Gpytorch: [Question] What is the difference between "model(test_x)" and "likelihood(model(test_x))" for prediction?

[mohammad-saber]

Hi,
I am trying regression with GPyTorch following the example in the documentation.

In the example, there are two ways to get mean and variance of prediction.

1)

f_preds = model(test_x)

2)

y_preds = likelihood(model(test_x))

I noticed that the mean of prediction is the same when I use model(test_x) and likelihood(model(test_x)), but variance is different. I didn't understand the reason.
More generally, I didn't understand the difference between model(test_x) and likelihood(model(test_x)).

Could you please guide me on this issue?

[jacobrgardner]

In the regression setting, the former does not include the likelihood noise (it is the latent variance) and the latter does include it.

[mohammad-saber]

Thank you.

Is likelihood noise similar to the noise that we can add to the kernel? For example, when I define a kernel as below:

RBFKernel() + WhiteNoiseKernel()

I checked the list of kernels. I couldn't find "WhiteNoiseKernel()". It seems that GPyTorch adds noise automatically to the kernel. Is my understanding correct?

[gpleiss]

Philosophically, it is different (is the "noise" due to your data observations or due to your uncertainty about your model). Practically, it is the same.

WhiteNoiseKernel has been replaced by FixedNoiseGaussianLikelihood. This adds different observational noise for each data point. The standard GaussianLikelihood adds the same observational noise to each data point.