Error metrics between saved and loaded GPRegression model is different.

[Atulsingh92]

Hello,

I have created and saved the following two GPRegression models,

x_train, x_test = train_test_split(normalized_x, 
                                   train_size=training_size, 
                                   random_state=12, 
                                   shuffle=False)
# similarly for other inputs to m's

knu = GPy.kern.Matern32(input_dim=3, lengthscale=2)
kff = GPy.kern.Matern32(input_dim=3, lengthscale=2) 

m_nu = GPy.models.GPRegression(x_train, nu_train, knu)
m_nu.Gaussian_noise = 0.0   
m_nu.Gaussian_noise.variance = 1e-5 
m_nu.Gaussian_noise.variance.constrain_fixed() 
m_nu.optimize(max_iters = 2000, optimizer='lbfgs')
m_nu.optimize_restarts(num_restarts=5)

m_ff = GPy.models.GPRegression(x_train, ff_train, kff)
m_ff.Gaussian_noise = 0.0
m_ff.Gaussian_noise.variance = 1e-5
m_ff.Gaussian_noise.variance.constrain_fixed()
m_ff.optimize(max_iters = 2000, optimizer='lbfgs')
m_ff.optimize_restarts(num_restarts=5)

nu_gp = np.save('nugpr.npy', m_nu.param_array)
ff_gp = np.save('ffgpr.npy', m_ff.param_array)

The above gives me following error metrics

=======================================================
model			 RMSE 			 MAE 			 Rsquared
GP_Nu			0.0008			0.0440			0.99999
GP_ff			0.0008			0.0373			0.99998
=======================================================

Now, I try and load the above two files as mentioned here in a seperate code, where I have defined the same X, and y for both the models as I did to save them, and even with the same random state value as above. However, the same error metrics obtained in this case are as follows.

=======================================================
model			 RMSE 			 MAE 			 Rsquared
GP_Nu			0.0169			1.1933			0.99423
GP_ff			0.0205			1.5545			0.98807
=======================================================

So, my question is, if I haven't changed neither of my X, nor y, for either of my 2 gpr models, shouldn't I be getting the same error metrics after reloading the saved model?
(Yes, the saved model, on reload, shows the same parameters for the GPRregression models with print(m_nu) statements, however, the objective in loaded models is different than in saved model.)

Any pointers, on what could I look into?