
Submitted by
Assigned_Reviewer_1
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
This paper proposes a novel model selection criterion
for binary latent feature models. It is like variational Bayes, except
that rather than assuming a factorized posterior over latent variables and
parameters, it approximately integrates out the parameters using the BIC.
They demonstrate improved heldout likelihood scores compared to several
existing IBP implementations.
The proposed approach seems like a
reasonable thing to do, and is motivated by a plausible asymptotic
argument. The main advantage relative to other methods for IBP inference
is that computationally, it corresponds to an EM algorithm with some
additional complexity penalties, rather than the more expensive sampling
or variational Bayes algorithms.
The technical contributions seem
novel but incremental: they are essentially an extension of the FAB work
of [3] and [4].
Some parts of the exposition were confusing
because the math seems imprecise. In equation (3), the log sum of the z
values is infinite if all of the values are zero. Since this has nonzero
probability under any nondegenerate variational distribution q, why isn't
the FIC score always infinite?
Theorem 2 states that the marginal
likelihood "can be asymptotically approximated as" something, but it's not
stated what the asymptotic regime is or what the assumptions are. In
particular, how is K assumed to behave as N gets larger? Since the BIC is
applied to each component individually, the theorem seems to require a
fixed finite K, so that the number of activations of every feature would
approach infinity. Under the IBP model, the number of components is
infinite, and new components would continue to be observed as the amount
of data increases, so assuming finite K removes one of the motivations for
using the IBP.
More minor points: in section 2, shouldn't p_k(X 
z_{\cdot, k}) include only the data points assigned to mixture component
k, rather than the entire dataset? In equation (4), there should be an
expectation on the left hand side.
In the quantiative results in
Table 1, the proposed method achieves higher predictive likelihood scores
in less time compared to alternative methods. While FAB finishes faster by
orders of magnitude in some cases, it's not clear how to interpret this
result because the stopping criterion isn't specified. It seems like an
arbitrary decision when to stop the Gibbs sampler, in particular.
The improvements in predictive likelihood are significant, but
where does the difference come from? The results would be more convincing
if there's evidence that the difference is due to the model selection
criterion rather than which algorithms get stuck in worse local optima,
since the latter probably depends more on the details of the
implementation (initialization strategies, etc.). (The fact that the Gibbs
sampler learns an excessively large number of components in some of the
datasets suggests that it's a problem with local optima, since in theory
it should be exactly computing the likelihood which FAB is approximating.)
Q2: Please summarize your review in 12
sentences
The proposed approach seems to make sense, but is
somewhat incremental. Some of the math seems a bit imprecise. The
experimental results show improvements in running time and predictive
likelihood compared to previous approaches, but as stated above, I don't
think enough analysis was done to be able to interpret these results.
Submitted by
Assigned_Reviewer_5
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
Summary:
The authors propose an
algorithm/approximation method for efficient model selection for latent
feature models by using factorized asymptotic bayesian (FAB) inference and
the factorized information criterion (FIC). FAB and FIC are well known for
mixture models, where the latter approximates a model's log likelihood via
factorization and Laplace approximation for tractable model selection. The
contribution is the generalization of FAB to latent feature models, which
uses a mean field approximation for inference of the latents and
accelerated shrinkage of the global number of features selected.
A
feature of the approach is more automaticity of the model selection, with
little hand tweaking. Results are shown on synthetic and real data, and
the gain in computational efficiency is significant.
Quality:
Presented results involve thorough analysis and the method is
evaluated in comparison to a wide range of competing methods on multiple
data sets. References are sufficient.
Clarity: The paper is
clearly written and well structured.
Originality/Significance:
Seems to be a logical extension and solid generalization of previous
work in the area of model selection in LFMs using FAB inference and FIC.
Namely, the using a combination of several approximations into one novel
method that works well.
It would be nice to understand when/how
these approximations may lead to poor performance, i.e. "push" the method
until it breaks, given that there are several approximations (FIC, mean
field, shrinkage) playing a roll at the same
time. Q2: Please summarize your review in 12
sentences
The authors propose an algorithm/approximation method
for efficient model selection for latent feature models by using
factorized asymptotic bayesian (FAB) inference and the factorized
information criterion (FIC). Results are shown on synthetic and real data,
and the gain in computational efficiency is
significant. Submitted by
Assigned_Reviewer_6
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
Summary:
The paper presents an inference
algorithm for the binary latent feature model (LFM) which expresses each
observation x_n as a K size binary vector z_n where z_{nk} = 1 means that
x_n has the kth latent feature present. The goal of inference is to learn
the z's for all observations (along with the other model parameters). The
presented EM based algorithm uses a shrinkage mechasnism to learn the z's
as well as infer the number of latent features (K). This is similar in
spirit to nonparametric Bayesian latent feature models such as the Indian
Buffet Process (IBP). However, the presented algorithm doesn't actually
use prior distributions inducing model parsimony but rather uses a model
selection criteria  Factorized Asymptotic Bayesian Inference (FAB) 
recently introduced in the context of mixture models and HMMs. THe FAB
idea is based on expressing the log marginal likelihood in terms of the
expected complete loglikelihood plus a model selection term that
encourages shrinkage of the number of latent features (by specifying an
upperbound on K and *learning* the correct K during inference). On some
large datasets, the FAB is shown to outperform other inference methods
including Gibbs sampling, variational inference, and MAP estimation
methods for the IBP (in terms of running time and inference quality).
Quality: The technical quality seems reasonably sound and
algorithmic details seem correct. The ability of dealing with large
datasets and also learning the number of latent features is very
appealing.
Clarity: The paper is reasonably clear in the
methodology part. However, some of the experimental details are somewhat
unclear (discussed below).
Originality: The proposed method is
based on recently proposed framework on Factorized Asymptotic Bayesian
(FAB) Inference applied for mixture models and HMMs. The application of
FAB to latent feature models however is novel.
Significance: The
paper is addressing an important problem (efficient inference in latent
feature models while also inferring the number of latent features).
Weak Points:
 There is no discussion about the
limitations of the proposed algorithm. Are there any cases when the
algorithm might perform worse than vanilla Gibbs sampling?
 There
is no discussion about the possible difficulties in convergence (given it
is an EM like procedure).
 The algorithm is limited to binary
latent feature models (can't be applied for factor analysis or
probabilistic PCA).
 The experimental evaluation is not thorough
enough (and seems flawed at some points; see comments below).
 In
the smalldata regime (when the asymptotic argument doesn't hold), it is
unclear how the algorithm will behave (there should be some discussion or
experiments).
 Some other recent works on efficient inference in
LFMs has not been discussed in the paper (see comments below).

The MEIBP algorithm proposed in [22] is applicable only for nonnegative
linear Gaussian models (W has to be positive, not realvalued). Therefore,
the artificial simulation and the block data experiments are simply
invalid for the MEIBP baseline. If you were to compare with MEIBP then the
symthetic dataset should have been generated such that the loading matrix
W is positive.
Other Comments:
 For block images
data, since the noise value is known (and given to the FAB algorithm), for
fairness the IBP Gibbs sampler should also be given the same value
(instead of the 0.75 stddev heuristic).
 For VBIBP [2], the
infinite variational version could be used (the experiments used finite
variational version). The experimental settings for VB isn't described in
enough details (e.g., how many restarts were given?).
I am
surprised that the accelerated Gibbs sampling discovered about 70 latent
features on the 49 dimensional Sonar data!). I suspect it is because of
bad initialization and/or badly specified noise variance value.

Line 70: The reference [21] isn't about Gibbs sampling but rather MAP
estimate for the IBP (just like reference [22]). Please modify the text
and correct the description.
 There is recent work on efficient
inference using smallvariance asymptotic in case of nonparametric LFMs
(see "MADBayes: MAPbased Asymptotic Derivations from Bayes" from ICML
2013). It would be nice to discuss this work as well.
Minor
comments:
 Line 349: For realdata, the suggestion in [1,22] was
not to set stddev equal to 0.75, but to set it equal to 0.25 *times* the
stddev of examples across all the dimensions.
********************************************* Comments after
the authorfeedback: The feedback answered some of the questions. There
are a few things that need to be fixed/improved before the paper could be
accepted. In particular:  Experimental methodology (for the proposed
method and the baseline) need to be better explained, and there should be
justifications/explanations about why certain algorithms behaved in a
certain way (e.g., Gibbs sampler used a fixed alpha that might have led to
an overestimated K, or noise variance hyperparamters weren't properly
set).  Reference [21] does MAP inference, not sampling. Please fix
this.  Include the reference on MADBayes inference for the
IBP. Q2: Please summarize your review in 12
sentences
The proposed inference method for LFMs is interesting
and the fact that it scales to large datasets (in addition to inferring K)
is appealing. However, the experimental evaluation should have been more
carefully done. Submitted by
Assigned_Reviewer_7
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
In this paper, the authors extend factorized
asymptotic Bayesian (FAB) inference for latent feature models. FAB is a
recentlydeveloped model selection method with really good results for
mixture models (MMs) and hidden Markov models. In short, this method
maximizes a lower bound of a factorized information criterion (FIC) which
converges to marginal loglikelihood. The limitation of the FAB is that it
has only been applicable to models satisfying the condition that the
Hessian matrix of a complete likelihood should be block diagonal. The
authors extend FAB to latent feature models (LFMs) despite the fact the
condition is not satisfied. They effectively derive a lower bound of FIC
for LFMS and show that it has the same representation ad the FIC for MMs.
They provide results on both synthetic and real world datasets and compare
FAB/LFM to other methods such as fast GIbbs sampling in models that use
Indian Bufffet process, models that use variational Bayes (VB) and
maximumexpectation IBP (MEIBP). The results illustrate the superiority of
FAB?LFM; the proposed method claimed better performance not only in the
prediction task but also in terms of computational cost.
The paper
is well written and the authors thoroughly describe the derivation steps
of their method.
The proposed model extends FAB/MMs to FAB/LFMs
and would consider it incremental. It is quite interesting and the results
underline it's efficiency. Although I am not an expert on this, I think
that it would be of great interest to the NIPS community.
Q2: Please summarize your review in 12 sentences
All in all, it is a nice paper that presents a really
interesting idea. The results are convincing and I support its
acceptance.
Q1:Author
rebuttal: Please respond to any concerns raised in the reviews. There are
no constraints on how you want to argue your case, except for the fact
that your text should be limited to a maximum of 6000 characters. Note
however that reviewers and area chairs are very busy and may not read long
vague rebuttals. It is in your own interest to be concise and to the
point.
Thank you for giving us a lot of insightful and
helpful discussions.
Before starting our response, we would like
to clarify that we do not intend to claim finite LFMs are better than
infinite LFMs in general. Of course, as reviewers pointed, infinite ones
does not require the ``finite K'' assumption. Our observation is that, as
a combination of model and algorithm, finite LFM + FAB achieved better
predictive accuracy with less computational cost than infinite LFMs (IBPs)
+ existing inference methods (Gibbs, VB).
[For
Assigned_Reviewer_1]
> In equation (3), the log sum of the z
values is infinite ...
If z_nk=0 for n=1,...,N, w_dk does not
appear in the likelihood p(XZ,Theta), and the marginalization w.r.t. w_dk
does not affect to the (true) marginal likelihood (see 651 of the
supplementary material). Without loss of generality, we can marginalize
out such w_dk before applying Laplace's method, which is equivalent to
remove z_k from the log sum z term, and FIC does not go infinity.
> Theorem 2 states that ..., but it's not stated what the
asymptotic regime is or what the assumptions are.
As described at
the beginning, we assume that K is finite regardless of N. While this
assumption is different from IBP, We believe there are many situations
that our assumption is valid in the real world (at least the real data
sets we evaluated).
> ... it's not clear how to interpret
this result (Table 1) because the stopping criterion isn't specified.
As stopping criteria, we basically followed the original papers
and we believe this setting is fair: [Gibbs] Stopped after 500 iterations
(same setting for real data in [1]). [VB] Stopped when the improvement of
the lower bound was less than the threshold. [MEIBP] Same as VB (we set
its threshold as 10^4 as used in [22].) In addition, for the real data,
we forced to stop all the methods when the runtime exceeded 50 hours (see
374).
> The improvements in predictive likelihood are
significant, but where does the difference come from?
One
plausible reason is the difference of the regularizations. Experimental
results show FAB could better mitigate overfitting (TLL and PLL were
close) while IBP was likely to overfit particularly to small datasets.
[For Assigned_Reviewer_6]
> Are there any cases
when the algorithm might perform worse than vanilla Gibbs sampling?
In principle, LFM/FAB does not have ``tunable'' hyperparameters
because of its asymptotic prior ignorance. Since LFM/IBP has a few
hyperparameters and therefore it could outperform FAB in the scenario
where domain knowledge can be represented as IBP prior (i.e., those
hyperparameters can be determined on the basis of domain knowledge).
> There is no discussion about the possible difficulties in
convergence (given it is an EM like procedure).
The FAB E and
Mstep monotonically maximize the FIC lower bound as described in Theorem
6 of [5] and Theorem 2 of [4], and the parameters converge in local maxima
after sufficiently large number of iterations.
> In the
smalldata regime (when the asymptotic argument doesn't hold), it is
unclear how the algorithm will behave
Since FAB is an asymptotic
method, it's important issue to investigate its behavior over N. Fig.2
shows that FAB worked fairly well in relatively small sample cases (N=100,
200, ..). We observed the same tendency in Sonar data.
> For
block images data, ...
We're afraid that this point is a
reviewer's misunderstanding. FAB learns data variance (see Eq.18) and we
did not specify the true noise variance for all experiments. Since the
Gibbs sampling method does not learn the variance (at least in its
software), we specified it by the 0.75 heuristic by following [22]. We
believe this experimental setting was fair.
It is worth noting
that we specified the true variance for IBP methods in the artificial
simulations except the block data (see 348) but still FAB performed
better.
> The MEIBP algorithm ...
We agree that
some experiments were inappropriate for MEIBP (we did not notice that
MEIBP is for nonnegative data only.) We fix this in the final manuscript.
Nevertheless, we believe the other experiments including real world
datasets show the superiority of FAB over the other methods.
>
The experimental settings for VB isn't described in enough details.
We set alpha (hyperparameter of IBP prior) as 3 and sigma_n and
sigma_z as 0.75 by following [22]. For other parameters, we followed the
default setting of tester.m in
http://people.csail.mit.edu/finale/code/ibpgibbs.tar, e.g. # random
restart of VB is 5. We omitted the results of infinite VB because of the
space limitation and its performance was roughly same as the finite one.
> I am surprised that the accelerated Gibbs sampling discovered
about 70 latent features ...
As you mentioned, in a few data sets
(Sonar, Auslan, and EEG), estimated K of IBP was larger than D, but TLL
was the highest, which implies the model was correctly learned. This fact
seems not to support that there were bad initialization and/or wrong
specification of the variance. We guess this is because the model
regularization of IBP did not work well (note that we set alpha as 3 by
following [22].)
> MADBayes
Thank you for the
suggestion. We did not know the work. We will add a discussion with this
work in a final manuscript.
> the suggestion in [1,22] was not
to set stddev equal to 0.75, but to set it equal to 0.25 *times* the
stddev of examples ...
As described in 319, we firstly normalized
all the data (std of the resulting data is 1) and then set the noise std
as 0.75, and it was almost equivalent to set 0.75 * std. We also tested
std=0.25, but std=0.75 (this setting is described in [22]) was overall
better in terms of PLL so we employed this setting.
 