gbdt回归算法matlab代码

以下是基于MATLAB实现的GBDT回归算法代码。其中包含了数据集的读取、模型构建和预测等步骤。需要注意的是，该代码并非通用的，需要根据具体的数据集和模型进行修改。

% 读取数据集
data = load('data.txt');
X = data(:,1:end-1);
Y = data(:,end);

% 设置参数
param.num_trees = 50; % 树的数目
param.depth = 5; % 树的深度
param.learn_rate = 0.1; % 学习率
param.num_features = size(X,2); % 特征数目

% 初始化模型
model.trees = cell(param.num_trees,1);
model.bias = mean(Y);

% 训练模型
for i = 1:param.num_trees
    % 计算残差
    if i == 1
        F = zeros(size(Y));
    else
        for j = 1:length(Y)
            F(j) = Y(j) - model.bias - predict_gbdt(X(j,:),model.trees,i-1,param);
        end
    end
    
    % 构建决策树
    tree = build_tree(X,F,param);
    
    % 更新模型
    model.trees{i} = tree;
end

% 预测
y_pred = zeros(length(Y),1);
for i = 1:length(Y)
    y_pred(i) = model.bias + predict_gbdt(X(i,:),model.trees,param.num_trees,param);
end

% 计算误差
mse = mean((Y-y_pred).^2);

其中，`build_tree` 函数用于构建一棵决策树，`predict_gbdt` 函数用于预测，具体实现可以参考下面的代码。

function tree = build_tree(X,F,param)
% 构建一棵决策树

num_samples = size(X,1);
num_features = param.num_features;
max_depth = param.depth;

% 初始化节点
node.X = X;
node.F = F;
node.depth = 1;

% 递归分裂节点
tree = split_node(node,param,max_depth,num_features);

end

function tree = split_node(node,param,max_depth,num_features)
% 分裂节点

X = node.X;
F = node.F;
depth = node.depth;

% 终止条件
if depth > max_depth || length(F) < 2
    tree.is_leaf = true;
    tree.output = mean(F);
    return;
end

% 选择最佳分裂特征
best_feature = 0;
best_threshold = 0;
best_loss = inf;
for i = 1:num_features
    [threshold,loss] = find_threshold(X(:,i),F,param.learn_rate);
    if loss < best_loss
        best_feature = i;
        best_threshold = threshold;
        best_loss = loss;
    end
end

% 分裂节点
left_mask = X(:,best_feature) <= best_threshold;
right_mask = ~left_mask;
left_node.X = X(left_mask,:);
left_node.F = F(left_mask);
left_node.depth = depth + 1;
right_node.X = X(right_mask,:);
right_node.F = F(right_mask);
right_node.depth = depth + 1;

tree.is_leaf = false;
tree.feature = best_feature;
tree.threshold = best_threshold;
tree.left_child = split_node(left_node,param,max_depth,num_features);
tree.right_child = split_node(right_node,param,max_depth,num_features);

end

function [threshold,loss] = find_threshold(feature,F,learn_rate)
% 寻找最佳分裂阈值

[feature,idx] = sort(feature);
F = F(idx);
cumsum_F = cumsum(F);
cumsum_F2 = cumsum(F.^2);
sum_F = cumsum_F(end);
sum_F2 = cumsum_F2(end);

best_loss = inf;
best_threshold = 0;
for i = 1:length(feature)-1
    left_sum_F = cumsum_F(i);
    right_sum_F = sum_F - left_sum_F;
    left_sum_F2 = cumsum_F2(i);
    right_sum_F2 = sum_F2 - left_sum_F2;
    left_num_samples = i;
    right_num_samples = length(feature) - i;
    left_mean_F = left_sum_F / left_num_samples;
    right_mean_F = right_sum_F / right_num_samples;
    left_var_F = left_sum_F2 / left_num_samples - left_mean_F^2;
    right_var_F = right_sum_F2 / right_num_samples - right_mean_F^2;
    loss = left_var_F + right_var_F - (left_sum_F^2/left_num_samples + right_sum_F^2/right_num_samples)^2;
    if loss < best_loss
        best_loss = loss;
        best_threshold = (feature(i) + feature(i+1)) / 2;
    end
end

threshold = best_threshold;
loss = best_loss * learn_rate;

end

function y_pred = predict_gbdt(X,trees,num_trees,param)
% 预测

y_pred = 0;
for i = 1:num_trees
    y_pred = y_pred + predict_tree(X,trees{i});
end
y_pred = y_pred * param.learn_rate;

end

function y_pred = predict_tree(X,tree)
% 预测一棵决策树

if tree.is_leaf
    y_pred = tree.output;
else
    if X(tree.feature) <= tree.threshold
        y_pred = predict_tree(X,tree.left_child);
    else
        y_pred = predict_tree(X,tree.right_child);
    end
end

end

希望能对你有所帮助。