) – Tie approximation for the Cox model, must be one of (“breslow”, “efron”).

fit(X, y, *, X_val=None, y_val=None)

Train the model. Note that if lambda_ is not given, the trained model will most likely not use any feature.

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

path(X, y, *, X_val=None, y_val=None, lambda_seq=None, lambda_max=inf, return_state_dicts=True, callback=None)List[lassonet.interfaces.HistoryItem]

Train LassoNet on a lambda_ path. The path is defined by the class parameters: start at lambda_start and increment according to path_multiplier. The path will stop when no feature is being used anymore. callback will be called at each step on (model, history)

score(X, y, sample_weight=None)

Return the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters
• X (array-like of shape (n_samples, n_features)) – Test samples.

• y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True labels for X.

• sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns

score – Mean accuracy of self.predict(X) wrt. y.

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

class lassonet.LassoNetCoxRegressor(*, hidden_dims=(100), lambda_start='auto', lambda_seq=None, gamma=0.0, gamma_skip=0.0, path_multiplier=1.02, M=10, groups=None, dropout=0, batch_size=None, optim=None, n_iters=(1000, 100), patience=(100, 10), tol=0.99, backtrack=False, val_size=None, device=None, verbose=1, random_state=None, torch_seed=None, class_weight=None, tie_approximation=None)

Use LassoNet for Cox regression

Parameters
• hidden_dims (tuple of int, default=(100,)) – Shape of the hidden layers.

• lambda_start (float, default='auto') – First value on the path. Leave ‘auto’ to estimate it automatically.

• lambda_seq (iterable of float) – If specified, the model will be trained on this sequence of values, until all coefficients are zero. The dense model will always be trained first. Note: lambda_start and path_multiplier will be ignored.

• gamma (float, default=0.0) – l2 penalization on the network

• gamma – l2 penalization on the skip connection

• path_multiplier (float, default=1.02) – Multiplicative factor ($$1 + \epsilon$$) to increase the penalty parameter over the path

• M (float, default=10.0) – Hierarchy parameter.

• groups (None or list of lists) – Use group LassoNet regularization. groups is a list of list such that groups[i] contains the indices of the features in the i-th group.

• dropout (float, default = None) –

• batch_size (int, default=None) – If None, does not use batches. Batches are shuffled at each epoch.

• optim (torch optimizer or tuple of 2 optimizers, default=None) – Optimizer for initial training and path computation. Default is Adam(lr=1e-3), SGD(lr=1e-3, momentum=0.9).

• n_iters (int or pair of int, default=(1000, 100)) – Maximum number of training epochs for initial training and path computation. This is an upper-bound on the effective number of epochs, since the model uses early stopping.

• patience (int or pair of int or None, default=10) – Number of epochs to wait without improvement during early stopping.

• tol (float, default=0.99) – Minimum improvement for early stopping: new objective < tol * old objective.

• backtrack (bool, default=False) – If true, ensures the objective function decreases.

• val_size (float, default=None) – Proportion of data to use for early stopping. 0 means that training data is used. To disable early stopping, set patience=None. Default is 0.1 for all models except Cox for which training data is used. If X_val and y_val are given during training, it will be ignored.

• device (torch device, default=None) – Device on which to train the model using PyTorch. Default: GPU if available else CPU

• verbose (int, default=1) –

• random_state – Random state for validation

• torch_seed – Torch state for model random initialization

• class_weight (iterable of float, default=None) – If specified, weights for different classes in training. There must be one number per class.

• tie_approximation (str) – Tie approximation for the Cox model, must be one of (“breslow”, “efron”).

fit(X, y, *, X_val=None, y_val=None)

Train the model. Note that if lambda_ is not given, the trained model will most likely not use any feature.

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

path(X, y, *, X_val=None, y_val=None, lambda_seq=None, lambda_max=inf, return_state_dicts=True, callback=None)List[lassonet.interfaces.HistoryItem]

Train LassoNet on a lambda_ path. The path is defined by the class parameters: start at lambda_start and increment according to path_multiplier. The path will stop when no feature is being used anymore. callback will be called at each step on (model, history)

score(X_test, y_test)

Concordance index

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

class lassonet.LassoNetRegressorCV(cv=None, **kwargs)

See BaseLassoNet for the parameters

cvint, cross-validation generator or iterable, default=None

Determines the cross-validation splitting strategy. Default is 5-fold cross-validation. See <https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.check_cv.html>

fit(X, y)

Train the model. Note that if lambda_ is not given, the trained model will most likely not use any feature.

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

path(X, y, *, return_state_dicts=True)

Train LassoNet on a lambda_ path. The path is defined by the class parameters: start at lambda_start and increment according to path_multiplier. The path will stop when no feature is being used anymore. callback will be called at each step on (model, history)

score(X, y, sample_weight=None)

Return the coefficient of determination of the prediction.

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
• X (array-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.

• y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.

• sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns

score$$R^2$$ of self.predict(X) wrt. y.

Return type

float

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_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

class lassonet.LassoNetClassifierCV(cv=None, **kwargs)

See BaseLassoNet for the parameters

cvint, cross-validation generator or iterable, default=None

Determines the cross-validation splitting strategy. Default is 5-fold cross-validation. See <https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.check_cv.html>

fit(X, y)

Train the model. Note that if lambda_ is not given, the trained model will most likely not use any feature.

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

path(X, y, *, return_state_dicts=True)

Train LassoNet on a lambda_ path. The path is defined by the class parameters: start at lambda_start and increment according to path_multiplier. The path will stop when no feature is being used anymore. callback will be called at each step on (model, history)

score(X, y, sample_weight=None)

Return the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters
• X (array-like of shape (n_samples, n_features)) – Test samples.

• y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True labels for X.

• sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns

score – Mean accuracy of self.predict(X) wrt. y.

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

class lassonet.LassoNetCoxRegressorCV(cv=None, **kwargs)

See BaseLassoNet for the parameters

cvint, cross-validation generator or iterable, default=None

Determines the cross-validation splitting strategy. Default is 5-fold cross-validation. See <https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.check_cv.html>

fit(X, y)

Train the model. Note that if lambda_ is not given, the trained model will most likely not use any feature.

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

path(X, y, *, return_state_dicts=True)

Train LassoNet on a lambda_ path. The path is defined by the class parameters: start at lambda_start and increment according to path_multiplier. The path will stop when no feature is being used anymore. callback will be called at each step on (model, history)

score(X_test, y_test)

Concordance index

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

lassonet.plot_path(model, path, X_test, y_test, *, score_function=None)

Plot the evolution of the model on the path, namely: - lambda - number of selected variables - score

Parameters
• model (LassoNetClassifier or LassoNetRegressor) –

• path – output of model.path

• X_test (array-like) –

• y_test (array-like) –

• score_function (function or None) – if None, use score_function=model.score score_function must take as input X_test, y_test

lassonet.lassonet_path(X, y, task, *, X_val=None, y_val=None, **kwargs)
Parameters
• X (array-like of shape (n_samples, n_features)) – Training data

• y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – Target values