# dlib C++ Library - random_forest_regression.h

    // Copyright (C) 2018  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_RANdOM_FOREST_REGRESSION_H_
    #define DLIB_RANdOM_FOREST_REGRESSION_H_

    #include "random_forest_regression_abstract.h"
    #include <vector>
    #include "../matrix.h"
    #include <algorithm>
    #include "../threads.h"

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        class dense_feature_extractor
        {

        public:
            typedef uint32_t feature;
            typedef matrix<double,0,1> sample_type;

            dense_feature_extractor(
            ) = default;

            void setup (
                const std::vector<sample_type>& x,
                const std::vector<double>& y
            )
            {
                DLIB_CASSERT(x.size() > 0);
                DLIB_CASSERT(x.size() == y.size());
                for (auto& el : x)
                    DLIB_CASSERT(el.size() == x[0].size(), "All the vectors in a training set have to have the same dimensionality.");

                DLIB_CASSERT(x[0].size() != 0, "The vectors can't be empty.");

                num_feats = x[0].size();
            }

            void get_random_features (
                dlib::rand& rnd,
                size_t num,
                std::vector<feature>& feats
            ) const
            {
                DLIB_ASSERT(max_num_feats() != 0);
                num = std::min(num, num_feats);

                feats.clear();
                for (size_t i = 0; i < num_feats; ++i)
                    feats.push_back(i);

                // now pick num features at random
                for (size_t i = 0; i < num; ++i)
                {
                    auto idx = rnd.get_integer_in_range(i,num_feats);
                    std::swap(feats[i], feats[idx]);
                }
                feats.resize(num);
            }

            double extract_feature_value (
                const sample_type& item,
                const feature& f
            ) const
            {
                DLIB_ASSERT(max_num_feats() != 0);
                return item(f);
            }

            size_t max_num_feats (
            ) const
            {
                return num_feats;
            }

            friend void serialize(const dense_feature_extractor& item, std::ostream& out)
            {
                serialize("dense_feature_extractor", out);
                serialize(item.num_feats, out);
            }

            friend void deserialize(dense_feature_extractor& item, std::istream& in)
            {
                check_serialized_version("dense_feature_extractor", in);
                deserialize(item.num_feats, in);
            }

        private:
            size_t num_feats = 0;
        };

    // ----------------------------------------------------------------------------------------

        template <
            typename feature_extractor
            >
        struct internal_tree_node
        {
            uint32_t left;
            uint32_t right;
            float split_threshold;
            typename feature_extractor::feature split_feature;
        };

        template <typename feature_extractor>
        void serialize(const internal_tree_node<feature_extractor>& item, std::ostream& out)
        {
            serialize(item.left, out);
            serialize(item.right, out);
            serialize(item.split_threshold, out);
            serialize(item.split_feature, out);
        }

        template <typename feature_extractor>
        void deserialize(internal_tree_node<feature_extractor>& item, std::istream& in)
        {
            deserialize(item.left, in);
            deserialize(item.right, in);
            deserialize(item.split_threshold, in);
            deserialize(item.split_feature, in);
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename feature_extractor = dense_feature_extractor
            >
        class random_forest_regression_function
        {

        public:

            typedef feature_extractor feature_extractor_type;
            typedef typename feature_extractor::sample_type sample_type;

            random_forest_regression_function(
            ) = default;

            random_forest_regression_function (
                feature_extractor_type&& fe_,
                std::vector<std::vector<internal_tree_node<feature_extractor>>>&& trees_,
                std::vector<std::vector<float>>&& leaves_
            ) :
                fe(std::move(fe_)),
                trees(std::move(trees_)),
                leaves(std::move(leaves_))
            {
                DLIB_ASSERT(trees.size() > 0);
                DLIB_ASSERT(trees.size() == leaves.size(), "Every set of tree nodes has to have leaves");
    #ifdef ENABLE_ASSERTS
                for (size_t i = 0; i < trees.size(); ++i)
                {
                    DLIB_ASSERT(trees[i].size() > 0, "A tree can't have 0 leaves.");
                    for (auto& node : trees[i])
                    {
                        DLIB_ASSERT(trees[i].size()+leaves[i].size() > node.left, "left node index in tree is too big. There is no associated tree node or leaf.");
                        DLIB_ASSERT(trees[i].size()+leaves[i].size() > node.right, "right node index in tree is too big. There is no associated tree node or leaf.");
                    }
                }
    #endif
            }

            size_t get_num_trees(
            ) const
            {
                return trees.size();
            }

            const std::vector<std::vector<internal_tree_node<feature_extractor>>>& get_internal_tree_nodes (
            ) const { return trees; }

            const std::vector<std::vector<float>>& get_tree_leaves (
            ) const { return leaves; }

            const feature_extractor_type& get_feature_extractor (
            ) const { return fe; }

            double operator() (
                const sample_type& x
            ) const
            {
                DLIB_ASSERT(get_num_trees() > 0);

                double accum = 0;

                for (size_t i = 0; i < trees.size(); ++i)
                {
                    auto& tree = trees[i];
                    // walk the tree to the leaf
                    uint32_t idx = 0;
                    while(idx < tree.size())
                    {
                        auto feature_value = fe.extract_feature_value(x, tree[idx].split_feature);
                        if (feature_value < tree[idx].split_threshold)
                            idx = tree[idx].left;
                        else
                            idx = tree[idx].right;
                    }
                    // compute leaf index
                    accum += leaves[i][idx-tree.size()];
                }

                return accum/trees.size();
            }

            friend void serialize(const random_forest_regression_function& item, std::ostream& out)
            {
                serialize("random_forest_regression_function", out);
                serialize(item.fe, out);
                serialize(item.trees, out);
                serialize(item.leaves, out);
            }

            friend void deserialize(random_forest_regression_function& item, std::istream& in)
            {
                check_serialized_version("random_forest_regression_function", in);
                deserialize(item.fe, in);
                deserialize(item.trees, in);
                deserialize(item.leaves, in);
            }

        private:

            /*!
                CONVENTION
                    - trees.size() == leaves.size()
                    - Any .left or .right index in trees that is larger than the number of
                      nodes in the tree references a leaf. Moreover, the index of the leaf is
                      computed by subtracting the number of nodes in the tree.
            !*/

            feature_extractor_type fe;

            // internal nodes of trees
            std::vector<std::vector<internal_tree_node<feature_extractor>>> trees;
            // leaves of trees
            std::vector<std::vector<float>> leaves;

        };

    // ----------------------------------------------------------------------------------------

        template <
            typename feature_extractor = dense_feature_extractor
            >
        class random_forest_regression_trainer
        {
        public:
            typedef feature_extractor feature_extractor_type;
            typedef random_forest_regression_function<feature_extractor> trained_function_type;
            typedef typename feature_extractor::sample_type sample_type;

            random_forest_regression_trainer (
            ) = default;

            const feature_extractor_type& get_feature_extractor (
            ) const
            {
                return fe_;
            }

            void set_feature_extractor (
                const feature_extractor_type& feat_extractor
            )
            {
                fe_ = feat_extractor;
            }

            void set_seed (
                const std::string& seed
            )
            {
                random_seed = seed;
            }

            const std::string& get_random_seed (
            ) const
            {
                return random_seed;
            }

            size_t get_num_trees (
            ) const
            {
                return num_trees;
            }

            void set_num_trees (
                size_t num
            )
            {
                DLIB_CASSERT(num > 0);
                num_trees = num;
            }

            void set_feature_subsampling_fraction (
                double frac
            )
            {
                DLIB_CASSERT(0 < frac && frac <= 1);
                feature_subsampling_frac = frac;
            }

            double get_feature_subsampling_frac(
            ) const
            {
                return feature_subsampling_frac;
            }

            void set_min_samples_per_leaf (
                size_t num
            )
            {
                DLIB_ASSERT(num > 0);
                min_samples_per_leaf = num;
            }

            size_t get_min_samples_per_leaf(
            ) const
            {
                return min_samples_per_leaf;
            }

            void be_verbose (
            )
            {
                verbose = true;
            }

            void be_quiet (
            )
            {
                verbose = false;
            }

            trained_function_type train (
                const std::vector<sample_type>& x,
                const std::vector<double>& y
            ) const
            {
                std::vector<double> junk;
                return do_train(x,y,junk,false);
            }

            trained_function_type train (
                const std::vector<sample_type>& x,
                const std::vector<double>& y,
                std::vector<double>& oob_values
            ) const
            {
                return do_train(x,y,oob_values,true);
            }

        private:

            trained_function_type do_train (
                const std::vector<sample_type>& x,
                const std::vector<double>& y,
                std::vector<double>& oob_values,
                bool compute_oob_values
            ) const
            {
                DLIB_CASSERT(x.size() == y.size());
                DLIB_CASSERT(x.size() > 0);

                feature_extractor_type fe = fe_;
                fe.setup(x,y);

                DLIB_CASSERT(fe.max_num_feats() != 0);

                std::vector<std::vector<internal_tree_node<feature_extractor>>> all_trees(num_trees);
                std::vector<std::vector<float>> all_leaves(num_trees);

                const size_t feats_per_node = std::max(1.0,std::round(fe.max_num_feats()*feature_subsampling_frac));

                // Each tree couldn't have more than this many interior nodes.  It might
                // end up having less though. We need to know this value because the way
                // we mark a left or right pointer in a tree as pointing to a leaf is by
                // making its index larger than the number of interior nodes in the tree.
                // But we don't know the tree's size before we finish building it.  So we
                // will use max_num_nodes as a proxy during tree construction and then go
                // back and fix it once a tree's size is known.
                const uint32_t max_num_nodes = y.size();

                std::vector<uint32_t> oob_hits;

                if (compute_oob_values)
                {
                    oob_values.resize(y.size());
                    oob_hits.resize(y.size());
                }

                std::mutex m;

                // Calling build_tree(i) creates the ith tree and stores the results in
                // all_trees and all_leaves.
                auto build_tree = [&](long i)
                {
                    dlib::rand rnd(random_seed + std::to_string(i));
                    auto& tree = all_trees[i];
                    auto& leaves = all_leaves[i];

                    // Check if there are fewer than min_samples_per_leaf and if so then
                    // don't make any tree.  Just average the things and be done.
                    if (y.size() <= min_samples_per_leaf)
                    {
                        leaves.push_back(mean(mat(y)));
                        return;
                    }

                    double sumy = 0;
                    // pick a random bootstrap of the data.
                    std::vector<std::pair<float,uint32_t>> idxs(y.size());
                    for (auto& idx : idxs) {
                        idx = std::make_pair(0.0f, static_cast<uint32_t>(rnd.get_integer(y.size())));
                        sumy += y[idx.second];
                    }

                    // We are going to use ranges_to_process as a stack that tracks which
                    // range of samples we are going to split next.
                    std::vector<range_t> ranges_to_process;
                    // start with the root of the tree, i.e. the entire range of training
                    // samples.
                    ranges_to_process.emplace_back(sumy, 0, static_cast<uint32_t>(y.size()));
                    // push an unpopulated root node into the tree.  We will populate it
                    // when we process its corresponding range.
                    tree.emplace_back();

                    std::vector<typename feature_extractor::feature> feats;

                    while(ranges_to_process.size() > 0)
                    {
                        // Grab the next range/node to process.
                        const auto range = ranges_to_process.back();
                        ranges_to_process.pop_back();

                        // Get the split features we will consider at this node.
                        fe.get_random_features(rnd, feats_per_node, feats);
                        // Then find the best split
                        auto best_split = find_best_split_among_feats(fe, range, feats, x, y, idxs);

                        range_t left_split(best_split.left_sum, range.begin, best_split.split_idx);
                        range_t right_split(best_split.right_sum, best_split.split_idx, range.end);

                        DLIB_ASSERT(left_split.begin < left_split.end);
                        DLIB_ASSERT(right_split.begin < right_split.end);

                        // Now that we know the split we can populate the parent node we popped
                        // from ranges_to_process.
                        tree[range.tree_idx].split_threshold = best_split.split_threshold;
                        tree[range.tree_idx].split_feature = best_split.split_feature;

                        // If the left split is big enough to make a new interior leaf
                        // node. We also stop splitting if all the samples went into this node.
                        // This could happen if the features are all uniform so there just
                        // isn't any way to split them anymore.
                        if (left_split.size() > min_samples_per_leaf && right_split.size() != 0)
                        {
                            // allocate an interior leaf node for it.
                            left_split.tree_idx = tree.size();
                            tree.emplace_back();
                            // set the pointer in the parent node to the newly allocated
                            // node.
                            tree[range.tree_idx].left  = left_split.tree_idx;

                            ranges_to_process.emplace_back(left_split);
                        }
                        else
                        {
                            // Add to leaves.  Don't forget to set the pointer in the
                            // parent node to the newly allocated leaf node.
                            tree[range.tree_idx].left = leaves.size() + max_num_nodes;
                            leaves.emplace_back(static_cast<float>(left_split.avg()));
                        }

                        // If the right split is big enough to make a new interior leaf
                        // node. We also stop splitting if all the samples went into this node.
                        // This could happen if the features are all uniform so there just
                        // isn't any way to split them anymore.
                        if (right_split.size() > min_samples_per_leaf && left_split.size() != 0)
                        {
                            // allocate an interior leaf node for it.
                            right_split.tree_idx = tree.size();
                            tree.emplace_back();
                            // set the pointer in the parent node to the newly allocated
                            // node.
                            tree[range.tree_idx].right  = right_split.tree_idx;

                            ranges_to_process.emplace_back(right_split);
                        }
                        else
                        {
                            // Add to leaves.  Don't forget to set the pointer in the
                            // parent node to the newly allocated leaf node.
                            tree[range.tree_idx].right = leaves.size() + max_num_nodes;
                            leaves.emplace_back(static_cast<float>(right_split.avg()));
                        }
                    } // end while (still building tree)

                    // Fix the leaf pointers in the tree now that we know the correct
                    // tree.size() value.
                    DLIB_CASSERT(max_num_nodes >= tree.size());
                    const auto offset = max_num_nodes - tree.size();
                    for (auto& n : tree)
                    {
                        if (n.left >= max_num_nodes)
                            n.left -= offset;
                        if (n.right >= max_num_nodes)
                            n.right -= offset;
                    }

                    if (compute_oob_values)
                    {
                        std::sort(idxs.begin(), idxs.end(),
                            [](const std::pair<float,uint32_t>& a, const std::pair<float,uint32_t>& b) {return a.second<b.second; });

                        std::lock_guard<std::mutex> lock(m);

                        size_t j = 0;
                        for (size_t i = 0; i < oob_values.size(); ++i)
                        {
                            // check if i is in idxs
                            while(j < idxs.size() && i > idxs[j].second)
                                ++j;

                            // i isn't in idxs so it's an oob sample and we should process it.
                            if (j == idxs.size() || idxs[j].second != i)
                            {
                                oob_hits[i]++;

                                // walk the tree to find the leaf value for this oob sample
                                uint32_t idx = 0;
                                while(idx < tree.size())
                                {
                                    auto feature_value = fe.extract_feature_value(x[i], tree[idx].split_feature);
                                    if (feature_value < tree[idx].split_threshold)
                                        idx = tree[idx].left;
                                    else
                                        idx = tree[idx].right;
                                }
                                oob_values[i] += leaves[idx-tree.size()];
                            }
                        }
                    }
                };

                if (verbose)
                    parallel_for_verbose(0, num_trees, build_tree);
                else
                    parallel_for(0, num_trees, build_tree);

                if (compute_oob_values)
                {
                    double meanval = 0;
                    double cnt = 0;
                    for (size_t i = 0; i < oob_values.size(); ++i)
                    {
                        if (oob_hits[i] != 0)
                        {
                            oob_values[i] /= oob_hits[i];
                            meanval += oob_values[i];
                            ++cnt;
                        }
                    }

                    // If there are some elements that didn't get hits, we set their oob values
                    // to the mean oob value.
                    if (cnt != 0)
                    {
                        const double typical_value = meanval/cnt;
                        for (size_t i = 0; i < oob_values.size(); ++i)
                        {
                            if (oob_hits[i] == 0)
                                oob_values[i] = typical_value;
                        }
                    }
                }

                return trained_function_type(std::move(fe), std::move(all_trees), std::move(all_leaves));
            }

            struct range_t
            {
                range_t(
                    double sumy,
                    uint32_t begin,
                    uint32_t end
                ) : sumy(sumy), begin(begin), end(end), tree_idx(0) {}

                double sumy;
                uint32_t begin;
                uint32_t end;

                // Every range object corresponds to an entry in a tree. This tells you the
                // tree node that owns the range.
                uint32_t tree_idx;

                uint32_t size() const { return end-begin; }
                double avg() const { return sumy/size(); }
            };

            struct best_split_details
            {
                double score = -std::numeric_limits<double>::infinity();
                double left_sum;
                double right_sum;
                uint32_t split_idx;
                double split_threshold;
                typename feature_extractor::feature split_feature;

                bool operator < (const best_split_details& rhs) const
                {
                    return score < rhs.score;
                }
            };

            static best_split_details find_best_split (
                const range_t& range,
                const std::vector<double>& y,
                const std::vector<std::pair<float,uint32_t>>& idxs
            )
            /*!
                requires
                    - max(mat(idxs)) < y.size()
                    - range.sumy == sum of y[idxs[j].second] for all valid j in range [range.begin, range.end).
                ensures
                    - finds a threshold T such that there exists an i satisfying the following:
                        - y[idxs[j].second] < T for all j <= i
                        - y[idxs[j].second] > T for all j > i
                      Therefore, the threshold T partitions the contents of y into two groups,
                      relative to the ordering established by idxs.  Moreover the partitioning
                      of y values into two groups has the additional requirement that it is
                      optimal in the sense that the sum of the squared deviations from each
                      partition's mean is minimized.
            !*/
            {

                size_t best_i = range.begin;
                double best_score = -1;
                double left_sum = 0;
                double best_left_sum = y[idxs[range.begin].second];
                const auto size = range.size();
                size_t left_size = 0;
                for (size_t i = range.begin; i+1 < range.end; ++i)
                {
                    ++left_size;
                    left_sum += y[idxs[i].second];

                    // Don't split here because the next element has the same feature value so
                    // we can't *really* split here.
                    if (idxs[i].first==idxs[i+1].first)
                        continue;

                    const double right_sum = range.sumy-left_sum;

                    const double score = left_sum*left_sum/left_size + right_sum*right_sum/(size-left_size);

                    if (score > best_score)
                    {
                        best_score = score;
                        best_i = i;
                        best_left_sum = left_sum;
                    }
                }

                best_split_details result;
                result.score = best_score;
                result.left_sum = best_left_sum;
                result.right_sum = range.sumy-best_left_sum;
                result.split_idx = best_i+1; // one past the end of the left range
                result.split_threshold = (idxs[best_i].first+idxs[best_i+1].first)/2;

                return result;
            }

            static best_split_details find_best_split_among_feats(
                const feature_extractor& fe,
                const range_t& range,
                const std::vector<typename feature_extractor::feature>& feats,
                const std::vector<sample_type>& x,
                const std::vector<double>& y,
                std::vector<std::pair<float,uint32_t>>& idxs
            )
            {
                auto compare_first = [](const std::pair<float,uint32_t>& a, const std::pair<float,uint32_t>& b) { return a.first<b.first; };
                best_split_details best;
                for (auto& feat : feats)
                {
                    // Extract feature values for this feature and sort the indexes based on
                    // that feature so we can then find the best split.
                    for (auto i = range.begin; i < range.end; ++i)
                        idxs[i].first = fe.extract_feature_value(x[idxs[i].second], feat);

                    std::stable_sort(idxs.begin()+range.begin, idxs.begin()+range.end, compare_first);

                    auto split = find_best_split(range, y, idxs);

                    if (best < split)
                    {
                        best = split;
                        best.split_feature = feat;
                    }
                }

                // resort idxs based on winning feat
                for (auto i = range.begin; i < range.end; ++i)
                    idxs[i].first = fe.extract_feature_value(x[idxs[i].second], best.split_feature);
                std::stable_sort(idxs.begin()+range.begin, idxs.begin()+range.end, compare_first);

                return best;
            }

            std::string random_seed;
            size_t num_trees = 1000;
            double feature_subsampling_frac = 1.0/3.0;
            size_t min_samples_per_leaf = 5;
            feature_extractor_type fe_;
            bool verbose = false;
        };

    // ----------------------------------------------------------------------------------------

    }

    #endif // DLIB_RANdOM_FOREST_REGRESSION_H_