Mixture model using GPs by summing Cov matrices


Is there a way to use gp.models.GPRegression implementation to build a mixture model that combines several GPs? Example: GP1 applies to time series [0, 0, 1, 1] and GP2 applies to time series [1, 1, 1, 0]. This means that for time series 2 (index starting at 0) I would like to add both GPs: GP1+GP2. For that, one possibility would be to sum the covariances instead of summing the GPs, as:

GP(\mu_1 + \mu_2 , K_1 + K_2) = GP(\mu_1, K_1) + GP(\mu_2 , K_2)

Is it doable using pyro GP API? I am pretty new to pyro.