Create regression_models_multivariate_cv.cpp
This commit is contained in:
Morten Hjorth-Jensen
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#include <iostream>
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#include <vector>
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#include <cmath>
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#include <random>
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#include <fstream>
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#include <numeric>
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#include <Eigen/Dense>
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#include <algorithm>
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using namespace std;
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using namespace Eigen;
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// Utility functions
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double mean_squared_error(const VectorXd& y_true, const VectorXd& y_pred) {
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return (y_true - y_pred).squaredNorm() / y_true.size();
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}
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double r2_score(const VectorXd& y_true, const VectorXd& y_pred) {
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double mean_y = y_true.mean();
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double total = (y_true.array() - mean_y).square().sum();
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double residual = (y_true - y_pred).squaredNorm();
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return 1.0 - residual / total;
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}
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void save_csv(const string& filename, const MatrixXd& X, const VectorXd& y_true, const VectorXd& y_pred) {
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ofstream file(filename);
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file << "X1,X2,...,True Y,Predicted Y\n";
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for (int i = 0; i < X.rows(); ++i) {
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for (int j = 0; j < X.cols(); ++j)
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file << X(i, j) << (j == X.cols() - 1 ? "," : ",");
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file << y_true(i) << "," << y_pred(i) << "\n";
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}
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file.close();
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}
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// k-fold cross-validation
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void cross_validate(const MatrixXd& X, const VectorXd& y, int k,
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function<void(const MatrixXd&, const VectorXd&)> fit_func,
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function<VectorXd(const MatrixXd&)> predict_func,
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double& avg_mse, double& avg_r2) {
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int n = X.rows();
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vector<int> indices(n);
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iota(indices.begin(), indices.end(), 0);
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random_shuffle(indices.begin(), indices.end());
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avg_mse = 0.0;
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avg_r2 = 0.0;
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for (int i = 0; i < k; ++i) {
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int start = i * n / k;
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int end = (i + 1) * n / k;
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vector<int> test_idx(indices.begin() + start, indices.begin() + end);
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vector<int> train_idx;
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for (int j = 0; j < n; ++j) {
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if (j < start || j >= end)
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train_idx.push_back(indices[j]);
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}
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MatrixXd X_train(train_idx.size(), X.cols());
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VectorXd y_train(train_idx.size());
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for (int j = 0; j < train_idx.size(); ++j) {
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X_train.row(j) = X.row(train_idx[j]);
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y_train(j) = y(train_idx[j]);
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}
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MatrixXd X_test(test_idx.size(), X.cols());
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VectorXd y_test(test_idx.size());
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for (int j = 0; j < test_idx.size(); ++j) {
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X_test.row(j) = X.row(test_idx[j]);
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y_test(j) = y(test_idx[j]);
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}
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fit_func(X_train, y_train);
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VectorXd y_pred = predict_func(X_test);
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avg_mse += mean_squared_error(y_test, y_pred);
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avg_r2 += r2_score(y_test, y_pred);
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}
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avg_mse /= k;
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avg_r2 /= k;
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}
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// Linear Regression
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class LinearRegression {
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public:
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VectorXd weights;
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void fit(const MatrixXd& X, const VectorXd& y) {
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MatrixXd X_bias(X.rows(), X.cols() + 1);
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X_bias << MatrixXd::Ones(X.rows(), 1), X;
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weights = (X_bias.transpose() * X_bias).ldlt().solve(X_bias.transpose() * y);
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}
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VectorXd predict(const MatrixXd& X) const {
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MatrixXd X_bias(X.rows(), X.cols() + 1);
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X_bias << MatrixXd::Ones(X.rows(), 1), X;
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return X_bias * weights;
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}
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};
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// Ridge Regression
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class RidgeRegression {
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public:
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VectorXd weights;
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double alpha;
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RidgeRegression(double alpha = 1.0) : alpha(alpha) {}
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void fit(const MatrixXd& X, const VectorXd& y) {
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MatrixXd X_bias(X.rows(), X.cols() + 1);
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X_bias << MatrixXd::Ones(X.rows(), 1), X;
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MatrixXd I = MatrixXd::Identity(X_bias.cols(), X_bias.cols());
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I(0, 0) = 0;
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weights = (X_bias.transpose() * X_bias + alpha * I).ldlt().solve(X_bias.transpose() * y);
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}
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VectorXd predict(const MatrixXd& X) const {
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MatrixXd X_bias(X.rows(), X.cols() + 1);
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X_bias << MatrixXd::Ones(X.rows(), 1), X;
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return X_bias * weights;
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}
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};
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// Kernel Ridge Regression
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class KernelRidgeRegression {
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public:
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double alpha, gamma;
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MatrixXd X_train;
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VectorXd alpha_vec;
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KernelRidgeRegression(double alpha = 1.0, double gamma = 1.0) : alpha(alpha), gamma(gamma) {}
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MatrixXd rbf_kernel(const MatrixXd& A, const MatrixXd& B) const {
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MatrixXd K(A.rows(), B.rows());
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for (int i = 0; i < A.rows(); ++i) {
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for (int j = 0; j < B.rows(); ++j) {
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K(i, j) = exp(-gamma * (A.row(i) - B.row(j)).squaredNorm());
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}
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}
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return K;
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}
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void fit(const MatrixXd& X, const VectorXd& y) {
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X_train = X;
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MatrixXd K = rbf_kernel(X, X);
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alpha_vec = (K + alpha * MatrixXd::Identity(K.rows(), K.cols())).ldlt().solve(y);
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}
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VectorXd predict(const MatrixXd& X) const {
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MatrixXd K = rbf_kernel(X, X_train);
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return K * alpha_vec;
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}
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};
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// Lasso Regression
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class LassoRegression {
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public:
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VectorXd weights;
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double alpha;
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int max_iter;
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double tol;
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LassoRegression(double alpha = 0.1, int max_iter = 1000, double tol = 1e-4)
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: alpha(alpha), max_iter(max_iter), tol(tol) {}
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void fit(const MatrixXd& X, const VectorXd& y) {
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MatrixXd X_bias(X.rows(), X.cols() + 1);
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X_bias << MatrixXd::Ones(X.rows(), 1), X;
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int n_samples = X_bias.rows();
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int n_features = X_bias.cols();
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weights = VectorXd::Zero(n_features);
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for (int iter = 0; iter < max_iter; ++iter) {
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VectorXd weights_old = weights;
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for (int j = 0; j < n_features; ++j) {
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double tmp = 0.0;
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for (int i = 0; i < n_samples; ++i) {
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double dot = 0.0;
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for (int k = 0; k < n_features; ++k) {
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if (k != j)
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dot += X_bias(i, k) * weights(k);
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}
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tmp += X_bias(i, j) * (y(i) - dot);
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}
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double rho = tmp;
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double norm_sq = X_bias.col(j).squaredNorm();
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if (j == 0) {
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weights(j) = rho / norm_sq;
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} else {
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if (rho < -alpha / 2)
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weights(j) = (rho + alpha / 2) / norm_sq;
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else if (rho > alpha / 2)
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weights(j) = (rho - alpha / 2) / norm_sq;
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else
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weights(j) = 0.0;
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}
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}
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if ((weights - weights_old).lpNorm<1>() < tol)
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break;
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}
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}
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VectorXd predict(const MatrixXd& X) const {
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MatrixXd X_bias(X.rows(), X.cols() + 1);
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X_bias << MatrixXd::Ones(X.rows(), 1), X;
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return X_bias * weights;
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}
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};
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int main() {
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// Generate multivariate synthetic data
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int n_samples = 150;
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int n_features = 3;
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MatrixXd X = MatrixXd::Random(n_samples, n_features);
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VectorXd y = 2.0 + X * VectorXd::LinSpaced(n_features, 1.0, 3.0) + VectorXd::Random(n_samples) * 0.5;
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LinearRegression linear;
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RidgeRegression ridge(1.0);
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LassoRegression lasso(0.1);
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KernelRidgeRegression kernel(1.0, 2.0);
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linear.fit(X, y);
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ridge.fit(X, y);
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lasso.fit(X, y);
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kernel.fit(X, y);
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VectorXd y_pred_linear = linear.predict(X);
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VectorXd y_pred_ridge = ridge.predict(X);
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VectorXd y_pred_lasso = lasso.predict(X);
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VectorXd y_pred_kernel = kernel.predict(X);
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save_csv("predictions_linear.csv", X, y, y_pred_linear);
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save_csv("predictions_ridge.csv", X, y, y_pred_ridge);
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save_csv("predictions_lasso.csv", X, y, y_pred_lasso);
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save_csv("predictions_kernel.csv", X, y, y_pred_kernel);
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cout << "Cross-validation results (5-fold):\n";
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double mse_avg, r2_avg;
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cross_validate(X, y, 5,
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[&](const MatrixXd& Xtr, const VectorXd& ytr){ linear.fit(Xtr, ytr); },
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[&](const MatrixXd& Xte){ return linear.predict(Xte); },
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mse_avg, r2_avg);
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cout << "Linear -> MSE: " << mse_avg << ", R2: " << r2_avg << endl;
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cross_validate(X, y, 5,
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[&](const MatrixXd& Xtr, const VectorXd& ytr){ ridge.fit(Xtr, ytr); },
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[&](const MatrixXd& Xte){ return ridge.predict(Xte); },
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mse_avg, r2_avg);
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cout << "Ridge -> MSE: " << mse_avg << ", R2: " << r2_avg << endl;
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cross_validate(X, y, 5,
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[&](const MatrixXd& Xtr, const VectorXd& ytr){ lasso.fit(Xtr, ytr); },
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[&](const MatrixXd& Xte){ return lasso.predict(Xte); },
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mse_avg, r2_avg);
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cout << "Lasso -> MSE: " << mse_avg << ", R2: " << r2_avg << endl;
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cross_validate(X, y, 5,
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[&](const MatrixXd& Xtr, const VectorXd& ytr){ kernel.fit(Xtr, ytr); },
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[&](const MatrixXd& Xte){ return kernel.predict(Xte); },
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mse_avg, r2_avg);
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cout << "Kernel -> MSE: " << mse_avg << ", R2: " << r2_avg << endl;
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return 0;
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}
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