.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/linear_model/plot_elastic_net_precomputed_gram_matrix_with_weighted_samples.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_linear_model_plot_elastic_net_precomputed_gram_matrix_with_weighted_samples.py: ========================================================================== Fitting an Elastic Net with a precomputed Gram Matrix and Weighted Samples ========================================================================== The following example shows how to precompute the gram matrix while using weighted samples with an ElasticNet. If weighted samples are used, the design matrix must be centered and then rescaled by the square root of the weight vector before the gram matrix is computed. .. note:: `sample_weight` vector is also rescaled to sum to `n_samples`, see the documentation for the `sample_weight` parameter to :func:`linear_model.ElasticNet.fit`. .. GENERATED FROM PYTHON SOURCE LINES 21-22 Let's start by loading the dataset and creating some sample weights. .. GENERATED FROM PYTHON SOURCE LINES 22-34 .. code-block:: default import numpy as np from sklearn.datasets import make_regression rng = np.random.RandomState(0) n_samples = int(1e5) X, y = make_regression(n_samples=n_samples, noise=0.5, random_state=rng) sample_weight = rng.lognormal(size=n_samples) # normalize the sample weights normalized_weights = sample_weight * (n_samples / (sample_weight.sum())) .. GENERATED FROM PYTHON SOURCE LINES 35-38 To fit the elastic net using the `precompute` option together with the sample weights, we must first center the design matrix, and rescale it by the normalized weights prior to computing the gram matrix. .. GENERATED FROM PYTHON SOURCE LINES 38-43 .. code-block:: default X_offset = np.average(X, axis=0, weights=normalized_weights) X_centered = X - np.average(X, axis=0, weights=normalized_weights) X_scaled = X_centered * np.sqrt(normalized_weights)[:, np.newaxis] gram = np.dot(X_scaled.T, X_scaled) .. GENERATED FROM PYTHON SOURCE LINES 44-48 We can now proceed with fitting. We must passed the centered design matrix to `fit` otherwise the elastic net estimator will detect that it is uncentered and discard the gram matrix we passed. However, if we pass the scaled design matrix, the preprocessing code will incorrectly rescale it a second time. .. GENERATED FROM PYTHON SOURCE LINES 48-52 .. code-block:: default from sklearn.linear_model import ElasticNet lm = ElasticNet(alpha=0.01, precompute=gram) lm.fit(X_centered, y, sample_weight=normalized_weights) .. raw:: html
```ElasticNet(alpha=0.01,
precompute=array([[ 9.98809919e+04, -4.48938813e+02, -1.03237920e+03, ...,
-2.25349312e+02, -3.53959628e+02, -1.67451144e+02],
[-4.48938813e+02,  1.00768662e+05,  1.19112072e+02, ...,
-1.07963978e+03,  7.47987268e+01, -5.76195467e+02],
[-1.03237920e+03,  1.19112072e+02,  1.00393284e+05, ...,
-3.07582983e+02,  6.66670169e+02,  2.65799352e+02],
...,
[-2.25349312e+02, -1.07963978e+03, -3.07582983e+02, ...,
9.99891212e+04, -4.58195950e+02, -1.58667835e+02],
[-3.53959628e+02,  7.47987268e+01,  6.66670169e+02, ...,
-4.58195950e+02,  9.98350372e+04,  5.60836363e+02],
[-1.67451144e+02, -5.76195467e+02,  2.65799352e+02, ...,
-1.58667835e+02,  5.60836363e+02,  1.00911944e+05]]))```
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.