粒子群优化高斯过程回归python代码

以下是使用粒子群优化算法进行高斯过程回归的Python代码示例：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import Matern

# 粒子群优化算法
def pso(func, n_dim, size_pop=20, max_iter=100, lb=-1, ub=1, w=0.8, c1=0.5, c2=0.5):
    # 初始化粒子位置和速度
    X = np.random.uniform(lb, ub, (size_pop, n_dim))
    V = np.random.rand(size_pop, n_dim) * 2 - 1
    fitness = np.zeros(size_pop)
    p_best = X.copy()
    p_best_fitness = np.zeros(size_pop)
    g_best = X[0].copy()
    g_best_fitness = 0

    for i in range(max_iter):
        for j in range(size_pop):
            fitness[j] = func(X[j])
            # 更新个体最优解
            if fitness[j] > p_best_fitness[j]:
                p_best[j] = X[j].copy()
                p_best_fitness[j] = fitness[j]
            # 更新全局最优解
            if fitness[j] > g_best_fitness:
                g_best = X[j].copy()
                g_best_fitness = fitness[j]

        # 更新粒子速度和位置
        V = w * V + c1 * np.random.rand(size_pop, n_dim) * (p_best - X) + c2 * np.random.rand(size_pop, n_dim) * (g_best - X)
        V = np.clip(V, -1, 1)
        X = X + V
        X = np.clip(X, lb, ub)

    return g_best, g_best_fitness

# 高斯过程回归
def gaussian_process(X, y, x_pred):
    kernel = Matern(length_scale=1.0, nu=1.5)
    gp = GaussianProcessRegressor(kernel=kernel, alpha=0.01, n_restarts_optimizer=10)
    gp.fit(X, y)
    y_pred, sigma = gp.predict(x_pred, return_std=True)
    return y_pred, sigma

# 目标函数
def fitness(X):
    x = X[0]
    y = X[1]
    z = np.sin(np.sqrt(x ** 2 + y ** 2)) / (np.sqrt(x ** 2 + y ** 2))
    return z

if __name__ == '__main__':
    X = np.random.rand(10, 2) * 2 - 1
    y = np.array([fitness(X[i]) for i in range(10)])
    x_pred = np.linspace(-1, 1, 100).reshape(-1, 1)

    # 使用粒子群优化算法选择最优超参数
    def func(hyperparameters):
        kernel = Matern(length_scale=hyperparameters[0], nu=hyperparameters[1])
        gp = GaussianProcessRegressor(kernel=kernel, alpha=0.01, n_restarts_optimizer=10)
        gp.fit(X, y)
        y_pred, sigma = gp.predict(x_pred, return_std=True)
        return -gp.log_marginal_likelihood()  # 最大化负对数边缘似然

    best_hyperparameters, best_fitness = pso(func, n_dim=2, max_iter=100)

    # 使用最优超参数进行高斯过程回归
    kernel = Matern(length_scale=best_hyperparameters[0], nu=best_hyperparameters[1])
    gp = GaussianProcessRegressor(kernel=kernel, alpha=0.01, n_restarts_optimizer=10)
    gp.fit(X, y)
    y_pred, sigma = gp.predict(x_pred, return_std=True)

    # 绘制结果
    plt.scatter(X[:, 0], X[:, 1], c=y)
    plt.colorbar()
    plt.xlim(-1, 1)
    plt.ylim(-1, 1)
    plt.title('Fitness')
    plt.show()

    plt.plot(x_pred, y_pred, label='Prediction')
    plt.fill_between(x_pred.ravel(), y_pred - sigma, y_pred + sigma, alpha=0.5)
    plt.scatter(X[:, 0], y, label='Observations')
    plt.legend()
    plt.title('Gaussian Process Regression')
    plt.show()

此代码演示了如何使用粒子群优化算法选择高斯过程回归模型的超参数，并绘制回归结果。