gbdt.cpp

#include "gbdt.h"

#include <LightGBM/utils/openmp_wrapper.h>

#include <LightGBM/utils/common.h>

#include <LightGBM/feature.h>
#include <LightGBM/objective_function.h>
#include <LightGBM/metric.h>

#include <ctime>

#include <sstream>
#include <chrono>
#include <string>
#include <vector>
#include <utility>

namespace LightGBM {

GBDT::GBDT()
  :iter_(0),
  train_data_(nullptr),
  object_function_(nullptr),
  early_stopping_round_(0),
  max_feature_idx_(0),
  num_class_(1),
  sigmoid_(1.0f),
  num_iteration_for_pred_(0),
  shrinkage_rate_(0.1f),
  num_init_iteration_(0) {
#pragma omp parallel
#pragma omp master
    {
      num_threads_ = omp_get_num_threads();
    }
}

GBDT::~GBDT() {

}

void GBDT::Init(const BoostingConfig* config, const Dataset* train_data, const ObjectiveFunction* object_function,
     const std::vector<const Metric*>& training_metrics) {
  iter_ = 0;
  num_iteration_for_pred_ = 0;
  max_feature_idx_ = 0;
  num_class_ = config->num_class;
  for (int i = 0; i < num_threads_; ++i) {
    random_.emplace_back(config->bagging_seed + i);
  }
  train_data_ = nullptr;
  gbdt_config_ = nullptr;
  tree_learner_ = nullptr;
  ResetTrainingData(config, train_data, object_function, training_metrics);
}

void GBDT::ResetTrainingData(const BoostingConfig* config, const Dataset* train_data, const ObjectiveFunction* object_function,
  const std::vector<const Metric*>& training_metrics) {
  auto new_config = std::unique_ptr<BoostingConfig>(new BoostingConfig(*config));
  if (train_data_ != nullptr && !train_data_->CheckAlign(*train_data)) {
    Log::Fatal("cannot reset training data, since new training data has different bin mappers");
  }
  early_stopping_round_ = new_config->early_stopping_round;
  shrinkage_rate_ = new_config->learning_rate;

  object_function_ = object_function;

  sigmoid_ = -1.0f;
  if (object_function_ != nullptr
    && std::string(object_function_->GetName()) == std::string("binary")) {
    // only binary classification need sigmoid transform
    sigmoid_ = new_config->sigmoid;
  }

  if (train_data_ != train_data && train_data != nullptr) {
    if (tree_learner_ == nullptr) {
      tree_learner_ = std::unique_ptr<TreeLearner>(TreeLearner::CreateTreeLearner(new_config->tree_learner_type, &new_config->tree_config));
    }
    // init tree learner
    tree_learner_->Init(train_data);

    // push training metrics
    training_metrics_.clear();
    for (const auto& metric : training_metrics) {
      training_metrics_.push_back(metric);
    }
    training_metrics_.shrink_to_fit();
    // not same training data, need reset score and others
    // create score tracker
    train_score_updater_.reset(new ScoreUpdater(train_data, num_class_));
    // update score
    for (int i = 0; i < iter_; ++i) {
      for (int curr_class = 0; curr_class < num_class_; ++curr_class) {
        auto curr_tree = (i + num_init_iteration_) * num_class_ + curr_class;
        train_score_updater_->AddScore(models_[curr_tree].get(), curr_class);
      }
    }
    num_data_ = train_data->num_data();
    // create buffer for gradients and hessians
    if (object_function_ != nullptr) {
      size_t total_size = static_cast<size_t>(num_data_) * num_class_;
      gradients_.resize(total_size);
      hessians_.resize(total_size);
    }
    // get max feature index
    max_feature_idx_ = train_data->num_total_features() - 1;
    // get label index
    label_idx_ = train_data->label_idx();
    // get feature names
    feature_names_ = train_data->feature_names();
    // get feature infos
    feature_infos_.clear();
    for (int i = 0; i < max_feature_idx_ + 1; ++i) {
      int feature_idx = train_data->GetInnerFeatureIndex(i);
      if (feature_idx < 0) { 
        feature_infos_.push_back("trival feature"); 
      } else {
        feature_infos_.push_back(train_data->FeatureAt(feature_idx)->bin_mapper()->bin_info());
      }
    }
  }

  if ((train_data_ != train_data && train_data != nullptr)
    || (gbdt_config_ != nullptr && gbdt_config_->bagging_fraction != new_config->bagging_fraction)) {
    // if need bagging, create buffer
    if (new_config->bagging_fraction < 1.0 && new_config->bagging_freq > 0) {
      bag_data_cnt_ =
        static_cast<data_size_t>(new_config->bagging_fraction * num_data_);
      bag_data_indices_.resize(num_data_);
      tmp_indices_.resize(num_data_);
      offsets_buf_.resize(num_threads_);
      left_cnts_buf_.resize(num_threads_);
      right_cnts_buf_.resize(num_threads_);
      left_write_pos_buf_.resize(num_threads_);
      right_write_pos_buf_.resize(num_threads_);
    } else {
      bag_data_cnt_ = num_data_;
      bag_data_indices_.clear();
      tmp_indices_.clear();
    }
  }
  train_data_ = train_data;
  if (train_data_ != nullptr) {
    // reset config for tree learner
    tree_learner_->ResetConfig(&new_config->tree_config);
  }
  gbdt_config_.reset(new_config.release());
}

void GBDT::AddValidDataset(const Dataset* valid_data,
  const std::vector<const Metric*>& valid_metrics) {
  if (!train_data_->CheckAlign(*valid_data)) {
    Log::Fatal("cannot add validation data, since it has different bin mappers with training data");
  }
  // for a validation dataset, we need its score and metric
  auto new_score_updater = std::unique_ptr<ScoreUpdater>(new ScoreUpdater(valid_data, num_class_));
  // update score
  for (int i = 0; i < iter_; ++i) {
    for (int curr_class = 0; curr_class < num_class_; ++curr_class) {
      auto curr_tree = (i + num_init_iteration_) * num_class_ + curr_class;
      new_score_updater->AddScore(models_[curr_tree].get(), curr_class);
    }
  }
  valid_score_updater_.push_back(std::move(new_score_updater));
  valid_metrics_.emplace_back();
  if (early_stopping_round_ > 0) {
    best_iter_.emplace_back();
    best_score_.emplace_back();
    best_msg_.emplace_back();
  }
  for (const auto& metric : valid_metrics) {
    valid_metrics_.back().push_back(metric);
    if (early_stopping_round_ > 0) {
      best_iter_.back().push_back(0);
      best_score_.back().push_back(kMinScore);
      best_msg_.back().emplace_back();
    }
  }
  valid_metrics_.back().shrink_to_fit();
}

data_size_t GBDT::BaggingHelper(data_size_t start, data_size_t cnt, data_size_t* buffer){
  const int tid = omp_get_thread_num();
  data_size_t bag_data_cnt =
    static_cast<data_size_t>(gbdt_config_->bagging_fraction * cnt);
  data_size_t cur_left_cnt = 0;
  data_size_t cur_right_cnt = 0;
  // random bagging, minimal unit is one record
  for (data_size_t i = 0; i < cnt; ++i) {
    double prob =
      (bag_data_cnt - cur_left_cnt) / static_cast<double>(cnt - i);
    if (random_[tid].NextDouble() < prob) {
      buffer[cur_left_cnt++] = start + i;
    } else {
      buffer[bag_data_cnt + cur_right_cnt++] = start + i;
    }
  }
  CHECK(cur_left_cnt == bag_data_cnt);
  return cur_left_cnt;
}

void GBDT::Bagging(int iter) {
  // if need bagging
  if (bag_data_cnt_ < num_data_ && iter % gbdt_config_->bagging_freq == 0) {
    const data_size_t min_inner_size = 10000;
    data_size_t inner_size = (num_data_ + num_threads_ - 1) / num_threads_;
    if (inner_size < min_inner_size) { inner_size = min_inner_size; }

#pragma omp parallel for schedule(static, 1)
    for (int i = 0; i < num_threads_; ++i) {
      left_cnts_buf_[i] = 0;
      right_cnts_buf_[i] = 0;
      data_size_t cur_start = i * inner_size;
      if (cur_start > num_data_) { continue; }
      data_size_t cur_cnt = inner_size;
      if (cur_start + cur_cnt > num_data_) { cur_cnt = num_data_ - cur_start; }
      data_size_t cur_left_count = BaggingHelper(cur_start, cur_cnt, tmp_indices_.data() + cur_start);
      offsets_buf_[i] = cur_start;
      left_cnts_buf_[i] = cur_left_count;
      right_cnts_buf_[i] = cur_cnt - cur_left_count;
    }
    data_size_t left_cnt = 0;
    left_write_pos_buf_[0] = 0;
    right_write_pos_buf_[0] = 0;
    for (int i = 1; i < num_threads_; ++i) {
      left_write_pos_buf_[i] = left_write_pos_buf_[i - 1] + left_cnts_buf_[i - 1];
      right_write_pos_buf_[i] = right_write_pos_buf_[i - 1] + right_cnts_buf_[i - 1];
    }
    left_cnt = left_write_pos_buf_[num_threads_ - 1] + left_cnts_buf_[num_threads_ - 1];

#pragma omp parallel for schedule(static, 1)
    for (int i = 0; i < num_threads_; ++i) {
      if (left_cnts_buf_[i] > 0) {
        std::memcpy(bag_data_indices_.data() + left_write_pos_buf_[i],
          tmp_indices_.data() + offsets_buf_[i], left_cnts_buf_[i] * sizeof(data_size_t));
      }
      if (right_cnts_buf_[i] > 0) {
        std::memcpy(bag_data_indices_.data() + left_cnt + right_write_pos_buf_[i],
          tmp_indices_.data() + offsets_buf_[i] + left_cnts_buf_[i], right_cnts_buf_[i] * sizeof(data_size_t));
      }
    }
    Log::Debug("Re-bagging, using %d data to train", bag_data_cnt_);
    // set bagging data to tree learner
    tree_learner_->SetBaggingData(bag_data_indices_.data(), bag_data_cnt_);
  }
}

void GBDT::UpdateScoreOutOfBag(const Tree* tree, const int curr_class) {
  // we need to predict out-of-bag socres of data for boosting
  if (num_data_ - bag_data_cnt_ > 0) {
    train_score_updater_->AddScore(tree, bag_data_indices_.data() + bag_data_cnt_, num_data_ - bag_data_cnt_, curr_class);
  }
}

bool GBDT::TrainOneIter(const score_t* gradient, const score_t* hessian, bool is_eval) {
  // boosting first
  if (gradient == nullptr || hessian == nullptr) {
    Boosting();
    gradient = gradients_.data();
    hessian = hessians_.data();
  }
  // bagging logic
  Bagging(iter_);
  for (int curr_class = 0; curr_class < num_class_; ++curr_class) {

    // train a new tree
    std::unique_ptr<Tree> new_tree(tree_learner_->Train(gradient + curr_class * num_data_, hessian + curr_class * num_data_));
    // if cannot learn a new tree, then stop
    if (new_tree->num_leaves() <= 1) {
      Log::Info("Stopped training because there are no more leafs that meet the split requirements.");
      return true;
    }

    // shrinkage by learning rate
    new_tree->Shrinkage(shrinkage_rate_);
    // update score
    UpdateScore(new_tree.get(), curr_class);
    UpdateScoreOutOfBag(new_tree.get(), curr_class);

    // add model
    models_.push_back(std::move(new_tree));
  }
  ++iter_;
  if (is_eval) {
    return EvalAndCheckEarlyStopping();
  } else {
    return false;
  }

}

void GBDT::RollbackOneIter() {
  if (iter_ <= 0) { return; }
  int cur_iter = iter_ + num_init_iteration_ - 1;
  // reset score
  for (int curr_class = 0; curr_class < num_class_; ++curr_class) {
    auto curr_tree = cur_iter * num_class_ + curr_class;
    models_[curr_tree]->Shrinkage(-1.0);
    train_score_updater_->AddScore(models_[curr_tree].get(), curr_class);
    for (auto& score_updater : valid_score_updater_) {
      score_updater->AddScore(models_[curr_tree].get(), curr_class);
    }
  }
  // remove model
  for (int curr_class = 0; curr_class < num_class_; ++curr_class) {
    models_.pop_back();
  }
  --iter_;
}

bool GBDT::EvalAndCheckEarlyStopping() {
  bool is_met_early_stopping = false;
  // print message for metric
  auto best_msg = OutputMetric(iter_);
  is_met_early_stopping = !best_msg.empty();
  if (is_met_early_stopping) {
    Log::Info("Early stopping at iteration %d, the best iteration round is %d",
      iter_, iter_ - early_stopping_round_);
    Log::Info("Output of best iteration round:\n%s", best_msg.c_str());
    // pop last early_stopping_round_ models
    for (int i = 0; i < early_stopping_round_ * num_class_; ++i) {
      models_.pop_back();
    }
  }
  return is_met_early_stopping;
}

void GBDT::UpdateScore(const Tree* tree, const int curr_class) {
  // update training score
  train_score_updater_->AddScore(tree_learner_.get(), curr_class);
  // update validation score
  for (auto& score_updater : valid_score_updater_) {
    score_updater->AddScore(tree, curr_class);
  }
}

std::string GBDT::OutputMetric(int iter) {
  bool need_output = (iter % gbdt_config_->output_freq) == 0;
  std::string ret = "";
  std::stringstream msg_buf;
  std::vector<std::pair<size_t, size_t>> meet_early_stopping_pairs;
  // print training metric
  if (need_output) {
    for (auto& sub_metric : training_metrics_) {
      auto name = sub_metric->GetName();
      auto scores = sub_metric->Eval(train_score_updater_->score());
      for (size_t k = 0; k < name.size(); ++k) {
        std::stringstream tmp_buf;
        tmp_buf << "Iteration:" << iter
          << ", training " << name[k]
          << " : " << scores[k];
        Log::Info(tmp_buf.str().c_str());
        if (early_stopping_round_ > 0) {
          msg_buf << tmp_buf.str() << std::endl;
        }
      }
    }
  }
  // print validation metric
  if (need_output || early_stopping_round_ > 0) {
    for (size_t i = 0; i < valid_metrics_.size(); ++i) {
      for (size_t j = 0; j < valid_metrics_[i].size(); ++j) {
        auto test_scores = valid_metrics_[i][j]->Eval(valid_score_updater_[i]->score());
        auto name = valid_metrics_[i][j]->GetName();
        for (size_t k = 0; k < name.size(); ++k) {
          std::stringstream tmp_buf;
          tmp_buf << "Iteration:" << iter
            << ", valid_" << i + 1 << " " << name[k]
            << " : " << test_scores[k];
          if (need_output) {
            Log::Info(tmp_buf.str().c_str());
          }
          if (early_stopping_round_ > 0) {
            msg_buf << tmp_buf.str() << std::endl;
          }
        }
        if (ret.empty() && early_stopping_round_ > 0) {
          auto cur_score = valid_metrics_[i][j]->factor_to_bigger_better() * test_scores.back();
          if (cur_score > best_score_[i][j]) {
            best_score_[i][j] = cur_score;
            best_iter_[i][j] = iter;
            meet_early_stopping_pairs.emplace_back(i, j);
          } else {
            if (iter - best_iter_[i][j] >= early_stopping_round_) { ret = best_msg_[i][j]; }
          }
        }
      }
    }
  }
  for (auto& pair : meet_early_stopping_pairs) {
    best_msg_[pair.first][pair.second] = msg_buf.str();
  }
  return ret;
}

/*! \brief Get eval result */
std::vector<double> GBDT::GetEvalAt(int data_idx) const {
  CHECK(data_idx >= 0 && data_idx <= static_cast<int>(valid_score_updater_.size()));
  std::vector<double> ret;
  if (data_idx == 0) {
    for (auto& sub_metric : training_metrics_) {
      auto scores = sub_metric->Eval(train_score_updater_->score());
      for (auto score : scores) {
        ret.push_back(score);
      }
    }
  }
  else {
    auto used_idx = data_idx - 1;
    for (size_t j = 0; j < valid_metrics_[used_idx].size(); ++j) {
      auto test_scores = valid_metrics_[used_idx][j]->Eval(valid_score_updater_[used_idx]->score());
      for (auto score : test_scores) {
        ret.push_back(score);
      }
    }
  }
  return ret;
}

/*! \brief Get training scores result */
const double* GBDT::GetTrainingScore(int64_t* out_len) {
  *out_len = static_cast<int64_t>(train_score_updater_->num_data()) * num_class_;
  return train_score_updater_->score();
}

void GBDT::GetPredictAt(int data_idx, double* out_result, int64_t* out_len) {
  CHECK(data_idx >= 0 && data_idx <= static_cast<int>(valid_score_updater_.size()));

  const double* raw_scores = nullptr;
  data_size_t num_data = 0;
  if (data_idx == 0) {
    raw_scores = GetTrainingScore(out_len);
    num_data = train_score_updater_->num_data();
  } else {
    auto used_idx = data_idx - 1;
    raw_scores = valid_score_updater_[used_idx]->score();
    num_data = valid_score_updater_[used_idx]->num_data();
    *out_len = static_cast<int64_t>(num_data) * num_class_;
  }
  if (num_class_ > 1) {
#pragma omp parallel for schedule(static)
    for (data_size_t i = 0; i < num_data; ++i) {
      std::vector<double> tmp_result(num_class_);
      for (int j = 0; j < num_class_; ++j) {
        tmp_result[j] = raw_scores[j * num_data + i];
      }
      Common::Softmax(&tmp_result);
      for (int j = 0; j < num_class_; ++j) {
        out_result[j * num_data + i] = static_cast<double>(tmp_result[j]);
      }
    }
  } else if(sigmoid_ > 0.0f){
#pragma omp parallel for schedule(static)
    for (data_size_t i = 0; i < num_data; ++i) {
      out_result[i] = static_cast<double>(1.0f / (1.0f + std::exp(-2.0f * sigmoid_ * raw_scores[i])));
    }
  } else {
#pragma omp parallel for schedule(static)
    for (data_size_t i = 0; i < num_data; ++i) {
      out_result[i] = static_cast<double>(raw_scores[i]);
    }
  }

}

void GBDT::Boosting() {
  if (object_function_ == nullptr) {
    Log::Fatal("No object function provided");
  }
  // objective function will calculate gradients and hessians
  int64_t num_score = 0;
  object_function_->
    GetGradients(GetTrainingScore(&num_score), gradients_.data(), hessians_.data());
}

std::string GBDT::DumpModel(int num_iteration) const {
  std::stringstream str_buf;

  str_buf << "{";
  str_buf << "\"name\":\"" << SubModelName() << "\"," << std::endl;
  str_buf << "\"num_class\":" << num_class_ << "," << std::endl;
  str_buf << "\"label_index\":" << label_idx_ << "," << std::endl;
  str_buf << "\"max_feature_idx\":" << max_feature_idx_ << "," << std::endl;
  str_buf << "\"sigmoid\":" << sigmoid_ << "," << std::endl;

  str_buf << "\"feature_names\":[\"" 
     << Common::Join(feature_names_, "\",\"") << "\"]," 
     << std::endl;

  str_buf << "\"tree_info\":[";
  int num_used_model = static_cast<int>(models_.size());
  if (num_iteration > 0) {
    num_used_model = std::min(num_iteration * num_class_, num_used_model);
  } 
  for (int i = 0; i < num_used_model; ++i) {
    if (i > 0) {
      str_buf << ",";
    }
    str_buf << "{";
    str_buf << "\"tree_index\":" << i << ",";
    str_buf << models_[i]->ToJSON();
    str_buf << "}";
  }
  str_buf << "]" << std::endl;

  str_buf << "}" << std::endl;

  return str_buf.str();
}

std::string GBDT::SaveModelToString(int num_iterations) const {
    std::stringstream ss;

    // output model type
    ss << SubModelName() << std::endl;
    // output number of class
    ss << "num_class=" << num_class_ << std::endl;
    // output label index
    ss << "label_index=" << label_idx_ << std::endl;
    // output max_feature_idx
    ss << "max_feature_idx=" << max_feature_idx_ << std::endl;
    // output objective name
    if (object_function_ != nullptr) {
      ss << "objective=" << object_function_->GetName() << std::endl;
    }
    // output sigmoid parameter
    ss << "sigmoid=" << sigmoid_ << std::endl;

    ss << "feature_names=" << Common::Join(feature_names_, " ") << std::endl;

    ss << std::endl;
    int num_used_model = static_cast<int>(models_.size());
    if (num_iterations > 0) {
      num_used_model = std::min(num_iterations * num_class_, num_used_model);
    }
    // output tree models
    for (int i = 0; i < num_used_model; ++i) {
      ss << "Tree=" << i << std::endl;
      ss << models_[i]->ToString() << std::endl;
    }

    std::vector<std::pair<size_t, std::string>> pairs = FeatureImportance();
    ss << std::endl << "feature importances:" << std::endl;
    for (size_t i = 0; i < pairs.size(); ++i) {
      ss << pairs[i].second << "=" << std::to_string(pairs[i].first) << std::endl;
    }

    ss << std::endl << "feature information:" << std::endl;
    for (int i = 0; i < max_feature_idx_ + 1; ++i) {
      ss << feature_names_[i] << "=" << feature_infos_[i] << std::endl;
    }

    return ss.str();
}

bool GBDT::SaveModelToFile(int num_iteration, const char* filename) const {
  /*! \brief File to write models */
  std::ofstream output_file;
  output_file.open(filename);

  output_file << SaveModelToString(num_iteration);

  output_file.close();

  return (bool)output_file;
}

bool GBDT::LoadModelFromString(const std::string& model_str) {
  // use serialized string to restore this object
  models_.clear();
  std::vector<std::string> lines = Common::Split(model_str.c_str(), '\n');

  // get number of classes
  auto line = Common::FindFromLines(lines, "num_class=");
  if (line.size() > 0) {
    Common::Atoi(Common::Split(line.c_str(), '=')[1].c_str(), &num_class_);
  } else {
    Log::Fatal("Model file doesn't specify the number of classes");
    return false;
  }
  // get index of label
  line = Common::FindFromLines(lines, "label_index=");
  if (line.size() > 0) {
    Common::Atoi(Common::Split(line.c_str(), '=')[1].c_str(), &label_idx_);
  } else {
    Log::Fatal("Model file doesn't specify the label index");
    return false;
  }
  // get max_feature_idx first
  line = Common::FindFromLines(lines, "max_feature_idx=");
  if (line.size() > 0) {
    Common::Atoi(Common::Split(line.c_str(), '=')[1].c_str(), &max_feature_idx_);
  } else {
    Log::Fatal("Model file doesn't specify max_feature_idx");
    return false;
  }
  // get sigmoid parameter
  line = Common::FindFromLines(lines, "sigmoid=");
  if (line.size() > 0) {
    Common::Atof(Common::Split(line.c_str(), '=')[1].c_str(), &sigmoid_);
  } else {
    sigmoid_ = -1.0f;
  }
  // get feature names
  line = Common::FindFromLines(lines, "feature_names=");
  if (line.size() > 0) {
    feature_names_ = Common::Split(line.substr(std::strlen("feature_names=")).c_str(), " ");
    if (feature_names_.size() != static_cast<size_t>(max_feature_idx_ + 1)) {
      Log::Fatal("Wrong size of feature_names");
      return false;
    }
  } else {
    Log::Fatal("Model file doesn't contain feature names");
    return false;
  }

  // get tree models
  size_t i = 0;
  while (i < lines.size()) {
    size_t find_pos = lines[i].find("Tree=");
    if (find_pos != std::string::npos) {
      ++i;
      int start = static_cast<int>(i);
      while (i < lines.size() && lines[i].find("Tree=") == std::string::npos) { ++i; }
      int end = static_cast<int>(i);
      std::string tree_str = Common::Join<std::string>(lines, start, end, "\n");
      auto new_tree = std::unique_ptr<Tree>(new Tree(tree_str));
      models_.push_back(std::move(new_tree));
    } else {
      ++i;
    }
  }
  Log::Info("Finished loading %d models", models_.size());
  num_iteration_for_pred_ = static_cast<int>(models_.size()) / num_class_;
  num_init_iteration_ = num_iteration_for_pred_;
  iter_ = 0;

  return true;
}

std::vector<std::pair<size_t, std::string>> GBDT::FeatureImportance() const {

  std::vector<size_t> feature_importances(max_feature_idx_ + 1, 0);
    for (size_t iter = 0; iter < models_.size(); ++iter) {
        for (int split_idx = 0; split_idx < models_[iter]->num_leaves() - 1; ++split_idx) {
            ++feature_importances[models_[iter]->split_feature_real(split_idx)];
        }
    }
    // store the importance first
    std::vector<std::pair<size_t, std::string>> pairs;
    for (size_t i = 0; i < feature_importances.size(); ++i) {
      if (feature_importances[i] > 0) {
        pairs.emplace_back(feature_importances[i], feature_names_[i]);
      }
    }
    // sort the importance
    std::sort(pairs.begin(), pairs.end(),
      [](const std::pair<size_t, std::string>& lhs,
        const std::pair<size_t, std::string>& rhs) {
      return lhs.first > rhs.first;
    });
    return pairs;
}

std::vector<double> GBDT::PredictRaw(const double* value) const {
  std::vector<double> ret(num_class_, 0.0f);
  for (int i = 0; i < num_iteration_for_pred_; ++i) {
    for (int j = 0; j < num_class_; ++j) {
      ret[j] += models_[i * num_class_ + j]->Predict(value);
    }
  }
  return ret;
}

std::vector<double> GBDT::Predict(const double* value) const {
  std::vector<double> ret(num_class_, 0.0f);
  for (int i = 0; i < num_iteration_for_pred_; ++i) {
    for (int j = 0; j < num_class_; ++j) {
      ret[j] += models_[i * num_class_ + j]->Predict(value);
    }
  }
  // if need sigmoid transform
  if (sigmoid_ > 0 && num_class_ == 1) {
    ret[0] = 1.0f / (1.0f + std::exp(- 2.0f * sigmoid_ * ret[0]));
  } else if (num_class_ > 1) {
    Common::Softmax(&ret);
  }
  return ret;
}

std::vector<int> GBDT::PredictLeafIndex(const double* value) const {
  std::vector<int> ret;
  for (int i = 0; i < num_iteration_for_pred_; ++i) {
    for (int j = 0; j < num_class_; ++j) {
      ret.push_back(models_[i * num_class_ + j]->PredictLeafIndex(value));
    }
  }
  return ret;
}

}  // namespace LightGBM