gaussian process.py

import numpy as np
import pandas as pd
data = pd.read_csv("C:\\Users\\NIU004\\OneDrive - CSIRO\\Desktop\\Mineral sorting\\Kansanshi\\multiscale.csv")
X = np.array(data['x']).reshape(-1,1)
y = np.array(data['y'])


# X = np.linspace(start=0, stop=10, num=1_000).reshape(-1, 1)
# y = np.squeeze(X * np.sin(X))
import matplotlib.pyplot as plt

plt.plot(X, y, label=r"$f(x) = x \sin(x)$", linestyle="dotted")
plt.legend()
plt.xlabel("$x$")
plt.ylabel("$f(x)$")
_ = plt.title("True generative process")


rng = np.random.RandomState(1)
training_indices = rng.choice(np.arange(y.size), size=6, replace=False)
X_train, y_train = X, y

from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF,Exponentiation,RationalQuadratic

kernel = Exponentiation(RationalQuadratic(), exponent=2)
gaussian_process = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=10)
gaussian_process.fit(X_train, y_train)
gaussian_process.kernel_

mean_prediction, std_prediction = gaussian_process.predict(X, return_std=True)

plt.plot(X, y, label=r"$f(x) = x \sin(x)$", linestyle="dotted")
plt.scatter(X_train, y_train, label="Observations")
plt.plot(X, mean_prediction, label="Mean prediction")
plt.fill_between(
    X.ravel(),
    mean_prediction - 1.96 * std_prediction,
    mean_prediction + 1.96 * std_prediction,
    alpha=0.5,
    label=r"95% confidence interval",
)
plt.legend()
plt.xlabel("$x$")
plt.ylabel("$f(x)$")
_ = plt.title("Gaussian process regression on noise-free dataset")