# LinearRegression ### *class* cuml.linear_model.LinearRegression(, algorithm='auto', fit_intercept=True, copy_X=True, verbose=False, output_type=None) Ordinary least squares Linear Regression. * **Parameters:** **algorithm** : The algorithm to use when fitting: - ‘auto’: will select ‘eig’ if supported, falling back to ‘lsmr’ if X is sparse, and ‘svd’ otherwise. - ‘eig’: uses an eigendecomposition of the covariance matrix. It is faster than SVD, but potentially unstable. It doesn’t support multi-target `y` or sparse `X`. - ‘svd’ or ‘svd-jacobi’: uses an SVD decomposition. It’s slower, but stable. It doesn’t support sparse `X`. - ‘lsmr’: uses `cupyx.scipy.sparse.linalg.lsmr`, an iterative algorithm. It supports all input types and is typically very fast. - ‘qr’: uses QR decomposition and solves `Rx = Q^T y`. It’s faster than SVD, but doesn’t support multi-target `y` or sparse `X`. - ‘svd-qr’: computes SVD decomposition using QR algorithm. It’s the slowest option. It doesn’t support multi-target `y` or sparse `X`. **fit_intercept** : If True, LinearRegression tries to correct for the global mean of y. If False, the model expects that you have centered the data. **copy_X** : If True, X will never be mutated. Setting to False may reduce memory usage, at the cost of potentially mutating X. **verbose** : Sets logging level. It must be one of `cuml.common.logger.level_*`. See [Verbosity Levels](../../cuml/index.html.md#verbosity-levels) for more info. **output_type** : Return results and set estimator attributes to the indicated output type. If None, the output type set at the module level (`cuml.global_settings.output_type`) will be used. See [Output Data Type Configuration](../../cuml/index.html.md#output-data-type-configuration) for more info. * **Attributes:** **coef_** : The estimated coefficients for the linear regression model. **intercept_** : The independent term. If `fit_intercept` is False, will be 0. Will be an array when fit on multi-target y, otherwise will be a float. ### Methods | [`fit`](#cuml.linear_model.LinearRegression.fit)(self, X, y[, sample_weight]) | Fit the model with X and y. | |-------------------------------------------------------------------------------------|-------------------------------| ### Notes LinearRegression suffers from multicollinearity (when columns are correlated with each other), and variance explosions from outliers. Consider using [`Ridge`](../cuml.linear_model.Ridge/index.html.md#cuml.linear_model.Ridge) to fix the multicollinearity problem, and consider maybe first `DBSCAN` to remove the outliers, or statistical analysis to filter possible outliers. **Applications of LinearRegression** > LinearRegression is used in regression tasks where one wants to predict > say sales or house prices. It is also used in extrapolation or time > series tasks, dynamic systems modelling and many other machine learning > tasks. This model should be first tried if the machine learning problem > is a regression task (predicting a continuous variable). For additional information, see scikit-learn’s documentation for [`sklearn.linear_model.LinearRegression`](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression). For an additional example see [the OLS notebook](https://github.com/NVIDIA/cuml/blob/main/notebooks/linear_regression_demo.ipynb). ### Examples ```pycon >>> import cupy as cp >>> from cuml.linear_model import LinearRegression >>> X = cp.array([[1, 1], [1, 2], [2, 2], [2, 3]], dtype=cp.float32) >>> y = cp.array([6.0, 8.0, 9.0, 11.0], dtype=cp.float32) >>> model = LinearRegression().fit(X, y) ``` ```pycon >>> X_test = cp.array([[3, 5], [2, 5]], dtype=cp.float32) >>> model.predict(X_test) array([16. , 14.999999], dtype=float32) ``` #### as_sklearn()[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/internals/interop.py#L206) Convert this estimator into an equivalent scikit-learn (or scikit-learn extension) estimator. * **Returns:** sklearn.base.BaseEstimator : A scikit-learn compatible estimator instance that mirrors the trained state of the current estimator. #### fit(self, X, y, sample_weight=None) → 'LinearRegression'[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/linear_model/linear_regression.pyx#L315) Fit the model with X and y. * **Parameters:** **X** : Dense matrix with dtype float32 or float64. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series. **y** : Dense matrix with dtype float32 or float64. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series. **sample_weight** : The weights for each observation in X. If None, all observations are assigned equal weight. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series. #### *classmethod* from_sklearn(model)[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/internals/interop.py#L222) Create a cuml estimator from a scikit-learn estimator. * **Parameters:** **model** : A compatible scikit-learn (or scikit-learn extension) estimator. * **Returns:** cls : A new instance of this cuml estimator class that mirrors the state of the input estimator. ### Notes `output_type` of the estimator is set to “numpy” by default, as these cannot be inferred from training arguments. If something different is required, then please use cuml’s output_type configuration utilities. #### get_params(deep=True)[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/internals/base.py#L191) Returns a dict of all params owned by this class. If the child class has appropriately overridden the `_get_param_names` method and does not need anything other than what is there in this method, then it doesn’t have to override this method #### predict(X)[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/linear_model/base.py#L14) Predicts `y` values for `X`. * **Parameters:** **X** : Dense matrix with dtype float32 or float64. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series. * **Returns:** **preds** : Predicted values
For more information on how to configure cuML’s output type, refer to: [Output Data Type Configuration](../../cuml/index.html.md#output-data-type-configuration). #### score(X, y, sample_weight=None, \*\*kwargs)[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/internals/mixins.py#L66) Scoring function for regression estimators Returns the coefficient of determination R^2 of the prediction. * **Parameters:** **X** : Dense matrix with dtype float32 or float64. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series. **y** : Dense matrix with dtype float32 or float64. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series. **sample_weight** : The weights for each observation in X. If None, all observations are assigned equal weight. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series. * **Returns:** **score** : R^2 of self.predict(X) wrt. y. #### set_params(\*\*params)[[source]](https://github.com/NVIDIA/cuml/blob/93418baf5/python/cuml/cuml/internals/base.py#L200) Accepts a dict of params and updates the corresponding ones owned by this class. If the child class has appropriately overridden the `_get_param_names` method and does not need anything other than what is, there in this method, then it doesn’t have to override this method