address issue #807 Poisson regression objective. (#863)

* Attempt to address issue #807 Poisson regression objective.

* Fix coding style.

* Added label non-negative safety check.

src/objective/regression_objective.hpp

 #ifndef LIGHTGBM_OBJECTIVE_REGRESSION_OBJECTIVE_HPP_
 #define LIGHTGBM_OBJECTIVE_REGRESSION_OBJECTIVE_HPP_
 
+#include <LightGBM/meta.h>
+
 #include <LightGBM/objective_function.h>
 #include <LightGBM/utils/common.h>
 
@@ -312,23 +314,49 @@ public:
     num_data_ = num_data;
     label_ = metadata.label();
     weights_ = metadata.weights();
+
+    // Safety check of labels
+    float miny;
+    double sumy;
+    Common::obtain_min_max_sum(label_, num_data_, &miny, nullptr, &sumy);
+    if (miny < 0.0f) {
+      Log::Fatal("[%s]: at least one target label is negative.", GetName());
+    }
+    if (sumy == 0.0f) {
+      Log::Fatal("[%s]: sum of labels is zero.", GetName());
+    }
   }
 
+  /* Parametrize with unbounded internal score "f"; then
+   *  loss = exp(f) - label * f
+   *  grad = exp(f) - label
+   *  hess = exp(f)
+   *
+   * And the output is exp(f); so the associated metric get s=exp(f)
+   * so that its loss = s - label * log(s); a little awkward maybe.
+   *
+   */
   void GetGradients(const double* score, score_t* gradients,
                     score_t* hessians) const override {
     if (weights_ == nullptr) {
       #pragma omp parallel for schedule(static)
       for (data_size_t i = 0; i < num_data_; ++i) {
-        gradients[i] = static_cast<score_t>(score[i] - label_[i]);
-        hessians[i] = static_cast<score_t>(score[i] + max_delta_step_);
+        const double ef = std::exp(score[i]);
+        gradients[i] = static_cast<score_t>(ef - label_[i]);
+        hessians[i] = static_cast<score_t>(ef);
       }
     } else {
       #pragma omp parallel for schedule(static)
       for (data_size_t i = 0; i < num_data_; ++i) {
-        gradients[i] = static_cast<score_t>((score[i] - label_[i]) * weights_[i]);
-        hessians[i] = static_cast<score_t>((score[i] + max_delta_step_) * weights_[i]);
+        const double ef = std::exp(score[i]);
+        gradients[i] = static_cast<score_t>((ef - label_[i]) * weights_[i]);
+        hessians[i] = static_cast<score_t>(ef * weights_[i]);
+      }
     }
   }
+
+  void ConvertOutput(const double* input, double* output) const override {
+    output[0] = std::exp(input[0]);
   }
 
   const char* GetName() const override {
@@ -343,6 +371,27 @@ public:
 
   bool BoostFromAverage() const override { return true; }
 
+  bool GetCustomAverage(double *initscore) const override {
+    if (initscore == nullptr) return false;
+    double sumw = 0.0f;
+    double sumy = 0.0f;
+    if (weights_ == nullptr) {
+      for (data_size_t i = 0; i < num_data_; i++) {
+        sumy += label_[i];
+      }
+      sumw = static_cast<double>(num_data_);
+    } else {
+      for (data_size_t i = 0; i < num_data_; i++) {
+        sumy += weights_[i] * label_[i];
+        sumw += weights_[i];
+      }
+    }
+    const double yavg = sumy / sumw;
+    *initscore = std::log(yavg);
+    Log::Info("[%s:%s]: yavg=%f -> initscore=%f",  GetName(), __func__, yavg, *initscore);
+    return true;
+  }
+
 private:
   /*! \brief Number of data */
   data_size_t num_data_;