Move skl eval_metric and early_stopping rounds to model params. (#6751)

A new parameter `custom_metric` is added to `train` and `cv` to distinguish the behaviour from the old `feval`.  And `feval` is deprecated.  The new `custom_metric` receives transformed prediction when the built-in objective is used.  This enables XGBoost to use cost functions from other libraries like scikit-learn directly without going through the definition of the link function.

`eval_metric` and `early_stopping_rounds` in sklearn interface are moved from `fit` to `__init__` and is now saved as part of the scikit-learn model.  The old ones in `fit` function are now deprecated. The new `eval_metric` in `__init__` has the same new behaviour as `custom_metric`.

Added more detailed documents for the behaviour of custom objective and metric.

demo/guide-python/custom_rmsle.py

@@ -144,7 +144,7 @@ def py_rmsle(dtrain: xgb.DMatrix, dtest: xgb.DMatrix) -> Dict:
               dtrain=dtrain,
               num_boost_round=kBoostRound,
               obj=squared_log,
-              feval=rmsle,
+              custom_metric=rmsle,
               evals=[(dtrain, 'dtrain'), (dtest, 'dtest')],
               evals_result=results)
 

demo/guide-python/custom_softmax.py

@@ -3,6 +3,9 @@ only applicable after (excluding) XGBoost 1.0.0, as before this version XGBoost
 returns transformed prediction for multi-class objective function.  More
 details in comments.
 
+See https://xgboost.readthedocs.io/en/latest/tutorials/custom_metric_obj.html for detailed
+tutorial and notes.
+
 '''
 
 import numpy as np
@@ -95,7 +98,12 @@ def predict(booster: xgb.Booster, X):
 
 def merror(predt: np.ndarray, dtrain: xgb.DMatrix):
     y = dtrain.get_label()
-    # Like custom objective, the predt is untransformed leaf weight
+    # Like custom objective, the predt is untransformed leaf weight when custom objective
+    # is provided.
+
+    # With the use of `custom_metric` parameter in train function, custom metric receives
+    # raw input only when custom objective is also being used.  Otherwise custom metric
+    # will receive transformed prediction.
     assert predt.shape == (kRows, kClasses)
     out = np.zeros(kRows)
     for r in range(predt.shape[0]):
@@ -134,7 +142,7 @@ def main(args):
                                m,
                                num_boost_round=kRounds,
                                obj=softprob_obj,
-                               feval=merror,
+                               custom_metric=merror,
                                evals_result=custom_results,
                                evals=[(m, 'train')])
 
@@ -143,6 +151,7 @@ def main(args):
     native_results = {}
     # Use the same objective function defined in XGBoost.
     booster_native = xgb.train({'num_class': kClasses,
+                                "objective": "multi:softmax",
                                 'eval_metric': 'merror'},
                                m,
                                num_boost_round=kRounds,