[MRG + 1] Return correct ridge parameter alpha_ and lambda_ for Bayesian ridge regression (scikit-learn#8567)

* Return correct ridge parameter alpha_ and lambda_ for regression

* Add test for coefficients and fix style

* Move sklearn.utils.testing to a more reasonable position.

* Make flake8 happy

* Code cleanup and entry in whats_new.rst

Author: gedeck

doc/whats_new.rst

@@ -244,6 +244,11 @@ Bug fixes
      multiple inheritance context.
      :issue:`8316` by :user:`Holger Peters <HolgerPeters>`.
 
+   - Fix :func:`sklearn.linear_model.BayesianRidge.fit` to return 
+     ridge parameter `alpha_` and `lambda_` consistent with calculated
+     coefficients `coef_` and `intercept_`.
+     :issue:`8224` by :user:`Peter Gedeck <gedeck>`.
+
 API changes summary
 -------------------
 

sklearn/linear_model/bayes.py

@@ -201,6 +201,11 @@ def fit(self, X, y):
                     logdet_sigma_[:n_samples] += alpha_ * eigen_vals_
                     logdet_sigma_ = - np.sum(np.log(logdet_sigma_))
 
+            # Preserve the alpha and lambda values that were used to
+            # calculate the final coefficients
+            self.alpha_ = alpha_
+            self.lambda_ = lambda_
+
             # Update alpha and lambda
             rmse_ = np.sum((y - np.dot(X, coef_)) ** 2)
             gamma_ = (np.sum((alpha_ * eigen_vals_) /
@@ -229,8 +234,6 @@ def fit(self, X, y):
                 break
             coef_old_ = np.copy(coef_)
 
-        self.alpha_ = alpha_
-        self.lambda_ = lambda_
         self.coef_ = coef_
         sigma_ = np.dot(Vh.T,
                         Vh / (eigen_vals_ + lambda_ / alpha_)[:, np.newaxis])

sklearn/linear_model/tests/test_bayes.py

@@ -6,12 +6,13 @@
 import numpy as np
 
 from sklearn.utils.testing import assert_array_equal
+from sklearn.utils.testing import assert_array_almost_equal
+from sklearn.utils.testing import assert_almost_equal
 from sklearn.utils.testing import SkipTest
 from sklearn.linear_model.bayes import BayesianRidge, ARDRegression
+from sklearn.linear_model import Ridge
 from sklearn import datasets
 
-from sklearn.utils.testing import assert_array_almost_equal
-
 
 def test_bayesian_on_diabetes():
     # Test BayesianRidge on diabetes
@@ -34,6 +35,19 @@ def test_bayesian_on_diabetes():
     assert_array_equal(np.diff(clf.scores_) > 0, True)
 
 
+def test_bayesian_ridge_parameter():
+    # Test correctness of lambda_ and alpha_ parameters (Github issue #8224)
+    X = np.array([[1, 1], [3, 4], [5, 7], [4, 1], [2, 6], [3, 10], [3, 2]])
+    y = np.array([1, 2, 3, 2, 0, 4, 5]).T
+
+    # A Ridge regression model using an alpha value equal to the ratio of
+    # lambda_ and alpha_ from the Bayesian Ridge model must be identical
+    br_model = BayesianRidge(compute_score=True).fit(X, y)
+    rr_model = Ridge(alpha=br_model.lambda_ / br_model.alpha_).fit(X, y)
+    assert_array_almost_equal(rr_model.coef_, br_model.coef_)
+    assert_almost_equal(rr_model.intercept_, br_model.intercept_)
+
+
 def test_toy_bayesian_ridge_object():
     # Test BayesianRidge on toy
     X = np.array([[1], [2], [6], [8], [10]])
@@ -64,7 +78,7 @@ def f(X):
         return np.dot(X, w) + b
 
     def f_noise(X, noise_mult):
-        return f(X) + np.random.randn(X.shape[0])*noise_mult
+        return f(X) + np.random.randn(X.shape[0]) * noise_mult
 
     d = 5
     n_train = 50