Making predictions in intrinsic coregionalization model

[enushi]

I am writing a simple example for a GP with instrinsic coregionalization kernel for two tasks. I understand that the model calculates the posterior mean and variance for each task separately according to the way that they are indexed in variable X when the model fitting happens. For example my tasks are indexed 0 and 1 so when calling m.predict( np.array([[3, 0]]) ) it should return the posterior mean and variance of task 0 at input 3. However as you can see in the following code it returns a posterior mean and variance even when I put there an index that is not asssociated to any task (i.e., "-1" and "-2"). Where do those posterior means and variances come from?

import GPy
import numpy as np
import matplotlib.pyplot as plt

X = np.array([[ 1,  0], [ 2,  0], [ 3,  0], [ 4,  0], [ 1,  1], [ 2,  1], [ 3,  1], [ 4,  1]])

Y = np.array([[-0.23632664], [0.67736248], [-1.71536046], [2.01622779],
              [3.51775273], [-2.78539508], [2.19422611], [1.13307012]])

kernel = GPy.kern.RBF(input_dim=1, variance=1, lengthscale=1)

kernel_IC = kernel**GPy.kern.Coregionalize(input_dim=1, output_dim=2, rank=1)

m = GPy.models.GPRegression(X, Y, kernel_IC, normalizer=True)

m.Gaussian_noise.constrain_fixed(1)

# These are the posterior predictions for each task according to the provided input
mu_task_1, var_task_1 = m.predict(np.array([[ i,  0] for i in np.linspace(1, 4, 20) ]) )

mu_task_2, var_task_2 = m.predict(np.array([[ i,  1] for i in np.linspace(1, 4, 20) ]) )


# What is happening here, to which task do the posteriors mu and var belong?
mu_task_unknown_1, var_task_unknown_1 = m.predict(np.array([[ i,  -1] for i in np.linspace(1, 4, 20) ]) )
mu_task_unknown_2, var_task_unknown_2 = m.predict(np.array([[ i,  -2] for i in np.linspace(1, 4, 20) ]) )


plt.plot(np.linspace(1, 4, 20), mu_task_1, label='mu task 1', c='r')

plt.plot(np.linspace(1, 4, 20), mu_task_2, label='mu task 2', c='b')

plt.plot(np.linspace(1, 4, 20), mu_task_unknown_1, label='mu task ?1', c='y')
plt.plot(np.linspace(1, 4, 20), mu_task_unknown_2, label='mu task ?2', c='orange')

plt.legend()

[MartinBubel]

sorry can't dive in that deep atm but combining a vanilla GPy.models.GPRegression with a Coregionalize kernel seems suspicous to me, when there exists a GPy.models.GPCoregionalizedRegression version as shown in GPy/examples/cpregionalization_toy.py.