I am trying to perform inference with a specific model in pyro which leads me to a more general question about Pyro's ability to perform inference in models where the log-pdf is not easily calculable.
I am trying to modify the SVI Part I tutorial to model a problem where a latent variable is the
max of two other latent variables. It seems to me that this violates the "we can compute the pointwise log pdf pi" requirement that is mentioned in the tutorials for doing variational inference.
- Would I need to find a bijective approximation for the max so that the log-likelihood can be computed?
- For general stochastic functions, i.e., with a compositional structure
p_i(x_i| f(z_i)) where the functions
f are complicated and perhaps non-invertible, how does pyro perform inference? Or are such functions disallowed?
In particular consider the following model
z1 ~ Normal(mu1, sigma1)
z2 ~ Normal(mu2, sigma2)
x ~ Normal(z1^2 + z2^2, sigma=1)
And my inference task is to estimate
E[z1|x = 5]. How does Pyro compute the pdf
P(x, z1, z2) to perform variational inference?
Any help or pointers would be greatly appreciated.