Fwd: [columbia mlrg] Tamir Hazan talk 1.30pm this Tuesday (16th October)

[Bob Carpenter]

I'm going to go to this talk in CS, which is
an hour after the Stan meeting.

We really do need to get around to implementing
MAP with optimization in Stan -- it should be pretty
easy to drop in L-BFGS or conjugate gradient and
apply it to our models

- Bob

From: Michael Collins <mcol...@csail.mit.edu>

Tamir Hazan is visiting on Tuesday - see the talk announcement below.

Please do let me know if you'd like to meet with Tamir.

Cheers,
Mike

===============================================================
Title: Inference and Learning with Random Maximum A-Posteriori Perturbations

Speaker: Tamir Hazan, TTI Chicago

Time: 1.30-2.30pm Tuesday 16th October
Location: CS Building room 477

Abstract:
Learning and inference in complex models drives much of the research in machine learning applications, from computer
vision, natural language processing, to computational biology. The inference problem in such cases involves assessing
the weights of possible structures, whether objects, parsers, or molecular structures. Although it is often feasible to
only find the most likely or maximum a-posteriori (MAP) assignment rather than considering all possible assignment, MAP
inference is limited when there are other likely assignments. In a fully probabilistic treatment, all possible
alternative assignments are considered thus requiring summing over the assignments with their respective weights which
is considerably harder (#P hard vs NP hard). The main surprising result of our work is that MAP inference (maximization)
can be used to approximate and bound the weighted counting. This leads us to a new approximate inference framework that
is based on MAP-statistics, thus does not depend on pseudo-probabilities, contrasting the current framework of Bethe
approximations which lacks statistical meaning. This approach excels in regimes where there are several but not
exponentially many prominent assignments. For example, this happens in cases where observations carry strong signals
(local evidence) but are also guided by strong consistency constraints (couplings).

Joint work with Tommi Jaakkola

[Andrew Gelman]

What's the point of putting in posterior mode with Stan? With big models, the mode is useless. Epecially if it's the joint mode, not even integrating anything out.

> --
>

[Bob Carpenter]

On 10/14/12 5:15 PM, Andrew Gelman wrote:
> What's the point of putting in posterior mode with Stan?

It'd be a lot faster and more scalable. Same reason
you use (bg)lmer instead of BUGS.

So while I don't care about regularized regression
per se, it'd be nice to say Stan could do that,
too.

> With big models, the mode is useless.

Ironically, I think it's big data that leads to all
the optimization approaches and approximations in
machine learning. But the models tend to be pretty
simple regularized regressions.

> Epecially if it's the joint mode, not even integrating anything out.

No reason you couldn't integrate out parameters.

The issue's whether we want to spend the time on it
to write it, test it, doc it and support queries about
it.

- Bob

[Andrew Gelman]

See repsonse belwo.

On Oct 14, 2012, at 8:05 PM, Bob Carpenter wrote:

>
> On 10/14/12 5:15 PM, Andrew Gelman wrote:
>> What's the point of putting in posterior mode with Stan?
>
> It'd be a lot faster and more scalable. Same reason
> you use (bg)lmer instead of BUGS.

No. Blmer computes (or approximates) the marginal posterior mode, not the joint posterior mode. Much different.

>
> > Epecially if it's the joint mode, not even integrating anything out.
>
> No reason you couldn't integrate out parameters.

How? I'm up for that but I don't know how to do it.

>
> The issue's whether we want to spend the time on it
> to write it, test it, doc it and support queries about
> it.

I really don't like it. But if you have some examples where it is a good idea, I could be convinced.

[Marcus Brubaker]

Tamir is great, enjoy the talk.  The work that he's discussing is primarily looking at distributions over discrete spaces I believe.

--

[Bob Carpenter]

>>> What's the point of putting in posterior mode with Stan?
>>
>> It'd be a lot faster and more scalable. Same reason
>> you use (bg)lmer instead of BUGS.
>
> No. Blmer computes (or approximates) the marginal posterior mode, not the joint posterior mode. Much different.

If we wrote a general optimizer, it wouldn't matter
whether it's a marginal, joint, or some systems engineering
problem. It'd be like Stan and optimize whatever
function you wrote.

How hard is it to express the log marginal posterior?

Or is some completely other kind of technique used
other than optimization to find the posterior mode.

> I really don't like it. But if you have some examples where it is a good idea, I could be convinced.

I'm certainly not going to get on the other side
of the debate about the utility of point estimates.

- Bob

[Andrew Gelman]

No, the big effort in lmer/blmer/etc is to compute the marginal likelihood (or approximate marginal likelihood) given the regression model. The whole point is that you write the model and lmer etc figures out the integral. It's done using a least squares computation, which probably isn't efficient and scalable approach. If we really wanted to outdo bglmer using Stan, I don't think we'd do it by writing the marginal likelihood or approx marginal likelihood as a C++ function.
A

> --
>

[Matt Hoffman]

This is something I've been thinking about some lately, and at some
point will likely find a reason to implement in Stan.

I don't like pure MAP, for all of the reasons Andrew mentions and
probably some more that he hasn't mentioned. But I love maximum
marginal likelihood, which is what E-M usually implements (modulo
local optima). Ideally, I think I'd usually like to be doing MML on
some set of hyperparameters. Trouble is, you can't do E-M for lots of
hierarchical models, since the E step (wherein you compute p(z|y,θ))
is intractable. You can use variational inference, which can be
interpreted as an approximation to E-M, but it's pretty biased and can
be quite sensitive to local optima.

But you can also use MCMC within stochastic (generalized) E-M, if you
use an appropriately decaying step size or some other noise-robust
optimization framework. Which would be a pretty cool thing to support
in Stan. (Cf. my paper with David Mimno and David Blei on Sparse
Stochastic Inference for LDA.)

Matt

> --
>
>

[Andrew Gelman]

I'm down with that.

> --
>