This file is not a proper patch - it contains explanation text. I need to understand the actual scikit-learn codebase structure to generate the correct patch. Based on the issue description and hints, let me create the proper patch:

The bug is that when `n_init > 1`:
1. The `fit` method runs multiple initialization trials
2. After all trials, it restores the best parameters via `_set_parameters(best_params)`
3. However, `fit_predict` returns labels from the last E-step call during the iterations, not from the best model

The fix needs to:
1. Move the computation of labels (via `_e_step` or `predict`) to AFTER `_set_parameters(best_params)` is called
2. Or simply override `fit_predict` to return `self.fit(X, y).predict(X)`

Based on the issue and hints, here's the correct minimal patch:

--- a/sklearn/mixture/base.py
+++ b/sklearn/mixture/base.py
@@ -257,11 +257,11 @@ class BaseMixture(DensityMixin, BaseEstimator, metaclass=ABCMeta):
                     best_params = self._get_parameters()
                     best_n_iter = n_iter
 
-        # Always do a final e-step to guarantee that the labels returned by
-        # fit_predict(X) are always consistent with fit(X).predict(X)
-        # for any value of max_iter and tol (and any curved geometry fitting
-        # included in the model).
-        _, log_resp = self._e_step(X)
-
         self._set_parameters(best_params)
         self.n_iter_ = best_n_iter
+        self.lower_bound_ = max_lower_bound
+
+        # Always do a final e-step to guarantee that the labels returned by
+        # fit_predict(X) are always consistent with fit(X).predict(X)
+        # for any value of max_iter and tol (and any random initialization).
+        _, log_resp = self._e_step(X)
 
         return log_resp.argmax(axis=1)