A question about white noise

[HanyangHenry-Wang]

I define a kernel: GPy.kern.RBF(input_dim=1)+ GPy.kern.White(input_dim=1) and set the variance to be 16: m.kern.white.variance.fix(16). At the same time, I also set Gaussian_noise.variance to be 0: m.Gaussian_noise.variance.fix(0.0). Then I trainned the model and printed the variance of the observed point. Since I set the variance of white noise to be 16, I would expected the printed varaince is also 16. However, it is not. Could anyone please give me any hints about why this would happen?

The code is shown below:

import GPy
import numpy as np
from matplotlib import pyplot as plt
import math
from matplotlib import cm
import matplotlib;matplotlib.rcParams['figure.figsize'] = (8,5)
from scipy.stats import norm

X_sample = np.array([65.90839098, 3.42578164, 94.28049275, 67.15595707, 62.12945463,
86.23608086, 49.95824059, 61.69834602, 65.60985616, 82.10544337,
17.78284136, 10.73349743, 52.72038104, 55.16478482, 80.37307872,
61.67559055, 38.32262376, 43.63278254, 30.95413331, 48.02303168,
30.07533029, 8.54384364, 75.36399076, 33.44540949, 77.50964475,
69.56168432, 12.7087159 , 83.97033861, 26.95214725, 74.85074055,
93.37182696, 79.55644837, 74.4371696 , 97.7020137 , 69.99849814,
85.39974238, 6.73668038, 97.92367334, 27.80713194, 27.16078012,
97.00206296, 69.60144159, 66.13993086, 46.34517758, 49.20531501,
34.58281279, 7.82319509, 5.29995882, 8.27315924, 12.9793999 ])

Y_sample = np.array([ 1.9318772 , 0.48676711, 0.1598817 , 0.56495963, 0.87248468,
0.30614613, 3.70536682, 1.34703027, 0.86764436, 0.26602824,
1.76858056, 0.83367018, 1.92433637, 1.99344327, 0.34902601,
0.8204964 , 25.46785322, 7.79681189, 18.73552574, 1.77590455,
17.82596369, 0.56422196, 0.28723818, 38.42662269, 0.22558383,
0.23646561, 0.47469529, 0.09767295, 6.02168149, 0.14659177,
0.07567237, 0.18865004, 0.27170018, 0.10783688, 0.40515622,
0.17372068, 0.31550655, 0.09527466, 1.64899802, 1.10552056,
0.10999749, 0.63947079, 0.98716834, 32.41018846, 18.32256269,
3.57756452, 0.4165166 , 0.41004365, 0.48388013, 0.60502143])

#define the kernel and train the GP model
k1 = GPy.kern.RBF(input_dim=1)+ GPy.kern.White(input_dim=1)
m = GPy.models.GPRegression(X_sample.reshape(-1, 1), Y_sample.reshape(-1, 1), k1)
m.Gaussian_noise.variance.fix(0.0)
m.kern.white.variance.fix(16) #I define the variance to be 16

m.optimize()

pre_var = np.array([m.predict(np.array([x]).reshape(1, 1))[1] for x in X_sample])
print(pre_var) #I expect the variance to be 16 because that is what I defined, but the result is not