title: Why GridSearchCV return score so different from the score returned by running model directly?
body: <p>I used GridSearchCV to find the best alpha for lasso model.</p>
  
  <pre><code>alphas = np.logspace(-5, 2, 30)
  grid = GridSearchCV(estimator=Lasso(),
  param_grid=dict(alpha=alphas), cv=10, scoring='r2')
  grid.fit(self.X, self.Y) # entire datasets were fed here
  
  print grid.best_params_, grid.best_score_ # score -0.0470788758558
  for params, mean_score, scores in grid.grid_scores_:
      print mean_score, params
  </code></pre>
  
  <p>I got the best parameter as 0.0014873521072935117, with negative r2 score -0.0470788758558.</p>
  
  <hr>
  
  <p>Then I tried this alpha on the model directly. I ran the following code in a loop.</p>
  
  <pre><code>X_train, X_test, y_train, y_test = train_test_split(self.X, self.Y, train_size=0.7)
  lasso = Lasso(alpha=0.001487)
  lasso.fit(X_train, y_train)
  print lasso.score(X_test, y_test)
  </code></pre>
  
  <p>Notice that I didn't set the random state, so it should work as a cross-validation. But the score I got here is around 0.11 (0.11-0.12) not matter how many times I ran the code.</p>
  
  <hr>
  
  <p><strong>Question</strong></p>
  
  <p>Why are the scores -0.0470788758558 and 0.11 so different for the two approaches? </p>