How to manually provide the gradient of log probability?

[Michael Prange]

I'm computing the log pdf in an external C++ routine and including it in Stan using increment_log_prob(). In order for the sampler to properly function, I understand that it also needs the gradient of this function. Is there an interface for me to provide this gradient?

I realize that Stan can automatically compute this gradient if I code everything in Stan, but my external libraries are too complicated to translate into Stan. These external libraries already provide gradients, so I only need an interface for including them in Stan.

Michael

[Bob Carpenter]

For all the gory details on the C++ and derivatives, see:

http://arxiv.org/abs/1509.07164

The in-between solution for external libraries without gradients
is to template out the scalar type. But if you have gradients,
then you want the above. Sorry it's so long --- you only need
the first bit on how to write simple functions.

For the interfacing with Stan itself, see:

https://github.com/stan-dev/stan/wiki/Contributing-New-Functions-to-Stan

It explains where things have to go in the symbol table to be
picked up by the Stan parser.

One of our to-do items for next year is making Stan extensible at
run time, which should be possible given that it's header only.

- Bob

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[Michael Prange]

The links you provide seem to be related to automatic differentiation. It would be easier for me if there were a set_gradient() function in Stan. Then I could call my external libraries for function values and gradient, and then within the Stan code call increment_log_prob() and set_gradient() with these values. 

To call these external libraries, I created some dummy functions within my Stan program and then edited the hpp file that stanc creates. This works well for the log probability, but I can't figure out how to input the gradient. Maybe this isn't possible, since I can't locate any gradient calculation within the stanc-generated hpp file.

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[Bob Carpenter]

> On Jan 5, 2016, at 5:18 PM, Michael Prange <pra...@alum.mit.edu> wrote:
>
> The links you provide seem to be related to automatic differentiation. It would be easier for me if there were a set_gradient() function in Stan.

There's not a direct way to do that. You need to
implement a function that integrates into our autodiff.

We provide a base class that makes it pretty easy --- you
really just need to set the gradients (on each component of
the value if it's a multivariate return function).

> Then I could call my external libraries for function values and gradient, and then within the Stan code call increment_log_prob() and set_gradient() with these values.
>
> To call these external libraries, I created some dummy functions within my Stan program and then edited the hpp file that stanc creates. This works well for the log probability, but I can't figure out how to input the gradient. Maybe this isn't possible, since I can't locate any gradient calculation within the stanc-generated hpp file.

It's all done using autodiff on the templated log_prob
function.

- Bob

[Michael Prange]

Thanks. I'll look into the links you provided me to learn how to do that.

[Bob Carpenter]

The key is the base class in stan-dev/math:

stan/math/rev/core/precomputed_gradients.hpp

That lets you just compute the gradients and store them
and compute the value and return it; then you just need
to wrap the whole thing up in a Stan function and expose it.

- Bob