多元岭回归 C++有截距和预测的带类实现 及案例

以下是一个简单的多元岭回归的 C++ 类实现，包含截距和预测功能：

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

class RidgeRegression {
private:
    vector<double> coef; // 回归系数
    double intercept; // 截距
    double alpha; // 防止过拟合的参数
    int n_samples; // 样本数量
    int n_features; // 特征数量

public:
    RidgeRegression(double alpha = 1.0) {
        this->alpha = alpha;
    }

    void fit(vector<vector<double>> &X, vector<double> &y) {
        n_samples = X.size();
        n_features = X[0].size();

        // 计算 X.T * X
        vector<vector<double>> xtx(n_features, vector<double>(n_features, 0.0));
        for (int i = 0; i < n_samples; ++i) {
            for (int j = 0; j < n_features; ++j) {
                for (int k = 0; k < n_features; ++k) {
                    xtx[j][k] += X[i][j] * X[i][k];
                }
            }
        }

        // 加上 alpha * I
        for (int i = 0; i < n_features; ++i) {
            xtx[i][i] += alpha;
        }

        // 计算 (X.T * X + alpha * I).inv * X.T
        vector<vector<double>> inv_xtx_x(n_features, vector<double>(n_samples, 0.0));
        for (int i = 0; i < n_features; ++i) {
            for (int j = 0; j < n_samples; ++j) {
                for (int k = 0; k < n_features; ++k) {
                    inv_xtx_x[i][j] += xtx[i][k] * X[j][k];
                }
                inv_xtx_x[i][j] /= n_samples;
            }
        }

        // 计算回归系数和截距
        coef.resize(n_features);
        for (int i = 0; i < n_features; ++i) {
            for (int j = 0; j < n_samples; ++j) {
                coef[i] += inv_xtx_x[i][j] * y[j];
            }
        }
        intercept = 0.0;
        for (int i = 0; i < n_samples; ++i) {
            intercept += y[i];
        }
        intercept /= n_samples;
        for (int i = 0; i < n_features; ++i) {
            intercept -= coef[i] * X[0][i];
        }
    }

    double predict(vector<double> &x) {
        double y_pred = intercept;
        for (int i = 0; i < n_features; ++i) {
            y_pred += coef[i] * x[i];
        }
        return y_pred;
    }
};

下面是一个使用该类的示例，用于预测房价：

int main() {
    // 样本数量和特征数量
    int n_samples = 5;
    int n_features = 2;

    // 训练数据
    vector<vector<double>> X(n_samples, vector<double>(n_features));
    vector<double> y(n_samples);
    X[0] = {0.18, 0.89};
    X[1] = {1.0, 0.26};
    X[2] = {0.92, 0.11};
    X[3] = {0.07, 0.37};
    X[4] = {0.85, 0.16};
    y = {109.85, 155.72, 137.66, 76.17, 139.75};

    // 创建 RidgeRegression 对象并拟合数据
    RidgeRegression rr(1.0);
    rr.fit(X, y);

    // 预测房价
    vector<double> x(n_features);
    x = {0.75, 0.5};
    double y_pred = rr.predict(x);
    cout << "Predicted price: " << y_pred << endl;

    return 0;
}

在这个示例中，我们使用了 5 个样本和 2 个特征来拟合一个多元线性回归模型，并且使用 Ridge Regression 算法来防止过拟合。最后，我们使用拟合好的模型来预测一个新的房价。