enable manual specification of model gradient and wrapper for Stan models

[dustinvtran]

Our algorithms perform inference on a Model class and requires only one thing from the class: the method log_prob(self, zs), which takes a n_minibatch x d matrix of latent variables z and outputs a vector [log p(x, z_{1,:}), ..., log p(x, z_{n_minibatch,:})]^T. (Any data x is fixed and stored inside the class.)

In cases where we use the reparameterization gradient, we also require the gradient of the log_prob() function with respect to z. This is done automatically if log_prob() is implemented in TensorFlow.

We want to extend this to a manual specification of the gradient. The motivation is twofold:

1. we want to be able to specify the model with a Stan program and use its log_prob() and grad_log_prob functions.
2. a user may not be familiar with TensorFlow and prefers to implement the model in vanilla numpy/scipy, in which they will hand-derive the gradient;

All of this should go behind the scenes: the algorithms will simply check if the grad_log_prob() method exists. If it exists, it uses the function. If it doesn't exist, then it tries to autodiff it using TensorFlow. This solves 1. To solve 2, we also require a wrapper than wraps a Stan program and data into this class with the two methods log_prob and grad_log_prob.

[dustinvtran]

53242c0

• Inference on models written in Stan or NumPy/SciPy are now supported using the score function gradient.

The remaining task is to enable automatic model gradients, so the reparameterization gradient is also available.

[dustinvtran]

I'm closing this issue and making another, which refers directly to the issue of enabling gradients in all the model wrappers. see #163