Variational number of samples + on non-convergence where do samples come from?

[John Reid]

When I ask for 200 samples in the variational command line I get 201 samples back with the first looking like an outlier. Can anyone let me know where this extra sample is coming from? Am I misinterpreting the output? My command line looks like:

../inst/Stan/MTKL variational output_samples=200 tol_rel_obj=0.01 iter=3500 data file=MTKL_data.R

Also when I reach the maximum iterations without convergence, do the samples come from the final iteration or the one with best ELBO?

Thanks,
John.

[Dustin Tran]

hi john,

the first “sample" is the mean set of parameters outputted by the variational distribution. it is not meant to be used as a sample but as a quick summary statistic of the distribution. you can find more in the manual in cmdstan—hope that helps

dustin

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[John Reid]

Yes that does help, I found that now in the manual. I suppose that in the mean field case that first line represents all the information about the inference. I.e. the rest of the samples are just samples from those parameters.

[Dustin Tran]

it outputs the mean of the parameters, but variational parameters such as the standard deviation for the normals are not outputted. so that line doesn’t fully characterize the (variational) distribution.

dustin

[John Reid]

Good point. If the algorithm does not converge from which iteration are the samples taken?

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[Alp Kucukelbir]

hi john,

if the algorithm does not converge, the samples are taken from the last (maximum) iteration.

cheers,

alp

[Bob Carpenter]

I think the sample file that's output from variational inference
should match the one output for MCMC if at all possible.

Would it be possible to take that summary of means and write it
out as a comment? Or in a separate output file?

Going forward, we're going to split the outputs in Stan 3 (if
I get my way) so that we don't try to overload CSV notation with
out-of-encoding comment information that needs to be parsed, which
is too hard to deal with other than with our own I/O tools (which
themselves become hard to maintain).

- Bob

[Dustin Tran]

sure, i added it as an issue on github: https://github.com/stan-dev/stan/issues/1661

Dustin

[John Reid]

Hi Alp,
Does it make more sense to take them from the iteration with the best ELBO?
Cheers, John.

[John Reid]

Also would it be possible to have cmdstan output samples from the best iteration so far if it is interrupted (Ctrl-C)?

[Alp Kucukelbir]

hi john,

i would vote against this for two reasons: 1) the ELBO really should
be increasing throughout the optimization and 2) our evaluation of the
ELBO itself is stochastic (noisy). therefore, taking samples from the
iteration with the best ELBO may not be reliable at all.

cheers
alp

[Alp Kucukelbir]

this is definitely something we should look into:

https://github.com/stan-dev/stan/issues/1663

[Andrew Gelman]

I agree. To put it another way: early stopping can be a good strategy, but if so we should think about it as a strategy rather than just picking an intermediate step in that way.