
Submitted by
Assigned_Reviewer_3
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 a hard clustering
algorithm for clustering batch sequential continuous data. The algorithm
is derived by performing a low variance asymptotic analysis of the Gibbs
sampling algorithm for the dependent Dirichlet process Gaussian mixture
model (DDPMM). ===== This is a well written paper that is easy to
follow. The work is technically sound and I only have a few minor
concerns.
Originality: Moderate. The authors perform a small
variance asymptotic analysis for the DDPMM Gibbs sampler and although a
similar analysis has previously been performed on the Dirichlet process
mixture Gibbs sampler, the model and algorithm considered here are
sufficiently different.
Significance: The paper is interesting in
two ways: 1)It demonstrates that it is possible to perform small variance
analysis on models more sophisticated than Dirichlet process mixtures and
2) It develops an efficient hard clustering algorithm for time evolving
data. =====
Detailed Comments: 1) It appears that the
analysis depends critically on the transition and observation
distributions being Gaussian. Are extensions to models using discrete
observation and transition distributions straightforward? 2) It is a
little concerning that the small variance analysis is performed on a
particular inference algorithm (Gibbs sampling) for the DDPMM. Can
something be said about the model directly, independent of the inference
algorithm? 3) Selection of the free parameters of the algorithm seems
cumbersome, performing an exhaustive parameter search is often not
feasible for large datasets. How were the parameters chosen for the
aircraft trajectory data? 4) In the toy experiment, how were the Gibbs
sampler and VB initialized? Particularly poor initializations, for e.g.,
all data being assigned to the same cluster, may partly be responsible for
the large performance gaps. Were multiple runs of VB performed? 5) It
is difficult to judge the aircraft trajectory clustering results from the
visualization alone. Quantitative numbers would be useful. How about L2
error on held out trajectories? This error would obviously be minimized if
each trajectory is its own cluster, but can still be useful in comparing
two clusterings with comparable number of clusters. 6) How were the
Gibbs sampling results unreliable?
Q2: Please
summarize your review in 12 sentences
Overall, this is a solid piece of work and a well
written paper. There are some minor concerns with the experimental
section. 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 paper presents a deterministic inference
algorithm for a clustering problem for batch sequential data (data in
each batch exist in clusters, and clusters across batches are related
as per some evolving structure). The Dependent Dirichlet Process
Gaussian mixture model (DDPGMM) is a nonparametric Bayesian method
for dealing with such data. The paper uses the idea of doing
lowvariance asymptotics on the Gibbs sampling update equations in a
DDPGMM model (a similar approach was recently proposed by Kulis and
Jordan for DPGMM in their DPmeans algorithm) and derives a
deterministic algorithm that is (1) more efficient to implement than Gibbs
sampling for DDPGMM, (2) can learn the number of clusters just like
DDPGMM. Experimental results on a synthetic and a real dataset show
that the proposed algorithm runs fasters than other inference methods
for DDPGMM such as Gibbs sampling, variational inference, and
sequential Monte Carlo.
Quality: The technical quality is rigorous
and the details appear to be correct.
Clarity: The paper is
wellwritten and the exposition is easy to follow.
Originality:
The paper is based on recently proposed idea of using lowvariance
asymptotics on the Gibbs sampling update equations in case of DP
mixture models.
Significance: The paper addresses an important
problem (scaling up nonparametric Bayesian methods for large
datasets).
Paper Strengths:
 The proposed algorithm is
intuitive, seems easy to implement, and is scalable for large
datasets.
 Although the basic recipe is borrowed from the
DPmeans work of Kulis and Jordan (taking the Gibbs sampling updates
and applying the lowvariance asymptotics), the ideas in section 3.2
(parameter updates) are rather novel in this context.
Paper
Weaknesses:
 The algorithm has 3 free parameters. For an
unsupervised algorithm (with no option of doing crossvalidation),
this is a bit worrying. Although the paper gives some suggestions on
how to choose the parameters, it is not clear how well they will work
in practice.
 There should have been a comparison with a
simple variant of the DPmeans algorithm (Kulis and Jordan, 2012) for
batchsequential data (see the suggestion in the comments below on how
to do it).
 On realdata, there is no comparison with variational
inference or particle learning.
Comments:
 It would
have been nice to compare the proposed dynamicmeans algorithm with a
very simple adaptation of the DPmeans algorithm: Run DPmeans on one
batch and initialize means for the next batch using the results of
this run. I would be curious to see how dynamicmeans compares against
this alternative.
 It turns out that instead of doing
smallvariance asymptotics on the Gibbs sampling updates, one could
also do MAPbased asymptotics to derive hardassignment based variants
of nonparametric Bayesian models such as DPGMM or IBPbased latent
feature models (there is a recent paper by Broderick et al from ICML
2013: "MADBayes: MAPbased Asymptotic Derivations from Bayes"). Is it
possible to derive the dynamicmeans algorithm using this approach?
Please comment.
 There is work on temporal DP mixture model based
on recurrent Chinese restaurant process which is similar in spirit to
dependent DP mixture models. Please see this: "Dynamic NonParametric
Mixture Models and The Recurrent Chinese Restaurant Process : with
Applications to Evolutionary Clustering" by Ahmad and Xing (2008). It
would be nice to have a discussion about this link of work. Please also
comment whether doing lowvariance asymptotics on these methods would
lead to similar algorithms as dynamicmeans?
 In the DPmeans
algorithm of Kulis and Jordan, the order of data points mattered. In
the cluster assignment step of the dynamicmeans algorithm, does the order
of data points (within a single batch) matter? Please
comment. Q2: Please summarize your review in 12
sentences
It is a reasonable paper, although somewhat
incremental (based on the DPmeans algorithm by Kulis and Jordan).
There might be some issues with its usefulness in practice (requires
choosing 3 parameters) and the experimental evidence in the paper is
somewhat limited. But I still consider the paper to be taking a step
(albeit small) in an important research direction (leveraging the
flexibility of nonparametric Bayesian models for largescale
datasets). 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)
The authors provide a novel small variance asymptotic
analysis of the Dependent Dirichlet Process (DDP). The authors first show
how to derive the small variance limits and then provide a deterministic
algorithm for inference. They show that their algorithm monotonically
decreases a (bounded) cost function, proving that their algorithm will
converge. The authors next apply the new algorithm, Dynamic Means to
synthetic data comparing to several Monte Carlo based inference methods
for the DDP and the DPMeans algorithm. Finally, the authors apply their
method to a real world problem of tracking aircraft trajectories, showing
improved performance vs DPMeans and Gibbs sampling of the DDP.
This a reasonably interesting paper. The idea of using small
variance asymptotics to derive hard clustering algorithms is not novel.
However, the specific application to the DDP does raise some novel
technical challenges. Deriving an algorithm which works for correlated
Dirichlet processes is interesting.
The main weakness of the paper
currently is the lack of adequate description of the alternative methods
used for benchmarking. In particular it is not clear:
1) How hard
clustering was done for the Monte Carl samplers? Was a maximum posterior
estimate taken, or was a more sophisticated approach based on the
posterior similarity matrices of the data points used?
2) It is
not clear what particle filtering or VB algorithm the authors use.
3) The authors mention the they enforced consistency across time
points when computing the accuracy metrics. Some clarification on this
would help.
For the synthetic data it would be useful to show the
accuracy of the methods vs time run plotted. I am extremely surprised the
Dynamic Means method performs so much better than sampling based
approaches, and suspect it is largely due to undersampling for the Gibbs
and PL. I realise the main point of the algorithm is that it performs much
better then than sampling methods at a similar computational budget, so I
think an exploration of time vs accuracy is important.
Typos:
 Line 44 "in the both the" should be "in both the"
 Line
102 $n_{k t}$ should be $n_{k \tau}$
 Lines 405406 I am not sure
why a 10 x 20 grid creates a 400 dimensonal feature vector, I would think
its 200.
Minor Comments:
 It would be nice if the
elements in equations (3) and (4) where in the same order.
 The
text on the figures is difficult to read. A larger font would be better.
Q2: Please summarize your review in 12
sentences
A reasonable paper which could pass the publication
threshold with some revisions.
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.
The authors kindly thank the reviewers for their
feedback. We have identified a few main points from the review that should
be addressed: 1) The algorithm has too many free parameters, resulting in
difficult tuning; 2) There is a lack of comparison with a modified
DPmeans algorithm; 3) Whether generalizations of the algorithm or
alternate derivations are possible; 4) There is insufficient description
and results in the experimental sections; and 5) Minor clarifications
about aspects of the paper and the algorithm itself.
Concerning
the number of parameters: A strong advantage of the present algorithm is
that it possesses the combination of low computational cost and relatively
smooth variation in performance with respect to its parameters. Due to
these properties, automatic optimization methods are particularly
applicable for parameter adjustment (e.g. gradientbased schemes[1] or
Bayesian optimization[2]). There exists a large body of literature
dedicated to addressing the issue of model selection[3], and as such these
techniques were not mentioned in the paper; the authors will make a note
of this in the final draft. Further, the existence of these parameters was
not a design choice made by the authors. They are a direct result of each
of the underlying processes (birth, transition, death) of the DDP mixture;
any asymptotic analysis would yield a set of three parameters, as is
required to describe those three actions. Finally, the authors provided a
transformation to make parameter selection based on expected data
characteristics more intuitive.
Regarding the proposed modified
DPmeans algorithm, the authors contend that the method has drawbacks
which prevent devoting attention to it in a short paper. Essentially, as
the cluster transition variance or death probability increases, the
proposed method degrades. Two simple examples (among many) of this
degradation: First, if a cluster moves further than lambda in one time
step, it will always create a new cluster, and the parameter from the past
time step will essentially never be used at all, preventing useful
tracking; second, as the cluster death probability approaches 1, any new
cluster near a recently deceased cluster will always be incorrectly linked
to that deceased cluster. Correctly accounting for death and transition is
what fundamentally sets the Dynamic Means algorithm apart from DPmeans.
In addition, the authors preferred to compare to more wellknown methods,
to demonstrate advantages over the stateoftheart.
It is
possible to extend this work to nonGaussian distributions, based on
recent work on smallvariance asymptotics for Dirichlet process mixtures
of general exponential family distributions[4]. In terms of alternative
derivations, there were two approaches mentioned by the reviewers: the
Recurrent CRP, and MADBayes. The former does not allow for the death of
clusters, and the same holds true upon taking the lowvariance asymptotic
limit of the Gibbs sampler. Otherwise, a similar algorithm would result
from a lowvariance asymptotic analysis. A MADBayeslike analysis of the
DDPGMM is possible; one would wrap the transition into the parameter
prior, and account for the death probability in the exchangeable partition
probability function. However, based on the lowvariance MAP analysis of
the DP/DPmeans, the lowvariance MAP and Gibbs sampler analyses are
expected to be similar to one another. The authors therefore decided upon
the Gibbs samplerbased approach for ease of understanding.
Regarding the experimental section, the authors agree that a time
budget vs. accuracy comparison would be an insightful inclusion, and will
add it in the final draft. In the ADSB section, PL and VB time results
can be added into final draft. The authors understand the desire for
quantitative analysis  however, L2 error isn't a good comparison metric.
Indeed, comparisons of unsupervised clustering algorithms without labelled
data is an open problem. Thus, the authors will handlabel a subset of the
data, and provide accuracy results on that subset.
One of the
reviewers was uncertain about the term "enforcing consistency"  this just
means that data have to be clustered with the correct old parameter. This
is of utmost importance in tracking the evolution of clusters over time.
For Gibbs sampling/VB/PL, the results show reasonable clustering in each
time step, but the data are being linked to the incorrect old clusters
(poor tracking). Note that "enforcing consistency" is not a part of any of
the algorithms; it is simply how accuracy was computed.
The
comparison algorithms used in the experimental section were "PL for
general mixtures" and "mean field variational inference" (as cited in the
introduction). The authors agree that this was not clear in the
experimental section, and citations will be added there in the final
draft. Furthermore, comparisons for the sampling methods were performed
conservatively (as described on lines 369372)  for these techniques, the
highest accuracy sample was selected, assuming knowledge of the true
labeling. Further, the algorithms were initialized as follows (based on
highest performance): Gibbs sampling was given "no initialization" (i.e.
parameters and labels are introduced as necessary), and VB/PL were
initialized randomly. Finally, the Dynamic Means algorithm's performance
does depend on the order in which the data is assigned its labels. The
authors acknowledge that this may not have been clear in the exposition of
the paper, and will include that in the final draft.
1  Yoshua
Bengio. "GradientBased Optimization of Hyperparameters", 2000. 2 
Jasper Snoek et al. "Practical Bayesian Optimization of Machine Learning
Algorithms", 2012. 3  Joseph Kadane et al. "Methods and Criteria for
Model Selection", 2004. 4  Ke Jiang et al. "SmallVariance
Asymptotics for Exponential Family Dirichlet Process Mixture Models",
2012.
 