scikit-learn
diff --git a/‎doc/whats_new/v0.23.rst
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diff --git a/‎sklearn/linear_model/_least_angle.py
Lines changed: 34 additions & 2 deletions b/‎sklearn/linear_model/_least_angle.py
Lines changed: 34 additions & 2 deletions
diff --git a/‎sklearn/linear_model/tests/test_least_angle.py
Lines changed: 24 additions & 0 deletions b/‎sklearn/linear_model/tests/test_least_angle.py
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@@ -298,6 +298,11 @@ Changelog
   of strictly inferior for maximum of `absgrad` and `tol` in `utils.optimize._newton_cg`.
   :pr:`16266` by :user:`Rushabh Vasani <rushabh-v>`.
 
+- |Enhancement| :class:`linear_model.LassoLars` and
+  :class:`linear_model.Lars` now support a `jitter` parameter that adds
+  random noise to the target. This might help with stability in some edge
+  cases. :pr:`15179` by :user:`angelaambroz`.
+
 :mod:`sklearn.metrics`
 ......................
 
 
@@ -21,6 +21,7 @@
 from ..base import RegressorMixin, MultiOutputMixin
 # mypy error: Module 'sklearn.utils' has no attribute 'arrayfuncs'
 from ..utils import arrayfuncs, as_float_array  # type: ignore
+from ..utils import check_random_state
 from ..model_selection import check_cv
 from ..exceptions import ConvergenceWarning
 
@@ -800,6 +801,16 @@ class Lars(MultiOutputMixin, RegressorMixin, LinearModel):
         setting ``fit_path`` to ``False`` will lead to a speedup, especially
         with a small alpha.
 
+    jitter : float, default=None
+        Upper bound on a uniform noise parameter to be added to the
+        `y` values, to satisfy the model's assumption of
+        one-at-a-time computations. Might help with stability.
+
+    random_state : int, RandomState instance or None (default)
+        Determines random number generation for jittering. Pass an int
+        for reproducible output across multiple function calls.
+        See :term:`Glossary <random_state>`. Ignored if `jitter` is None.
+
     Attributes
     ----------
     alphas_ : array-like of shape (n_alphas + 1,) | list of n_targets such \
@@ -846,7 +857,8 @@ class Lars(MultiOutputMixin, RegressorMixin, LinearModel):
 
     def __init__(self, fit_intercept=True, verbose=False, normalize=True,
                  precompute='auto', n_nonzero_coefs=500,
-                 eps=np.finfo(np.float).eps, copy_X=True, fit_path=True):
+                 eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,
+                 jitter=None, random_state=None):
         self.fit_intercept = fit_intercept
         self.verbose = verbose
         self.normalize = normalize
@@ -855,6 +867,8 @@ def __init__(self, fit_intercept=True, verbose=False, normalize=True,
         self.eps = eps
         self.copy_X = copy_X
         self.fit_path = fit_path
+        self.jitter = jitter
+        self.random_state = random_state
 
     @staticmethod
     def _get_gram(precompute, X, y):
@@ -954,6 +968,12 @@ def fit(self, X, y, Xy=None):
         else:
             max_iter = self.max_iter
 
+        if self.jitter is not None:
+            rng = check_random_state(self.random_state)
+
+            noise = rng.uniform(high=self.jitter, size=len(y))
+            y = y + noise
+
         self._fit(X, y, max_iter=max_iter, alpha=alpha, fit_path=self.fit_path,
                   Xy=Xy)
 
@@ -1031,6 +1051,16 @@ class LassoLars(Lars):
         algorithm are typically in congruence with the solution of the
         coordinate descent Lasso estimator.
 
+    jitter : float, default=None
+        Upper bound on a uniform noise parameter to be added to the
+        `y` values, to satisfy the model's assumption of
+        one-at-a-time computations. Might help with stability.
+
+    random_state : int, RandomState instance or None (default)
+        Determines random number generation for jittering. Pass an int
+        for reproducible output across multiple function calls.
+        See :term:`Glossary <random_state>`. Ignored if `jitter` is None.
+
     Attributes
     ----------
     alphas_ : array-like of shape (n_alphas + 1,) | list of n_targets such \
@@ -1083,7 +1113,7 @@ class LassoLars(Lars):
     def __init__(self, alpha=1.0, fit_intercept=True, verbose=False,
                  normalize=True, precompute='auto', max_iter=500,
                  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,
-                 positive=False):
+                 positive=False, jitter=None, random_state=None):
         self.alpha = alpha
         self.fit_intercept = fit_intercept
         self.max_iter = max_iter
@@ -1094,6 +1124,8 @@ def __init__(self, alpha=1.0, fit_intercept=True, verbose=False,
         self.copy_X = copy_X
         self.eps = eps
         self.fit_path = fit_path
+        self.jitter = jitter
+        self.random_state = random_state
 
 
 ###############################################################################
 
@@ -6,6 +6,7 @@
 import pytest
 from scipy import linalg
 
+from sklearn.base import clone
 from sklearn.model_selection import train_test_split
 from sklearn.utils._testing import assert_allclose
 from sklearn.utils._testing import assert_array_almost_equal
@@ -17,6 +18,7 @@
 from sklearn import linear_model, datasets
 from sklearn.linear_model._least_angle import _lars_path_residues
 from sklearn.linear_model import LassoLarsIC, lars_path
+from sklearn.linear_model import Lars, LassoLars
 
 # TODO: use another dataset that has multiple drops
 diabetes = datasets.load_diabetes()
@@ -733,6 +735,28 @@ def test_lasso_lars_fit_copyX_behaviour(copy_X):
     assert copy_X == np.array_equal(X, X_copy)
 
 
+@pytest.mark.parametrize('est', (LassoLars(alpha=1e-3), Lars()))
+def test_lars_with_jitter(est):
+    # Test that a small amount of jitter helps stability,
+    # using example provided in issue #2746
+
+    X = np.array([[0.0, 0.0, 0.0, -1.0, 0.0],
+                  [0.0, -1.0, 0.0, 0.0, 0.0]])
+    y = [-2.5, -2.5]
+    expected_coef = [0, 2.5, 0, 2.5, 0]
+
+    # set to fit_intercept to False since target is constant and we want check
+    # the value of coef. coef would be all zeros otherwise.
+    est.set_params(fit_intercept=False)
+    est_jitter = clone(est).set_params(jitter=10e-8, random_state=0)
+
     est.fit(X, y)
+    est_jitter.fit(X, y)
+
+    assert np.mean((est.coef_ - est_jitter.coef_)**2) > .1
+    np.testing.assert_allclose(est_jitter.coef_, expected_coef, rtol=1e-3)
+
+
 def test_X_none_gram_not_none():
     with pytest.raises(ValueError,
                        match="X cannot be None if Gram is not None"):