Sampling from two dependent variables / distributions

Misc.
1

I have two dependent variables x and y

x = pyro.sample('x', torch.distributions.Normal(2, 5))
y = pyro.sample('y', torch.distributions.Normal(3, 4))

I would like to sample from y based on the dependency with x. How do I do this exactly in pyro?

2

Hi @ebtudpy,

First note that you should use Pyro’s distributions (which wrap PyTorch’s) rather than raw PyTorch distributions when using Pyro

- torch.distributions.Normal(2, 5)
+ pyro.distributions.Normal(2, 5)

Now if you’d like y to depend on x you’ll just need to make the parameters of y depend somehow on x it’s up to you how. Here’s an example where y's prior mean is equal to x:

import pyro.distributions as dist
x = pyro.sample('x', dist.Normal(2, 5))
y = pyro.sample('y', dist.Normal(x, 4))

Here’s an example where both the location (mean) and scale (standard deviation) parameter of y depend on a complicated function of x.

f = torch.nn.linear(1, 2)
pyro.module("f", f)
x = pyro.sample('x', dist.Normal(2, 5))
loc, log_scale = f(x.unsqueeze(-1)).unbind(-1)
scale = log_scale.exp()
y = pyro.sample('y', dist.Normal(loc, scale))

Good luck!

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