python实现贝叶斯优化混合核极限学习机回归预测

贝叶斯优化混合核极限学习机回归预测是一种机器学习算法，可以用Python实现。下面是一个简单的实现过程：

1. 安装必要的Python库

pip install numpy scipy scikit-learn matplotlib

2. 导入必要的库

import numpy as np
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import Matern, WhiteKernel, ConstantKernel
from sklearn.metrics import mean_squared_error
from scipy.optimize import minimize

3. 定义模型

class BayesianOptimizationELM():
    def __init__(self, kernel, alpha, n_hidden):
        self.kernel = kernel
        self.alpha = alpha
        self.n_hidden = n_hidden

    def fit(self, X, y):
        self.X = X
        self.y = y
        self.gp = GaussianProcessRegressor(kernel=self.kernel, alpha=self.alpha)
        self.gp.fit(X, y)
        self.beta = self.gp.predict(X)

        H = np.random.normal(size=[self.X.shape[0], self.n_hidden])
        H = np.concatenate([H, np.ones([self.X.shape[0], 1])], axis=1)
        self.H = H

        self.W = np.dot(np.linalg.pinv(H), self.beta)

    def predict(self, X):
        H = np.random.normal(size=[X.shape[0], self.n_hidden])
        H = np.concatenate([H, np.ones([X.shape[0], 1])], axis=1)
        return np.dot(H, self.W)

4. 定义核函数

kernel = ConstantKernel(1.0, (1e-3, 1e3)) * Matern(length_scale=2, nu=3/2) + WhiteKernel(noise_level=1, noise_level_bounds=(1e-10, 1e+1))

5. 定义目标函数

def objective(params):
    alpha, n_hidden = params
    model = BayesianOptimizationELM(kernel=kernel, alpha=alpha, n_hidden=int(n_hidden))
    model.fit(X_train, y_train)
    y_pred = model.predict(X_val)
    return mean_squared_error(y_val, y_pred)

6. 进行优化

res = minimize(objective, [1, 10], bounds=((1e-5, 1e5), (1, 100)))
alpha, n_hidden = res.x

7. 使用最优的参数进行预测

model = BayesianOptimizationELM(kernel=kernel, alpha=alpha, n_hidden=int(n_hidden))
model.fit(X_train, y_train)
y_pred = model.predict(X_test)

这样就可以用Python实现贝叶斯优化混合核极限学习机回归预测了。