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)
As far as I can see, the method favors descriptions
which are mainly based on the spike count. I think, it would be
interesting to see, how the method performs in situations, in which there
are other higherorder dependencies apart from spike count. Specifically,
including a comparison between other methods such as BUB in situations, in
which spiketrains are, for example, generated according to a GLM, would
be a more convincing argument of the accuracy.
minor points:
line 163: reference missing line 221: \alpha=0 implies uniform
distribution? line 296: for >form Q2: Please
summarize your review in 12 sentences
The manuscript is well written and the feasibility of
the approach is sufficiently demonstrated by the presented experiments.
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)
Paper summary:
The paper describes two novel
entropy estimators for binary neural spike words. The estimators are
Bayesian and make use of a mixtureofDirichlet prior. The distribution is
hierarchical with a count distribution as the base measure of the
Dirichlet distribution. The authors evaluate their methods on artificial
data and on data recorded simultaneously from retinal ganglion cells and
compare them to established entropy estimators. They show that their
estimators need less samples for accurate estimations. Finally, they apply
their method to quantify temporal synergy in retinal ganglion cell data.
Quality:
The Bayesian entropy estimators are powerful,
elegantly evading the curse of dimensionality. By including prior
information about the structure of the problem, the method reduces the
number of required samples.
On the synthetic data, it is not
surprising that the proposed estimators outperform the alternative
estimators, since the distributions of the word data follow the model
structure of the estimators. The performance on the data recorded
simultaneously from retinal ganglion cells is impressive.
It is
not clear, though, how well the methods would do on other neural data. The
method contains the critical underlying assumption that the word
distribution is well characterized by the overall count distribution. For
the retinal ganglion cell data this is apparently the case, but further
evaluations will have to show whether or not this will also hold in
general. It might be worth to mention this problem with a sentence in the
discussion. In any case, the new estimators are certainly very useful.
Clarity:
The paper is nicely written.
Originality:
The proposed entropy estimators extend
the work by Nemenman et al., NIPS 2002 by including prior knowledge about
the structure of the spike trains. The general idea is similar to that of
the raster marginals model (Okun et al., J Neurosci 2012) in that the
total spike count distribution is used as a simplification to evade the
curse of dimensionality.
Significance:
Entropy
estimation is a very important problem, because information quantification
is a central problem of neural coding analyses. The demonstrated
performance gain compared to alternative methods is impressive.
Minor points: 080: In Section 3 introduce > In Section
3, we introduce 163: Citation missing 232: Incomplete sentence
234: the estimator fasttocompute > the estimator is
fasttocompute 290: We only then need only > We then need only
295: for > form Figures 4 and 5: DCnt > DCt
Q2: Please summarize your review in 12
sentences
The paper introduces entropy estimators for neural
spike trains that require less samples for accurate estimations. The
contribution is important and well implemented.
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)
This submission presents a straightforward improvement
on current estimators of entropy in multidimensional binary distributions.
Estimating entropy (and related measures like mutual information) is
considered important in advancing our understanding of the neural code.
This work is especially timely in that an increasing number of
multielectrode recordings are currently taking place whose
interpretability depends on better analysis methods like the one presented
here.
The work presented here relies on the fact that population
responses, esp. when binned in short time intervals, are very sparse: the
most frequent word is one in which no neuron spikes, with a word frequency
rapidly decreasing with the number of spikes, or ones, in a word. By
incorporating this prior knowledge into their Bayesian estimator, the
authors derive an estimator that achieve a bias comparable to that of
existing estimators using several orders of magnitude less data  a
critical constraint in empirical studies.
In an example
application of their method to real data, the authors find that retinal
ganglion cells "code synergistically" in time. While interesting, this
section would need to be expanded to yield robust and convincing insights.
The presentation of the derivation and the results is quite clear
and I only have minor comments. [deleted]
Q2: Please summarize your review in 12
sentences
Important improvement on entropy estimation methods
based on a more sophisticated prior than used previously.
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.
We thank all the reviewers for their careful
reading of our work, and for their many thoughtful comments and
helpful suggestions.
Reviewer 5:
Thank you for the
excellent suggestion regarding simulation from a GLM. We will attempt this
for the revision.
Reviewer 6:
We certainly agree that
performance of our estimator will depend upon the extent to which the
count distribution is capable of describing the full joint distribution of
words, and we will clarify this point in the discussion. We note, however,
that so long as the count distribution captures any aspect of the joint
that differs from uniform, we expect the DCt estimator to have an
advantage over NSB (i.e., since the latter effectively models all spike
patterns as equally likely a priori, whereas DCt will capture any tendency
for the count distribution to differ from a binomial centered at N/2).
Reviewer 7:
Although the current manuscript only shows
results for the case of small bin size, where spikes are sparse, further
experiments on the same RGC data with larger bin sizes show that the
method also performs well on lesssparse data. We will include an
additional figure showing this.
We agree that our application
section would benefit from expansion. The goal of the analyses shown in
Fig 6. was to demonstrate an application of entropy estimation to a
scientific question, which displaced an additional comparison between
entropy estimators on neural data. We will explore applications further in
future work.
