<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _fit_stage(self, i, X, y, y_pred, sample_weight, sample_mask, random_state, scale, X_idx_sorted, X_csc=None, X_csr=None):
 """Fit another stage of ``n_classes_`` trees to the boosting model. """


        assert sample_mask.dtype == numpy.bool
        loss = self.loss_

        # whether to use dropout in next iteration
        do_dropout = self.dropout_rate > 0. and 0 < i < len(scale) - 1

        for k in range(loss.K):
            residual = loss.negative_gradient(y, y_pred, k=k,
                                              sample_weight=sample_weight)

            # induce regression tree on residuals
            tree = DecisionTreeRegressor(
                criterion=self.criterion,
                splitter='best',
                max_depth=self.max_depth,
                min_samples_split=self.min_samples_split,
                min_samples_leaf=self.min_samples_leaf,
                min_weight_fraction_leaf=self.min_weight_fraction_leaf,
                min_impurity_split=self.min_impurity_split,
                min_impurity_decrease=self.min_impurity_decrease,
                max_features=self.max_features,
                max_leaf_nodes=self.max_leaf_nodes,
                random_state=random_state,
                presort=self.presort)

            if self.subsample < 1.0:
                # no inplace multiplication!
                sample_weight = sample_weight * sample_mask.astype(numpy.float64)

            X = X_csr if X_csr is not None else X
            tree.fit(X, residual, sample_weight=sample_weight,
                     check_input=False, X_idx_sorted=X_idx_sorted)

            # add tree to ensemble
            self.estimators_[i, k] = tree

            # update tree leaves
            if do_dropout:
                # select base learners to be dropped for next iteration
                drop_model, n_dropped = _sample_binomial_plus_one(self.dropout_rate, i + 1, random_state)

                # adjust scaling factor of tree that is going to be trained in next iteration
                scale[i + 1] = 1. / (n_dropped + 1.)

                y_pred[:, k] = 0
                for m in range(i + 1):
                    if drop_model[m] == 1:
                        # adjust scaling factor of dropped trees
                        scale[m] *= n_dropped / (n_dropped + 1.)
                    else:
                        # pseudoresponse of next iteration (without contribution of dropped trees)
                        y_pred[:, k] += self.learning_rate * scale[m] * self.estimators_[m, k].predict(X).ravel()
            else:
                # update tree leaves
                loss.update_terminal_regions(tree.tree_, X, y, residual, y_pred,
                                             sample_weight, sample_mask,
                                             self.learning_rate, k=k)

        return y_pred