Prior draws in Your first Edward program

[raulsoutelo]

I am new to Edward.

The samples drawn from the prior in Your first Edward program (Jupyter notebook version) seem to be drawn from qW_0, qW_1, qb_0 and qb_1 instead of W_0, W_1, b_0 and b_1. Shouldn't it be the other way around? If I understood correctly, the latter are the priors and the former are the distributions intended to approximate the posterior. I don't see why the initial values of q() would have anything to do with the prior.

Thanks

[russellizadi]

Initial values of q() are exactly the priors and here W_0, W_1, b_0, and b_1 are ed.model objects used as the model parameters for the definition of network. Actually, during the inference as below, the initialized q() distributions will be taken as the prior: inference = ed.KLqp({W_0: qW_0, b_0: qb_0, W_1: qW_1, b_1: qb_1}, data={y: y_train})

[dustinvtran]

It's true that it's not technically the prior because it's not standard normally distributed. Rather, it's the variational distribution with parameters initialized randomly. Clarification of this in the notebook is welcome.

[raulsoutelo]

Thanks for the answers.

Sorry, I am not sure what you meant by 'it's not technically the prior because it's not standard normally distributed'.

I have reviewed the code (loss and gradients implemented in the build_reparam_entropy_loss_and_gradients function from edward/inferences/klqp.py) and, if I understood correctly, W_0, W_1, b_0 and b_1 are exactly the priors. They are used together with qW_0, qW_1, qb_0 and qb_1 in the kl_penalty term to calculate the kl divergence between the prior and the distribution q() used to approximate the posterior:

kl_penalty = tf.reduce_sum([ tf.reduce_sum(inference.kl_scaling.get(z, 1.0) * kl_divergence(qz, z)) for z, qz in six.iteritems(inference.latent_vars)])

Mentioning the use of the mean field approximation in the notebook would also be helpful.

I could modify both in case I am right.

[dustinvtran]

Looking purely at this line:

mus = tf.stack(
    [neural_network(x, qW_0.sample(), qW_1.sample(),
                    qb_0.sample(), qb_1.sample())
     for _ in range(10)])

This draws functions from the predictive distribution under samples from the variational distribution. Thus the first visualization is a figure given by the initialization of the variational distribution. That initialization is not fixed so that q starts as a standard normal.