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python - scikit-learn 高斯过程回归的错误输出

问题描述

我有一组数据(X,y)，其中X我的输入是二维的，y我的输出是一维的，每对(X,y)都有一个相应的非均匀噪声项。这是我应用高斯过程回归的一个工作示例：

import numpy as np 
from sklearn.gaussian_process import GaussianProcessRegressor 
from sklearn.gaussian_process.kernels import RBF, WhiteKernel, ConstantKernel as C  

lenX = 20
X1min = 0.
X1max = 1.
X2min = 0.
X2max = 2.
X1 = np.linspace(X1min,X1max,lenX)
X2 = np.linspace(X2min,X2max,lenX)
time_spacing = X2[1] - X2[0]

X = []
i = 0
while i < lenX:
    j = 0
    while j < lenX:
        X.append([X1[i],X2[j]])
        j = j + 1
    i = i + 1

X = np.array(X)

def fun_y(X):
    y = 5.*((np.sin(X[:,0]))**2.)*(np.e**(-(X[:,1]**2.)))
    y[y < 0.001] = 0.0
    return y

y = fun_y(X)
noise = 0.1*y #0.2/y + 0.2#*np.linspace(1.0,0.1,len(X))

len_x1 = 10
len_x2 = 100
x1_min = X1min
x2_min = X2min
x1_max = X1max
x2_max = X2max
x1 = np.linspace(x1_min, x1_max, len_x1)
x2 = np.linspace(x2_min, x2_max, len_x2) 

i = 0 
inputs_x = []
while i < len(x1):
    j = 0
    while j < len(x2):
        inputs_x.append([x1[i],x2[j]])
        j = j + 1
    i = i + 1
inputs_x_array = np.array(inputs_x)   #simply a set of inputs I want to predict at

kernel = C(1.0, (1e-10, 1000)) * RBF(length_scale = [1., 1.], length_scale_bounds=[(1e-5, 1e5),(1e-7, 1e7)]) \
        + WhiteKernel(noise_level=1, noise_level_bounds=(1e-10, 1e10)) #\

gp = GaussianProcessRegressor(kernel=kernel, alpha=noise ** 2, n_restarts_optimizer=100) 

# Fit to data using Maximum Likelihood Estimation of the parameters
gp.fit(X, y.reshape(-1,1)) #removing reshape results in a different error 

y_pred_index, y_pred_sigma_index = gp.predict(inputs_x_array, return_std=True)

尽管使用了许多内核变体，但在尝试找到超参数与数据的最佳拟合时，我继续观察收敛错误：

/.local/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:481: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([ 3.89194489e-03,  9.32690036e-03, -0.00000000e+00,  6.42836597e+01]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 128, 'nit': 26, 'warnflag': 2}
  ConvergenceWarning)

我试图添加/乘以 RBF 内核，改变超参数的边界，并 include WhiteNoise，但我的方法似乎都不起作用。关于我可以做些什么来避免这个错误并选择一个好的内核来拟合数据的任何想法？

标签： pythonmachine-learningscikit-learnregression

解决方案

我不确定这对您的数据来说是否是一个好的内核，但只是通过限制超参数界限，我确实设法摆脱了ConvergenceWarning：

kernel = C(1.0, (1e-3, 1e3)) * RBF(length_scale = [.1, .1], length_scale_bounds=[(1e-2, 1e2),(1e-2, 1e2)]) \
        + WhiteKernel(noise_level=1e-5, noise_level_bounds=(1e-10, 1e-4))

要求gp.kernel_.get_params(deep=True)收益

{'k1': 1.51**2 * RBF(length_scale=[0.843, 1.15]),
 'k1__k1': 1.51**2,
 'k1__k1__constant_value': 2.275727769273166,
 'k1__k1__constant_value_bounds': (0.001, 1000.0),
 'k1__k2': RBF(length_scale=[0.843, 1.15]),
 'k1__k2__length_scale': array([0.84331346, 1.15091614]),
 'k1__k2__length_scale_bounds': [(0.01, 100.0), (0.01, 100.0)],
 'k2': WhiteKernel(noise_level=1.4e-08),
 'k2__noise_level': 1.403204609548082e-08,
 'k2__noise_level_bounds': (1e-10, 0.0001)}

另见此注。

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