Add prediction of feature contributions (#2003)

* Add prediction of feature contributions

This implements the idea described at http://blog.datadive.net/interpreting-random-forests/
which tries to give insight in how a prediction is composed of its feature contributions
and a bias.

* Support multi-class models

* Calculate learning_rate per-tree instead of using the one from the first tree

* Do not rely on node.base_weight * learning_rate having the same value as the node mean value (aka leaf value, if it were a leaf); instead calculate them (lazily) on-the-fly

* Add simple test for contributions feature

* Check against param.num_nodes instead of checking for non-zero length

* Loop over all roots instead of only the first

src/c_api/c_api.cc

@@ -622,7 +622,8 @@ XGB_DLL int XGBoosterPredict(BoosterHandle handle,
       static_cast<std::shared_ptr<DMatrix>*>(dmat)->get(),
       (option_mask & 1) != 0,
       &preds, ntree_limit,
-      (option_mask & 2) != 0);
+      (option_mask & 2) != 0,
+      (option_mask & 4) != 0);
   *out_result = dmlc::BeginPtr(preds);
   *len = static_cast<xgboost::bst_ulong>(preds.size());
   API_END();