`X` in pyro GPLVM - why does it have a scale of one?

aditya · October 12, 2020, 10:08pm

On this line in the pyro GPLVM code:

pyro-ppl/pyro/blob/dev/pyro/contrib/gp/models/gplvm.py#L65


      
              model object. Note that ``base_model.X`` will be the initial value for the
              variational parameter ``X_loc``.
          """
          
          
def __init__(self, base_model):
              super().__init__()
              if base_model.X.dim() != 2:
                  raise ValueError(
                      "GPLVM model only works with 2D latent X, but got "
                      "X.dim() = {}.".format(base_model.X.dim())
                  )
              self.base_model = base_model
          
          
    self.X = PyroSample(
                  dist.Normal(base_model.X.new_zeros(base_model.X.shape), 1.0).to_event()
              )
              self.autoguide("X", dist.Normal)
              self.X_loc.data = base_model.X
          
          
@pyro_method
          def model(self):

… why is the scale of X set to 1?

fehiepsi · October 13, 2020, 6:28am

@aditya You can change it to

gplvm.X = PyroSample(dist.Normal(X.new_zeros(X.shape), 0.1).to_event())

if you want. The implementation is just an example of how to put a prior on a parameter for gp models (the gplvm tutorial does not even use GPLVM), so 1 is used for simplicity. There is no other reason for why 1 is used there.

aditya · October 13, 2020, 7:22am

I see, so it is a prior. If I use my own variational guide, is there any change that I’d have to make to gplvm.X?

fehiepsi · October 14, 2020, 12:20am

I think that “no”. Your code with VarParams in other thread looks correct to me.