Python sklearn.linear_model.LassoLars() Examples

def test_rank_deficient_design():
    # consistency test that checks that LARS Lasso is handling rank
    # deficient input data (with n_features < rank) in the same way
    # as coordinate descent Lasso
    y = [5, 0, 5]
    for X in (
              [[5, 0],
               [0, 5],
               [10, 10]],
              [[10, 10, 0],
               [1e-32, 0, 0],
               [0, 0, 1]]
             ):
        # To be able to use the coefs to compute the objective function,
        # we need to turn off normalization
        lars = linear_model.LassoLars(.1, normalize=False)
        coef_lars_ = lars.fit(X, y).coef_
        obj_lars = (1. / (2. * 3.)
                    * linalg.norm(y - np.dot(X, coef_lars_)) ** 2
                    + .1 * linalg.norm(coef_lars_, 1))
        coord_descent = linear_model.Lasso(.1, tol=1e-6, normalize=False)
        coef_cd_ = coord_descent.fit(X, y).coef_
        obj_cd = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, coef_cd_)) ** 2
                  + .1 * linalg.norm(coef_cd_, 1))
        assert_less(obj_lars, obj_cd * (1. + 1e-8)) 

def test_lasso_lars_vs_lasso_cd_early_stopping():
    # Test that LassoLars and Lasso using coordinate descent give the
    # same results when early stopping is used.
    # (test : before, in the middle, and in the last part of the path)
    alphas_min = [10, 0.9, 1e-4]

    for alpha_min in alphas_min:
        alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                       alpha_min=alpha_min)
        lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
        lasso_cd.alpha = alphas[-1]
        lasso_cd.fit(X, y)
        error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
        assert_less(error, 0.01)

    # same test, with normalization
    for alpha_min in alphas_min:
        alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                       alpha_min=alpha_min)
        lasso_cd = linear_model.Lasso(fit_intercept=True, normalize=True,
                                      tol=1e-8)
        lasso_cd.alpha = alphas[-1]
        lasso_cd.fit(X, y)
        error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
        assert_less(error, 0.01) 

def test_multitarget():
    # Assure that estimators receiving multidimensional y do the right thing
    Y = np.vstack([y, y ** 2]).T
    n_targets = Y.shape[1]
    estimators = [
        linear_model.LassoLars(),
        linear_model.Lars(),
        # regression test for gh-1615
        linear_model.LassoLars(fit_intercept=False),
        linear_model.Lars(fit_intercept=False),
    ]

    for estimator in estimators:
        estimator.fit(X, Y)
        Y_pred = estimator.predict(X)
        alphas, active, coef, path = (estimator.alphas_, estimator.active_,
                                      estimator.coef_, estimator.coef_path_)
        for k in range(n_targets):
            estimator.fit(X, Y[:, k])
            y_pred = estimator.predict(X)
            assert_array_almost_equal(alphas[k], estimator.alphas_)
            assert_array_almost_equal(active[k], estimator.active_)
            assert_array_almost_equal(coef[k], estimator.coef_)
            assert_array_almost_equal(path[k], estimator.coef_path_)
            assert_array_almost_equal(Y_pred[:, k], y_pred) 

def test_estimatorclasses_positive_constraint():
    # testing the transmissibility for the positive option of all estimator
    # classes in this same function here
    default_parameter = {'fit_intercept': False}

    estimator_parameter_map = {'LassoLars': {'alpha': 0.1},
                               'LassoLarsCV': {},
                               'LassoLarsIC': {}}
    for estname in estimator_parameter_map:
        params = default_parameter.copy()
        params.update(estimator_parameter_map[estname])
        estimator = getattr(linear_model, estname)(positive=False, **params)
        estimator.fit(X, y)
        assert estimator.coef_.min() < 0
        estimator = getattr(linear_model, estname)(positive=True, **params)
        estimator.fit(X, y)
        assert min(estimator.coef_) >= 0 

def test_lasso_lars_vs_lasso_cd_early_stopping(verbose=False):
    # Test that LassoLars and Lasso using coordinate descent give the
    # same results when early stopping is used.
    # (test : before, in the middle, and in the last part of the path)
    alphas_min = [10, 0.9, 1e-4]

    for alpha_min in alphas_min:
        alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                       alpha_min=alpha_min)
        lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
        lasso_cd.alpha = alphas[-1]
        lasso_cd.fit(X, y)
        error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
        assert_less(error, 0.01)

    # same test, with normalization
    for alpha_min in alphas_min:
        alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                       alpha_min=alpha_min)
        lasso_cd = linear_model.Lasso(fit_intercept=True, normalize=True,
                                      tol=1e-8)
        lasso_cd.alpha = alphas[-1]
        lasso_cd.fit(X, y)
        error = linalg.norm(lasso_path[:, -1] - lasso_cd.coef_)
        assert_less(error, 0.01) 

def test_rank_deficient_design():
    # consistency test that checks that LARS Lasso is handling rank
    # deficient input data (with n_features < rank) in the same way
    # as coordinate descent Lasso
    y = [5, 0, 5]
    for X in ([[5, 0],
               [0, 5],
               [10, 10]],

              [[10, 10, 0],
               [1e-32, 0, 0],
               [0, 0, 1]],
              ):
        # To be able to use the coefs to compute the objective function,
        # we need to turn off normalization
        lars = linear_model.LassoLars(.1, normalize=False)
        coef_lars_ = lars.fit(X, y).coef_
        obj_lars = (1. / (2. * 3.)
                    * linalg.norm(y - np.dot(X, coef_lars_)) ** 2
                    + .1 * linalg.norm(coef_lars_, 1))
        coord_descent = linear_model.Lasso(.1, tol=1e-6, normalize=False)
        coef_cd_ = coord_descent.fit(X, y).coef_
        obj_cd = ((1. / (2. * 3.)) * linalg.norm(y - np.dot(X, coef_cd_)) ** 2
                  + .1 * linalg.norm(coef_cd_, 1))
        assert_less(obj_lars, obj_cd * (1. + 1e-8)) 

def test_grid_search_regressor_float(self):
        tuned_parameters = [{'alpha': np.logspace(-4, -0.5, 4)}]
        clf = GridSearchCV(LassoLars(max_iter=100),
                           tuned_parameters, cv=5)
        model, X = fit_regression_model(clf)
        model_onnx = convert_sklearn(
            model, "GridSearchCV",
            [("input", FloatTensorType([None, X.shape[1]]))])
        self.assertIsNotNone(model_onnx)
        dump_data_and_model(
            X,
            model,
            model_onnx,
            basename="SklearnGridSearchRegressionFloat-OneOffArray-Dec4",
            allow_failure="StrictVersion("
            "onnxruntime.__version__) "
            "<= StrictVersion('0.2.1') or "
            "StrictVersion(onnx.__version__) "
            "== StrictVersion('1.4.1')",
        ) 

def test_model_lasso_lars_bool(self):
        model, X = fit_regression_model(
            linear_model.LassoLars(), is_bool=True)
        model_onnx = convert_sklearn(
            model, "lasso lars",
            [("input", BooleanTensorType([None, X.shape[1]]))])
        self.assertIsNotNone(model_onnx)
        dump_data_and_model(
            X,
            model,
            model_onnx,
            basename="SklearnLassoLarsBool",
            allow_failure="StrictVersion("
            "onnxruntime.__version__)"
            "<= StrictVersion('0.2.1')",
        ) 

def test_model_lasso_lars(self):
        model, X = fit_regression_model(linear_model.LassoLars(alpha=0.01))
        model_onnx = convert_sklearn(
            model, "lasso lars",
            [("input", FloatTensorType([None, X.shape[1]]))])
        self.assertIsNotNone(model_onnx)
        dump_data_and_model(
            X,
            model,
            model_onnx,
            basename="SklearnLassoLars-Dec4",
            allow_failure="StrictVersion("
            "onnxruntime.__version__)"
            "<= StrictVersion('0.2.1')",
        ) 

def test_multitarget():
    # Assure that estimators receiving multidimensional y do the right thing
    X = diabetes.data
    Y = np.vstack([diabetes.target, diabetes.target ** 2]).T
    n_targets = Y.shape[1]
    estimators = [
        linear_model.LassoLars(),
        linear_model.Lars(),
        # regression test for gh-1615
        linear_model.LassoLars(fit_intercept=False),
        linear_model.Lars(fit_intercept=False),
    ]

    for estimator in estimators:
        estimator.fit(X, Y)
        Y_pred = estimator.predict(X)
        alphas, active, coef, path = (estimator.alphas_, estimator.active_,
                                      estimator.coef_, estimator.coef_path_)
        for k in range(n_targets):
            estimator.fit(X, Y[:, k])
            y_pred = estimator.predict(X)
            assert_array_almost_equal(alphas[k], estimator.alphas_)
            assert_array_almost_equal(active[k], estimator.active_)
            assert_array_almost_equal(coef[k], estimator.coef_)
            assert_array_almost_equal(path[k], estimator.coef_path_)
            assert_array_almost_equal(Y_pred[:, k], y_pred) 

def test_lasso_lars_path_length():
    # Test that the path length of the LassoLars is right
    lasso = linear_model.LassoLars()
    lasso.fit(X, y)
    lasso2 = linear_model.LassoLars(alpha=lasso.alphas_[2])
    lasso2.fit(X, y)
    assert_array_almost_equal(lasso.alphas_[:3], lasso2.alphas_)
    # Also check that the sequence of alphas is always decreasing
    assert_true(np.all(np.diff(lasso.alphas_) < 0)) 

def test_lasso_lars_vs_lasso_cd(verbose=False):
    # Test that LassoLars and Lasso using coordinate descent give the
    # same results.
    X = 3 * diabetes.data

    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
    lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01)

    # similar test, with the classifiers
    for alpha in np.linspace(1e-2, 1 - 1e-2, 20):
        clf1 = linear_model.LassoLars(alpha=alpha, normalize=False).fit(X, y)
        clf2 = linear_model.Lasso(alpha=alpha, tol=1e-8,
                                  normalize=False).fit(X, y)
        err = linalg.norm(clf1.coef_ - clf2.coef_)
        assert_less(err, 1e-3)

    # same test, with normalized data
    X = diabetes.data
    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
    lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
                                  tol=1e-8)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01) 

def test_lars_lstsq():
    # Test that Lars gives least square solution at the end
    # of the path
    X1 = 3 * diabetes.data  # use un-normalized dataset
    clf = linear_model.LassoLars(alpha=0.)
    clf.fit(X1, y)
    coef_lstsq = np.linalg.lstsq(X1, y)[0]
    assert_array_almost_equal(clf.coef_, coef_lstsq) 

def test_objectmapper(self):
        df = pdml.ModelFrame([])
        self.assertIs(df.linear_model.ARDRegression, lm.ARDRegression)
        self.assertIs(df.linear_model.BayesianRidge, lm.BayesianRidge)
        self.assertIs(df.linear_model.ElasticNet, lm.ElasticNet)
        self.assertIs(df.linear_model.ElasticNetCV, lm.ElasticNetCV)

        self.assertIs(df.linear_model.HuberRegressor, lm.HuberRegressor)

        self.assertIs(df.linear_model.Lars, lm.Lars)
        self.assertIs(df.linear_model.LarsCV, lm.LarsCV)
        self.assertIs(df.linear_model.Lasso, lm.Lasso)
        self.assertIs(df.linear_model.LassoCV, lm.LassoCV)
        self.assertIs(df.linear_model.LassoLars, lm.LassoLars)
        self.assertIs(df.linear_model.LassoLarsCV, lm.LassoLarsCV)
        self.assertIs(df.linear_model.LassoLarsIC, lm.LassoLarsIC)

        self.assertIs(df.linear_model.LinearRegression, lm.LinearRegression)
        self.assertIs(df.linear_model.LogisticRegression, lm.LogisticRegression)
        self.assertIs(df.linear_model.LogisticRegressionCV, lm.LogisticRegressionCV)
        self.assertIs(df.linear_model.MultiTaskLasso, lm.MultiTaskLasso)
        self.assertIs(df.linear_model.MultiTaskElasticNet, lm.MultiTaskElasticNet)
        self.assertIs(df.linear_model.MultiTaskLassoCV, lm.MultiTaskLassoCV)
        self.assertIs(df.linear_model.MultiTaskElasticNetCV, lm.MultiTaskElasticNetCV)

        self.assertIs(df.linear_model.OrthogonalMatchingPursuit, lm.OrthogonalMatchingPursuit)
        self.assertIs(df.linear_model.OrthogonalMatchingPursuitCV, lm.OrthogonalMatchingPursuitCV)
        self.assertIs(df.linear_model.PassiveAggressiveClassifier, lm.PassiveAggressiveClassifier)
        self.assertIs(df.linear_model.PassiveAggressiveRegressor, lm.PassiveAggressiveRegressor)

        self.assertIs(df.linear_model.Perceptron, lm.Perceptron)
        self.assertIs(df.linear_model.RandomizedLasso, lm.RandomizedLasso)
        self.assertIs(df.linear_model.RandomizedLogisticRegression, lm.RandomizedLogisticRegression)
        self.assertIs(df.linear_model.RANSACRegressor, lm.RANSACRegressor)
        self.assertIs(df.linear_model.Ridge, lm.Ridge)
        self.assertIs(df.linear_model.RidgeClassifier, lm.RidgeClassifier)
        self.assertIs(df.linear_model.RidgeClassifierCV, lm.RidgeClassifierCV)
        self.assertIs(df.linear_model.RidgeCV, lm.RidgeCV)
        self.assertIs(df.linear_model.SGDClassifier, lm.SGDClassifier)
        self.assertIs(df.linear_model.SGDRegressor, lm.SGDRegressor)
        self.assertIs(df.linear_model.TheilSenRegressor, lm.TheilSenRegressor) 

def test_model_lasso_lars_int(self):
        model, X = fit_regression_model(linear_model.LassoLars(), is_int=True)
        model_onnx = convert_sklearn(
            model, "lasso lars",
            [("input", Int64TensorType([None, X.shape[1]]))])
        self.assertIsNotNone(model_onnx)
        dump_data_and_model(
            X,
            model,
            model_onnx,
            basename="SklearnLassoLarsInt-Dec4",
            allow_failure="StrictVersion("
            "onnxruntime.__version__)"
            "<= StrictVersion('0.2.1')",
        ) 

def test_lars_lstsq():
    # Test that Lars gives least square solution at the end
    # of the path
    X1 = 3 * X  # use un-normalized dataset
    clf = linear_model.LassoLars(alpha=0.)
    clf.fit(X1, y)
    # Avoid FutureWarning about default value change when numpy >= 1.14
    rcond = None if LooseVersion(np.__version__) >= '1.14' else -1
    coef_lstsq = np.linalg.lstsq(X1, y, rcond=rcond)[0]
    assert_array_almost_equal(clf.coef_, coef_lstsq) 

def update_spatial_perpx(y, alpha, sub, C):
    res = np.zeros_like(sub, dtype=y.dtype)
    if np.sum(sub) > 0:
        C = C[:, sub]
        clf = LassoLars(alpha=alpha, positive=True)
        coef = clf.fit(C, y).coef_
        res[np.where(sub)[0]] = coef
    return res 

def _create_regressor(self):
        if self.mode == 'default':
            return Lars()
        if self.mode == 'lasso':
            return LassoLars(alpha=self.alpha)
        raise ValueError('Unexpected mode ' + self.mode + '. Expected "default" or "lasso"') 

def getModels():
    result = []
    result.append("LinearRegression")
    result.append("BayesianRidge")
    result.append("ARDRegression")
    result.append("ElasticNet")
    result.append("HuberRegressor")
    result.append("Lasso")
    result.append("LassoLars")
    result.append("Rigid")
    result.append("SGDRegressor")
    result.append("SVR")
    result.append("MLPClassifier")
    result.append("KNeighborsClassifier")
    result.append("SVC")
    result.append("GaussianProcessClassifier")
    result.append("DecisionTreeClassifier")
    result.append("RandomForestClassifier")
    result.append("AdaBoostClassifier")
    result.append("GaussianNB")
    result.append("LogisticRegression")
    result.append("QuadraticDiscriminantAnalysis")
    return result 

def test_lasso_lars_path_length():
    # Test that the path length of the LassoLars is right
    lasso = linear_model.LassoLars()
    lasso.fit(X, y)
    lasso2 = linear_model.LassoLars(alpha=lasso.alphas_[2])
    lasso2.fit(X, y)
    assert_array_almost_equal(lasso.alphas_[:3], lasso2.alphas_)
    # Also check that the sequence of alphas is always decreasing
    assert np.all(np.diff(lasso.alphas_) < 0) 

def test_lasso_lars_vs_lasso_cd():
    # Test that LassoLars and Lasso using coordinate descent give the
    # same results.
    X = 3 * diabetes.data

    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
    lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01)

    # similar test, with the classifiers
    for alpha in np.linspace(1e-2, 1 - 1e-2, 20):
        clf1 = linear_model.LassoLars(alpha=alpha, normalize=False).fit(X, y)
        clf2 = linear_model.Lasso(alpha=alpha, tol=1e-8,
                                  normalize=False).fit(X, y)
        err = linalg.norm(clf1.coef_ - clf2.coef_)
        assert_less(err, 1e-3)

    # same test, with normalized data
    X = diabetes.data
    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso')
    lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
                                  tol=1e-8)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01) 

def getSKLearnModel(modelName):
    if modelName == 'LinearRegression':
        model = linear_model.LinearRegression()
    elif modelName == 'BayesianRidge':
        model = linear_model.BayesianRidge()
    elif modelName == 'ARDRegression':
        model = linear_model.ARDRegression()
    elif modelName == 'ElasticNet':
        model = linear_model.ElasticNet()
    elif modelName == 'HuberRegressor':
        model = linear_model.HuberRegressor()
    elif modelName == 'Lasso':
        model = linear_model.Lasso()
    elif modelName == 'LassoLars':
        model = linear_model.LassoLars()
    elif modelName == 'Rigid':
        model = linear_model.Ridge()
    elif modelName == 'SGDRegressor':
        model = linear_model.SGDRegressor()
    elif modelName == 'SVR':
        model = SVR()
    elif modelName=='MLPClassifier':
        model = MLPClassifier()
    elif modelName=='KNeighborsClassifier':
        model = KNeighborsClassifier()
    elif modelName=='SVC':
        model = SVC()
    elif modelName=='GaussianProcessClassifier':
        model = GaussianProcessClassifier()
    elif modelName=='DecisionTreeClassifier':
        model = DecisionTreeClassifier()
    elif modelName=='RandomForestClassifier':
        model = RandomForestClassifier()
    elif modelName=='AdaBoostClassifier':
        model = AdaBoostClassifier()
    elif modelName=='GaussianNB':
        model = GaussianNB()
    elif modelName=='LogisticRegression':
        model = linear_model.LogisticRegression()
    elif modelName=='QuadraticDiscriminantAnalysis':
        model = QuadraticDiscriminantAnalysis()

    return model 

def test_lasso_lars_vs_lasso_cd_positive():
    # Test that LassoLars and Lasso using coordinate descent give the
    # same results when using the positive option

    # This test is basically a copy of the above with additional positive
    # option. However for the middle part, the comparison of coefficient values
    # for a range of alphas, we had to make an adaptations. See below.

    # not normalized data
    X = 3 * diabetes.data

    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                   positive=True)
    lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8, positive=True)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01)

    # The range of alphas chosen for coefficient comparison here is restricted
    # as compared with the above test without the positive option. This is due
    # to the circumstance that the Lars-Lasso algorithm does not converge to
    # the least-squares-solution for small alphas, see 'Least Angle Regression'
    # by Efron et al 2004. The coefficients are typically in congruence up to
    # the smallest alpha reached by the Lars-Lasso algorithm and start to
    # diverge thereafter.  See
    # https://gist.github.com/michigraber/7e7d7c75eca694c7a6ff

    for alpha in np.linspace(6e-1, 1 - 1e-2, 20):
        clf1 = linear_model.LassoLars(fit_intercept=False, alpha=alpha,
                                      normalize=False, positive=True).fit(X, y)
        clf2 = linear_model.Lasso(fit_intercept=False, alpha=alpha, tol=1e-8,
                                  normalize=False, positive=True).fit(X, y)
        err = linalg.norm(clf1.coef_ - clf2.coef_)
        assert_less(err, 1e-3)

    # normalized data
    X = diabetes.data
    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                   positive=True)
    lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
                                  tol=1e-8, positive=True)
    for c, a in zip(lasso_path.T[:-1], alphas[:-1]):  # don't include alpha=0
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01) 

def test_lasso_lars_vs_lasso_cd_positive(verbose=False):
    # Test that LassoLars and Lasso using coordinate descent give the
    # same results when using the positive option

    # This test is basically a copy of the above with additional positive
    # option. However for the middle part, the comparison of coefficient values
    # for a range of alphas, we had to make an adaptations. See below.

    # not normalized data
    X = 3 * diabetes.data

    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                   positive=True)
    lasso_cd = linear_model.Lasso(fit_intercept=False, tol=1e-8, positive=True)
    for c, a in zip(lasso_path.T, alphas):
        if a == 0:
            continue
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01)

    # The range of alphas chosen for coefficient comparison here is restricted
    # as compared with the above test without the positive option. This is due
    # to the circumstance that the Lars-Lasso algorithm does not converge to
    # the least-squares-solution for small alphas, see 'Least Angle Regression'
    # by Efron et al 2004. The coefficients are typically in congruence up to
    # the smallest alpha reached by the Lars-Lasso algorithm and start to
    # diverge thereafter.  See
    # https://gist.github.com/michigraber/7e7d7c75eca694c7a6ff

    for alpha in np.linspace(6e-1, 1 - 1e-2, 20):
        clf1 = linear_model.LassoLars(fit_intercept=False, alpha=alpha,
                                      normalize=False, positive=True).fit(X, y)
        clf2 = linear_model.Lasso(fit_intercept=False, alpha=alpha, tol=1e-8,
                                  normalize=False, positive=True).fit(X, y)
        err = linalg.norm(clf1.coef_ - clf2.coef_)
        assert_less(err, 1e-3)

    # normalized data
    X = diabetes.data
    alphas, _, lasso_path = linear_model.lars_path(X, y, method='lasso',
                                                   positive=True)
    lasso_cd = linear_model.Lasso(fit_intercept=False, normalize=True,
                                  tol=1e-8, positive=True)
    for c, a in zip(lasso_path.T[:-1], alphas[:-1]):  # don't include alpha=0
        lasso_cd.alpha = a
        lasso_cd.fit(X, y)
        error = linalg.norm(c - lasso_cd.coef_)
        assert_less(error, 0.01)