Linear Regression

class snapml.LinearRegression(max_iter=1000, regularizer=1.0, device_ids=[], verbose=False, use_gpu=False, dual=True, n_jobs=1, penalty='l2', tol=0.001, generate_training_history=None, privacy=False, eta=0.3, batch_size=100, privacy_epsilon=10, grad_clip=1, fit_intercept=False, intercept_scaling=1.0, normalize=False, kernel='linear', gamma=1.0, n_components=100, random_state=None)

Linear Regression

This class implements regularized linear regression using the IBM Snap ML solver. It supports both local and distributed(MPI) methods of the snap ML solver. It handles both dense and sparse matrix inputs. Use csr, csc, ndarray, deviceNDArray or SnapML data partition format for training and csr, ndarray or SnapML data partition format for prediction. DeviceNDArray input data format is currently not supported for training with MPI implementation.

Parameters:

max_iterint, default=1000: Maximum number of iterations used by the solver to converge.
regularizerfloat, default=1.0: Regularization strength. It must be a positive float. Larger regularization values imply stronger regularization.
use_gpubool, default=False: Flag for indicating the hardware platform used for training. If True, the training is performed using the GPU. If False, the training is performed using the CPU.
device_idsarray-like of int, default=[]: If use_gpu is True, it indicates the IDs of the GPUs used for training. For single GPU training, set device_ids to the GPU ID to be used for training, e.g., [0]. For multi-GPU training, set device_ids to a list of GPU IDs to be used for training, e.g., [0, 1].
dualbool, default=True: Dual or primal formulation. Recommendation: if n_samples > n_features use dual=True.
verbosebool, default=False: If True, it prints the training cost, one per iteration. Warning: this will increase the training time. For performance evaluation, use verbose=False.
n_jobsint, default=1: The number of threads used for running the training. The value of this parameter should be a multiple of 32 if the training is performed on GPU (use_gpu=True).
penalty{‘l1’, ‘l2’}, default=’l2’: The regularization / penalty type. Possible values are “l2” for L2 regularization (RidgeRegression) or “l1” for L1 regularization (LassoRegression). L1 regularization is possible only for the primal optimization problem (dual=False).
tolfloat, default=0.001: The tolerance parameter. Training will finish when maximum change in model coefficients is less than tol.
generate_training_history{‘summary’, ‘full’, None}, default=None: Determines the level of summary statistics that are generated during training. By default no information is generated (None), but this parameter can be set to “summary”, to obtain summary statistics at the end of training, or “full” to obtain a complete set of statistics for the entire training procedure. Note, enabling either option will result in slower training. generate_training_history is not supported for DeviceNDArray input format.
privacybool, default=False: Train the model using a differentially private algorithm. Currently not supported for MPI implementation.
etafloat, default=0.3: Learning rate for the differentially private training algorithm. Currently not supported for MPI implementation.
batch_sizeint, default=100: Mini-batch size for the differentially private training algorithm. Currently not supported for MPI implementation.
privacy_epsilonfloat, default=10.0: Target privacy gaurantee. Learned model will be (privacy_epsilon, 0.01)-private. Currently not supported for MPI implementation.
grad_clipfloat, default=1.0: Gradient clipping parameter for the differentially private training algorithm. Currently not supported for MPI implementation.
fit_interceptbool, default=False: Add bias term – note, may affect speed of convergence, especially for sparse datasets.
intercept_scalingfloat, default=1.0: Scaling of bias term. The inclusion of a bias term is implemented by appending an additional feature to the dataset. This feature has a constant value, that can be set using this parameter.
normalizebool, default=False: Normalize rows of dataset (recommended for fast convergence).
kernel{‘rbf’, ‘linear’}, default=’linear’: Approximate feature map of a specified kernel function.
gammafloat, default=1.0: Parameter of RBF kernel: exp(-gamma * x^2)
n_componentsint, default=100: Dimensionality of the feature space when approximating a kernel function.
random_stateint, or None, default=None: If int, random_state is the seed used by the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes:

coef_array-like, shape (n_features,): Coefficients of the features in the trained model.
intercept_float: Independent term in the decision function. Set to 0.0 if fit_intercept == False.
support_array-like: Indices of the features that lie in the support ond contribute to the decision. (only available for L1). Currently not supported for MPI implementation.
model_sparsity_float: fraction of non-zeros in the model parameters. (only available for L1). Currently not supported for MPI implementation.
training_history_dict: Training history statistics.

fit(X_train, y_train=None)

Fit the model according to the given train dataset.

Parameters:

X_trainTrain dataset. Supports the following input data-types :

Sparse matrix (csr_matrix, csc_matrix) or dense matrix (ndarray)
DeviceNDArray. Not supported for MPI execution.
SnapML data partition of type DensePartition, SparsePartition or ConstantValueSparsePartition

y_trainThe target corresponding to X_train.

If X_train is sparse matrix or dense matrix, y_train should be array-like of shape = (n_samples,) In case of deviceNDArray, y_train should be array-like of shape = (n_samples, 1) If X_train is SnapML data partition type, then y_train is not required (i.e. None).

Returns:

selfobject

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

predict(X, n_jobs=None)

Class predictions

The returned class estimates.

Parameters:

XDataset used for predicting estimates or class. Supports the following input data-types :

Sparse matrix (csr_matrix, csc_matrix) or dense matrix (ndarray)
SnapML data partition of type DensePartition, SparsePartition or ConstantValueSparsePartition

n_jobsint, default=None

Number of threads used to run inference. By default the value of the class attribute is used.. This parameter is ignored for predict of a single observation.

Returns:

pred: array-like, shape = (n_samples,): Returns the predicted estimate/class of the sample.

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:

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_fit_request(*, X_train: bool | None | str = '$UNCHANGED$', y_train: bool | None | str = '$UNCHANGED$') → LinearRegression

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit 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 fit.
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.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

X_trainstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for X_train parameter in fit.
y_trainstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for y_train parameter in fit.

Returns:

selfobject: The updated object.

set_params(**params)

Set the parameters of this model.

Valid parameter keys can be listed with get_params().

Returns:

self

set_predict_request(*, n_jobs: bool | None | str = '$UNCHANGED$') → LinearRegression

Request metadata passed to the predict method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to predict 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 predict.
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.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

n_jobsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for n_jobs parameter in predict.

Returns:

selfobject: The updated object.

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

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see 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.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

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.