Gradient of the log probability

[arrjon]

It would be nice to be able to compute the gradient of the log probability (in the new BayesFlow version).

For example, with the jax-backend, I would like to be able to do something along this lines:

from jax import grad

def partial_objective(theta):
    log_prop = approximator.log_prob(
        data={'theta': theta, 'x': x},
        batch_size=1,
    )
    return log_prop[0]

grad(partial_objective)(theta)

The main reason this is not working at the moment, is the adapter:
TracerArrayConversionError: The numpy.ndarray conversion method __array__() was called on traced array with shape float32[1].
Any idea, how this could be done?

Edit: also just evaluating the log_prop at the moment works only if one does not use standardize in the adapter. I think this is related to #233. However, calling grad(approximator._log_prob(...)) circumventing the adapter works.

[stefanradev93]

Agreed that this is an important feature to have! We may want to implement an internal function log_prob_and_grad that does not trace the adapter transformations, but the naive implementation would give gradients wrt the transformed inputs, which may not be what one wants (e.g., gradients would also have a different scale).

[LarsKue]

I will look into what options we have to allow something like this. For now, you can use the protected _log_prob as a work-around. This returns a keras.backend.Tensor so the gradient should be enabled. The complete equivalent code should be:

def partial_objective(theta):
    data = approximator.adapter(data={"theta": theta, "x": x}, strict=False)
    data = keras.tree.map_structure(keras.ops.convert_to_tensor, data)
    log_prob = approximator._log_prob(**data)
    return log_prob[0]

[LarsKue]

We might implement this directly with a score method.