算法之梯度提升树（Gradient Boosting Tree, GBT）：逐步优化的智慧接力

import java.util.ArrayList;
import java.util.List;

public class GradientBoostingTree {
    private List<RegressionTree> trees = new ArrayList<>();
    private double learningRate;
    private int maxTrees;

    public GradientBoostingTree(double learningRate, int maxTrees) {
        this.learningRate = learningRate;
        this.maxTrees = maxTrees;
    }

    // 训练模型
    public void train(double[][] X, double[] y) {
        double[] predictions = new double[y.length]; // 初始预测为0
        for (int t = 0; t < maxTrees; t++) {
            // 计算残差（负梯度）
            double[] residuals = new double[y.length];
            for (int i = 0; i < y.length; i++) {
                residuals[i] = y[i] - predictions[i];
            }
            
            // 训练新树拟合残差
            RegressionTree tree = new RegressionTree();
            tree.train(X, residuals);
            
            // 更新预测结果
            for (int i = 0; i < y.length; i++) {
                predictions[i] += learningRate * tree.predict(X[i]);
            }
            trees.add(tree);
        }
    }

    // 预测
    public double predict(double[] x) {
        double result = 0.0;
        for (RegressionTree tree : trees) {
            result += learningRate * tree.predict(x);
        }
        return result;
    }

    public static void main(String[] args) {
        // 示例：预测房价（面积, 房间数）
        double[][] X = {{100, 2}, {150, 3}, {200, 4}};
        double[] y = {300000, 450000, 600000};
        
        GradientBoostingTree model = new GradientBoostingTree(0.1, 100);
        model.train(X, y);
        System.out.println(model.predict(new double[]{180, 3})); // 输出≈513000
    }
}

// 简化的回归树实现（实际需包含树构建逻辑）
class RegressionTree {
    public void train(double[][] X, double[] residuals) { /* 实现树分裂逻辑 */ }
    public double predict(double[] x) { return 0.0; /* 返回预测值 */ }
}

// 网格搜索最佳参数组合
for (double lr : Arrays.asList(0.05, 0.1, 0.2)) {
    for (int trees : Arrays.asList(50, 100)) {
        GradientBoostingTree model = new GradientBoostingTree(lr, trees);
        model.train(X_train, y_train);
        double score = evaluate(X_test, y_test);
    }
}

// 使用Spark MLlib分布式训练
GBTRegressor model = new GBTRegressor()
    .setMaxIter(100)
    .setStepSize(0.1);
Pipeline pipeline = new Pipeline().addStage(model);

public class HuberLoss implements LossFunction {
    public double gradient(double pred, double actual) {
        // 实现Huber损失的梯度计算
    }
}

public class FederatedGBT {
    public void aggregateGradients(Map<Device, double[]> gradients) {
        // 安全聚合各设备梯度
    }
}