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

include/xgboost/learner.h

@@ -103,12 +103,14 @@ class Learner : public rabit::Serializable {
    * \param ntree_limit limit number of trees used for boosted tree
    *   predictor, when it equals 0, this means we are using all the trees
    * \param pred_leaf whether to only predict the leaf index of each tree in a boosted tree predictor
+   * \param pred_contribs whether to only predict the feature contributions of all trees
    */
   virtual void Predict(DMatrix* data,
                        bool output_margin,
                        std::vector<bst_float> *out_preds,
                        unsigned ntree_limit = 0,
-                       bool pred_leaf = false) const = 0;
+                       bool pred_leaf = false,
+                       bool pred_contribs = false) const = 0;
   /*!
    * \brief Set additional attribute to the Booster.
    *  The property will be saved along the booster.