code: def test_bayesian_initial_params():
      # Test BayesianRidge with initial values (alpha_init, lambda_init)
      X = np.vander(np.linspace(0, 4, 5), 4)
      y = np.array(
          [0.0, 1.0, 0.0, -1.0, 0.0]
      )  # y = (x^3 - 6x^2 + 8x) / 3
  
      # In this case, starting from the default initial values will increase
      # the bias of the fitted curve. So, lambda_init should be small.
      reg = BayesianRidge(alpha_init=1.0, lambda_init=1e-3)
      # Check the R2 score nearly equals to one.
      r2 = reg.fit(X, y).score(X, y)
      assert_almost_equal(r2, 1.0)
  
imports: from math import log
  import numpy
  import pytest
  from sklearn import datasets
  from sklearn.linear_model import ARDRegression, BayesianRidge, Ridge
  from sklearn.utils import check_random_state
  from sklearn.utils._testing import assert_almost_equal, assert_array_almost_equal, assert_array_less
  from sklearn.utils.extmath import fast_logdet
label_desc: Use image node_id 6 for calling a global function with example usage: test_bayesian_initial_params() without return types