DOC Added example comparing L1-based models to ARD user guide (scikit-learn#31425)

Author: supersom

doc/modules/linear_model.rst

@@ -837,13 +837,11 @@ prior over all :math:`\lambda_i` is chosen to be the same gamma distribution
 given by the hyperparameters :math:`\lambda_1` and :math:`\lambda_2`.
 
 ARD is also known in the literature as *Sparse Bayesian Learning* and *Relevance
-Vector Machine* [3]_ [4]_. For a worked-out comparison between ARD and `Bayesian
-Ridge Regression`_, see the example below.
+Vector Machine* [3]_ [4]_.
 
-.. rubric:: Examples
-
-* :ref:`sphx_glr_auto_examples_linear_model_plot_ard.py`
+See :ref:`sphx_glr_auto_examples_linear_model_plot_ard.py` for a worked-out comparison between ARD and `Bayesian Ridge Regression`_.
 
+See :ref:`sphx_glr_auto_examples_linear_model_plot_lasso_and_elasticnet.py` for a comparison between various methods - Lasso, ARD and ElasticNet - on correlated data.
 
 .. rubric:: References
 

sklearn/linear_model/_bayes.py

@@ -568,11 +568,6 @@ class ARDRegression(RegressorMixin, LinearModel):
     --------
     BayesianRidge : Bayesian ridge regression.
 
-    Notes
-    -----
-    For an example, see :ref:`examples/linear_model/plot_ard.py
-    <sphx_glr_auto_examples_linear_model_plot_ard.py>`.
-
     References
     ----------
     D. J. C. MacKay, Bayesian nonlinear modeling for the prediction
@@ -594,6 +589,12 @@ class ARDRegression(RegressorMixin, LinearModel):
     ARDRegression()
     >>> clf.predict([[1, 1]])
     array([1.])
+
+    -   :ref:`sphx_glr_auto_examples_linear_model_plot_ard.py` demonstrates ARD
+        Regression.
+    -   :ref:`sphx_glr_auto_examples_linear_model_plot_lasso_and_elasticnet.py`
+        showcases ARD Regression alongside Lasso and Elastic-Net for sparse,
+        correlated signals, in the presence of noise.
     """
 
     _parameter_constraints: dict = {

sklearn/linear_model/_coordinate_descent.py

@@ -875,6 +875,10 @@ class ElasticNet(MultiOutputMixin, RegressorMixin, LinearModel):
     1.451
     >>> print(regr.predict([[0, 0]]))
     [1.451]
+
+    -   :ref:`sphx_glr_auto_examples_linear_model_plot_lasso_and_elasticnet.py`
+        showcases ElasticNet alongside Lasso and ARD Regression for sparse
+        signal recovery in the presence of noise and feature correlation.
     """
 
     # "check_input" is used for optimisation and isn't something to be passed
@@ -1304,6 +1308,11 @@ class Lasso(ElasticNet):
     [0.85 0.  ]
     >>> print(clf.intercept_)
     0.15
+
+    -   :ref:`sphx_glr_auto_examples_linear_model_plot_lasso_and_elasticnet.py`
+        compares Lasso with other L1-based regression models (ElasticNet and ARD
+        Regression) for sparse signal recovery in the presence of noise and
+        feature correlation.
     """
 
     _parameter_constraints: dict = {