lp in Stan's variational interface

[Jiqiang Guo]

Two questions:

lp in the output file is always zero?  Is this lp the same as lp__? 

Please see output below.

Jiqiang 

$ ./bernoulli variational data file=bernoulli.data.R output file=v.csv

 method = variational

   variational

     algorithm = meanfield (Default)

       meanfield

     iter = 10000 (Default)

     grad_samples = 1 (Default)

     elbo_samples = 100 (Default)

     eta_adagrad = 0.10000000000000001 (Default)

     tol_rel_obj = 0.01 (Default)

     eval_elbo = 100 (Default)

     output_samples = 1000 (Default)

 id = 0 (Default)

 data

   file = bernoulli.data.R

 init = 2 (Default)

 random

   seed = 2143042049

 output

   file = v.csv

   diagnostic_file =  (Default)

   refresh = 100 (Default)

This is Automatic Differentiation Variational Inference.

(EXPERIMENTAL ALGORITHM: expect frequent updates to the procedure.)

Gradient evaluation took 0 seconds

1000 iterations under these settings should take 0 seconds.

Adjust your expectations accordingly!

  iter       ELBO   delta_ELBO_mean   delta_ELBO_med   notes

     0     -2e+01             1.000            1.000

   100       -6.3             1.197            1.393

   200       -6.6             0.812            1.000   MAY BE DIVERGING... INSPECT ELBO

   300       -6.2             0.626            1.000   MAY BE DIVERGING... INSPECT ELBO

   400       -6.3             0.504            0.067   MAY BE DIVERGING... INSPECT ELBO

   500       -6.3             0.421            0.067

   600       -6.2             0.363            0.042

   700       -6.3             0.320            0.042

   800       -6.3             0.285            0.020

   900       -6.3             0.257            0.020

  1000       -6.1             0.160            0.020

  1100       -6.3             0.023            0.020

  1200       -6.2             0.020            0.017

  1300       -6.2             0.014            0.015

  1400       -6.5             0.016            0.015

  1500       -6.2             0.020            0.020

  1600       -6.2             0.019            0.020

  1700       -6.2             0.017            0.013

  1800       -6.2             0.018            0.013

  1900       -6.2             0.019            0.013

  2000       -6.3             0.017            0.012

  2100       -6.4             0.016            0.012

  2200       -6.2             0.018            0.012

  2300       -6.3             0.018            0.012

  2400       -6.2             0.015            0.012

  2500       -6.3             0.010            0.010   MEDIAN ELBO CONVERGED

$ R -q -e 'a<-read.csv("v.csv",header=T,comment.char="#"); str(a)'

> a<-read.csv("v.csv",header=T,comment.char="#"); str(a)

'data.frame':   1001 obs. of  2 variables:

 $ lp   : int  0 0 0 0 0 0 0 0 0 0 ...

 $ theta: num  0.214 0.222 0.109 0.264 0.347 ...

>

[Dustin Tran]

Yup. The log probability (lp) is not well-defined there for variational inference. Recall the solved parameters are parameters of the variational family, not the posterior, and the first line of the table simply takes the mean of the variational distribution, c.f., reference manual. Thus as a hack because Stan requires at least that column, we left it there while writing 0.

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[Jiqiang Guo]

Got it.  Thanks.

I meant to suggest adding two underscores to lp.

Jiqiang 

[Bob Carpenter]

Let's look into refactoring that into less of a hack. We shouldn't be requiring
lp__ in anything downstream. Feel free to bring these things up during
design, and we can look into redoing them as we go so we don't wind up with
a hack release that we want to fix later by getting rid of lp__.

- Bob

[Bob Carpenter]

Dustin --- would you mind opening an issue (CmdStan or Stan)
where this refactor should go? What exactly assumes that lp__ is defined?

- Bob

[Michael Betancourt]

The only thing that requires lp are the mcmc_writer
and the sample class, both of which shouldn’t be
used by anything other than MCMC algorithms...

[Dustin Tran]

Added it: https://github.com/stan-dev/stan/issues/1538

It’s the write_iteration function(s).

Dustin

[Ben Goodrich]

On Friday, July 10, 2015 at 3:08:15 PM UTC-4, Bob Carpenter wrote:

Let's look into refactoring that into less of a hack.  We shouldn't be requiring
lp__ in anything downstream.   Feel free to bring these things up during
design, and we can look into redoing them as we go so we don't wind up with
a hack release that we want to fix later by getting rid of lp__.

Is there a lesser hack that would allow us to avoid this hack and get 2.7.0 out?

Ben

[Ben Goodrich]

On Friday, July 10, 2015 at 12:19:00 PM UTC-4, Dustin Tran wrote:

Yup. The log probability (lp) is not well-defined there for variational inference. Recall the solved parameters are parameters of the variational family, not the posterior, and the first line of the table simply takes the mean of the variational distribution, c.f., reference manual. Thus as a hack because Stan requires at least that column, we left it there while writing 0.

Yes, but after it has optimized the ELBO and then draws from a multivariate normal in the unconstrained space and transforms those draws into the constrained space, can't it then evaluate the log-posterior? This seems like it would be no more or less useful than the lp__ that comes out of our MCMC algorithms. If we did that and changed the "lp" column of the csv file to "lp__", then we can worry about generalizing the csv writer until after 2.7.0.

Ben

[Dustin Tran]

Sure that sounds like the most ready option. I have the changes done locally but am stuck in a train and don't have internet on my laptop quite yet. Will push/submit the two pull requests (for both cmdstan and stan) once I do.

Dustin