高斯过程回归java代码

以下是一个简单的高斯过程回归的Java代码示例：

import org.apache.commons.math3.distribution.NormalDistribution;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.stat.correlation.Covariance;

public class GaussianProcessRegression {
    private RealMatrix X;
    private RealMatrix y;
    private double[] theta;

    public GaussianProcessRegression(RealMatrix X, RealMatrix y, double[] theta) {
        this.X = X;
        this.y = y;
        this.theta = theta;
    }

    public double predict(double[] x) {
        RealMatrix K = calculateCovarianceMatrix(X, X, theta);
        RealMatrix Ks = calculateCovarianceMatrix(X, new Array2DRowRealMatrix(x), theta);
        RealMatrix Kss = calculateCovarianceMatrix(new Array2DRowRealMatrix(x), new Array2DRowRealMatrix(x), theta);

        RealMatrix K_inv = new LUDecomposition(K).getSolver().getInverse();        RealMatrix mu = Ks.transpose().multiply(K_inv).multiply(y);
        RealMatrix sigma = Kss.subtract(Ks.transpose().multiply(K_inv).multiply(Ks));
        double std = Math.sqrt(sigma.getEntry(0, 0));

        NormalDistribution normal = new NormalDistribution();
        double u = normal.inverseCumulativeProbability(0.5 * (1 + mu.getEntry(0, 0) / std));
        double l = normal.inverseCumulativeProbability(0.5 * (1 - mu.getEntry(0, 0) / std));

        return (u + l) / 2;
    }

    private RealMatrix calculateCovarianceMatrix(RealMatrix X1, RealMatrix X2, double[] theta) {
        int n1 = X1.getRowDimension();
        int n2 = X2.getRowDimension();
        RealMatrix K = new Array2DRowRealMatrix(n1, n2);

        for (int i = 0; i < n1; i++) {
            for (int j = 0; j < n2; j++) {
                double[] x1 = X1.getRow(i);
                double[] x2 = X2.getRow(j);
                double k = calculateKernel(x1, x2, theta);
                K.setEntry(i, j, k);
            }
        }

        return K;
    }

    private double calculateKernel(double[] x1, double[] x2, double[] theta) {
        double k = 0;
        for (int i = 0; i < x1.length; i++) {
            k += Math.pow((x1[i] - x2[i]) / theta[i], 2);
        }
        return Math.exp(-0.5 * k);
    }

    public static void main(String[] args) {
        RealMatrix X = new Array2DRowRealMatrix(new double[][]{{0}, {1}, {2}, {3}, {4}});
        RealMatrix y = new Array2DRowRealMatrix(new double[][]{{0}, {1}, {4}, {9}, {16}});
        double[] theta = new double[]{1};

        GaussianProcessRegression gpr = new GaussianProcessRegression(X, y, theta);
        double[] x = new double[]{2.5};
        double y_pred = gpr.predict(x);
        System.out.println("Predicted value: " + y_pred);
    }
}

这个代码示例使用了Apache Commons Math库来进行矩阵计算和概率分布计算。它实现了一个简单的高斯过程回归模型，可以对给定的输入数据进行预测。