
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)
This paper addresses the challenge of inferring
synaptic connectivity in settings where one or more putative presynaptic
neurons are stimulated while the membrane potential of a single
postsynaptic neuron is recorded, as in modern twophoton microscopy
experiments. The authors present a new probabilistic model for this
experimental setup, along with a variational inference algorithm. They
then develop an online, active learning algorithm to select the most
informative stimuli. The efficacy of their algorithm is demonstrated using
synthetic data generated from the model.
The paper presents a
novel and wellmotivated modeling framework for a pertinent experimental
paradigm, along with an interesting online experimental design algorithm.
This problem is both relevant and interesting to the NIPS community. The
model that has been introduced seems quite reasonable. It is a novel
contribution, and indeed applies to many experimental settings. The
experimental results with synthetic data (from a more complex model)
suggest that the inference algorithm is robust, and provide compelling
evidence for the benefits of experimental design in the small$R$ case.
Obviously an application to biological recordings would make a
more compelling case, though this seems impractical given the space
limitations and the model details that must be conveyed. Both inference
and optimal experimental design require significant variational
approximations and Monte Carlo estimates. The experimental results, even
under the misspecified model, are encouraging, and suggest that these
approximations are not too detrimental. Nonetheless, an analysis of the
failure modes (e.g. sensitivity to $M$ and $L$) would be desirable.
Similarly, a comparison to Gibbs sampling could also justify the
variational approximations.
To the best of my knowledge, this
problem has not been addressed in a Bayesian manner. The model and
algorithms presented in this paper are novel and should be interesting and
relevant to a computational neuroscientists within the NIPS community.
Q2: Please summarize your review in 12
sentences
The authors provide a novel probabilistic model,
inference algorithm, and optimal experimental design procedure for the
interesting and relevant task of inferring synaptic connectivity given
access to subthreshold membrane potential recordings and singleneuron
stimulation capabilities. The result is polished and would be a nice
contribution to NIPS. 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)
Targeted stimulation of multiple presynaptic cells
combined with intracellular recording of a single postsynaptic cell is a
popular and important method for estimating synaptic connectivity between
these cells. The main drawback of this approach is that it is technically
difficult, so that only small number of connections can be estimated in a
given experiment. The authors aim to provide statistical methods for
speeding up these experiments, by firstly providing a full statistical
model which takes the sparsity of neural coupling into account, and
secondly by providing computationally efficient methods for choosing
targetlocations for stimulation.
The paper is sound and clearly
explained, and the methods are evaluated using synthetic data. The
drawbacks of this submission are that a) no results on real data are
presented b) the neuron/noise model used is a bit simplistic (see details
below) and that it is therefore not quite clear how well this method will
work in a real experimental context.
Overall, my verdict is that
this is a neat (but not outstanding) submission which could be a nice
addition to NIPS.
Quality: The statistical model is reasonable and
the evaluation of the model on synthetic data is sound. However, there are
a number of properties of the model which might provide problematic on
real data, and therefore, the important test of the relevance of this
study will be how well it works in such a setting. In the absence of real
data, it would have been important to include simulation results in a more
realistic setting, i.e. one in which the model does not perfectly describe
the data (e.g. using a different neuron model, correlated noise, possibly
input from other neurons, feedback couplings, etc..)
Hyperparameters: The statistical model includes some
hyperparameters which probably strongly affect model performance, but
which are not set by the method. While it is true that some of these
parameters can be set by using known connectionprobabilities, it is
unclear how appropriate this will be for a given experimental application.
How sensitive is the method to "wrong" hyperparameters e.g. on the
spikeandslab prior?"
Uncorrelated noise: The method assumes
uncorrelated noise on the membrane voltages, and says that it is
"straightforward" to extend this to correlated noise while I have no
doubts that it is straightforward mathematically, it would have been
important to see how strongly this affects performance e.g. in the
simulations. I could imagine that the inference task is substantially
harder if one also has to deal with correlated noise.
Simulations:
In the absence of real data, it would have been important to at least
include simulation results in a more realistic setting, i.e. one in which
the model does not perfectly describe the data (e.g. using a different
neuron model, correlated noise, possibly input from other neurons,
feedback couplings, etc..). One of the results of the simulation was that
the experimental design strategy does not show a great performance benefit
in the highnoise regime with multiple stimulated entries I would expect
that this is actually the most important regime?
Clarity: The
paper is mostly clearly written, but takes a long "run up" which sets up a
general statistical model which is then subsequently broken down to the
model which is actually used by the authors. (E.g. they write that
spikeandslab priors with any distribution can be used, and later say
that they consider only the Gaussian case). I would suggest just
describing what was actually done to streamline the exposition."
Originality: As far as I know, this study is original. While
there have been previous studies that address estimation of synaptic
connectivity (from presynaptic stimulation/postsynaptic membrane
mesuarements (e.g. Hu, Leonardo, Chklovskii) this is the first such study
which aims to provide a "realistic" statistical model and, importantly,
which addresses the question of experimental design for this task.
Significance: The impact of this study will be be stronlgy
dependent on how well this method works on real data.
Q2: Please summarize your review in 12
sentences
This neat paper describes Bayesian methods and
experimental design for inferring synaptic connectivity via stimulation of
presynaptic cells and intracellular recordings of a postsynaptic cell.
The statistical model set up for this task is reasonable (but does have
clear limitations), and the algorithmic methods seem sound therefore,
this is a solid (but not outstanding) submission which could be of
interest for the NIPS audience.
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)
A sequential Bayesian experimental design method is
proposed for mapping connectivity and weight strength between stimulated
presynaptic and postsynaptic neurons, the cumulative response of the
latter (after potential random delays) can be observed (not just the
spiking, but the subthreshold voltage trace).
The authors use an
interesting model, essentially sparse linear (after simplifications) with
spike and slab priors. They apply a standard variational approximation
from previous work, which works well for spike and slab priors. This
procedure assumes that weights are independent under the posterior, which
is slightly odd for the purpose of experimental design, but their
improvements seem convincing (given the experimental setup).
Sequential BED for SLMs has been done before, using less damaging
posterior approximations (but not with spike&slab), the work of
Steinke, Seeger, Tsuda, AISTATS 2007 should be cited. I am not that
convinced about the way they optimize over z_n (or better: x_n) by ranking
singleneuron stimuli, even ignoring P(xz). But given that, the trick
of scoring very efficiently is nice: essentially no variational
reoptimization is required.
In my opinion, the paper has the
following weak points. First, I find it little convincing that a
single and known f(.) is used for all neurons. I also find the
simplification in Sect. 4 rather drastic: why not integrate over the
delays as well? This is not explicitly said, but I hope the
experimental data is at least drawn from the original model. This should
be stated more clearly, because otherwise why even mention the
original model? The model in Sect. 4 is a standard sparse linear model,
nothing related to neuroscience. Previous work of Paninski etal treated
more realistic models, albeit not in a Bayesian way.
Second, the
treatment of X is wrong. You need to sample from P(XZ,y), the posterior,
not from the prior. Please at least state that what you are doing is
at most an approximation. An alternative to the ranking of independent
singleneuron stimuli in 5.2 would be a greedy approach, where one
component after the other in x_n is selected. Of course, this would take
longer by a factor of K.
I was also puzzled about where the
averaging over X went in the scoring: do you skip it there?
Finally, experimental results are a bit slim. Essentially, the
method is tested on data sampled from the model itself. I suppose that
real experiments are hard to do, but at least one could somehow use real
data. Otherwise, I wonder what the motivation of the authors is. Also,
while the description in the supplemental material is nice and fairly
complete, details are not given in the paper. It would be possible to save
quite some of the text in previous sections, and then describe the
experiments better (in the paper).
Also, you mentioned Gibbs
sampling in the paper, but quote no results, neither there nor in the
supplement. This is not useful, either quote and describe them, or remove
the remark.
Q2: Please summarize your review in
12 sentences
Sequential Bayesian experimental design in a sparse
linear model, where the combinatorial search over inputs is
approximated in a simple way. Inference is done by a variational method
with fully factorized posterior (from previous work), the sparsity
prior is spike&slab.
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 of the reviewers for the time they put
into our paper and their constructive feedback. We’ll address the common
issues first, then respond to the unique comments of each reviewer.
Real Data All of the reviewers were curious about applying our
work to real data, and truthfully, the authors are very curious about this
as well. However, our focus here is to clearly introduce our models and
algorithms. While we have access to data that fit our model, we do not
have data where the true connection weights are known. Therefore we would
not be able to evaluate how well we perform. That said, we are currently
working on applying our work to real data, and we plan to write up these
results in future work.
Hyperparameters Another main concern
is how robust our algorithms are with respect to incorrect
hyperparameters. As stated in the paper, nearly all of the hyperparameters
can be estimated a priori by running a set of calibration experiments.
Nonetheless, we agree it is important to test our algorithms when the
hyperparameters which may be estimated poorly a priori are not chosen
well. In the revised version of the paper, in Figure 3 we show that our
inference is robust to deviations from the true the spike and slab
hyperparameters. When attempting to test the sensitive of our algorithm to
tau, we found it was quite sensitive which lead to the reformulation in
the revised paper where we infer charge of a synaptic event as opposed to
max amplitude.
Paper Organization/Two Models Apparently the
purpose of the two different models and the organization of the paper were
confusing. To be clear, we first present a model in Section 2 that is
complex enough to sufficiently describe the true data and flexible enough
to be used under different experimental setups. We feel this model is a
worthwhile contribution, and this is the model we use for data generation.
We then introduce experimental design as a goal in Section 3. To execute
ED in an online setting, it was necessary to develop a simplified model
with a quick inference algorithm which we describe in Section 4. In short,
we introduce material as it becomes necessary to our goals: full model
> ED > a simplified model for fast computation. In the revised
version of the paper, this organization has been restructured such that
the models are now fully described in the (new) Sections 23, with ED
introduced in Section 4.
Gibbs Sampler We found that the VB
approach typically performed as well or better than the Gibbs sampler. In
contrast to an earlier draft, Gibbs sampling output is now included in all
figures. Note that Gibbs sampling performance improved in the new
formulation of the problem as well.
ED Performance as Noise Level
and R Change As we discuss in Section 6, we believe that the reduction
in the efficacy of ED as noise and R increase is not a negative result. As
we write in the paper, the noise levels which are realistic to a voltage
clamp recording are in the smaller range of values we explored, and large
values of R may disrupt some of our model’s assumptions and requires
specialized hardware. But even if large R was appropriate, we see that the
inference procedure works very well, reconstructing the signal in very few
measurements. (In the largeR regime, the results of ref [24] indicate
that ED and random stimulation will perform similarly.) Ultimately, our
goal is quality reconstruction in few measurements whether ED is necessary
or not, and we find in particular that ED helps most in the
physiologically relevant regime of modest values for R and the noise
level.
Reviewer 3 “The model could include multiple
postsynaptic targets... this is a significant modification, but could be
considered in the conclusion.” This is definitely something to
consider; however, there is currently no way to record subthreshold
responses from a population of neurons. Also, it is possible that ED will
not be effective when there are so many competing independent interests
(each row of the connection matrix is independent given the data). In
short, the inference procedure in the paper would already work on the
population level as it would simply be K independent iterations of the
problem, but we are not sure how this would affect ED. We would like to
explore this as future work.
Reviewer 6 “In the absence of
real data... possibly input from other neurons, feedback couplings,
etc...” We are currently working on addressing some of these issues
such as nonevoked events, but this may be for future work.
Reviewer 7 “Sequential BED for SLMs has been done before...
even ignoring P(xz).” The approximations we make here  both during
inference and stimulus selection are for computational purposes. We
enforce that a decision must be returned to the experimenter in roughly
one second or less so that decision time is on the same scale as
experimental time. Regarding Steinke et al, while it’s not an exact
comparison, the runtime of the algorithm in that paper is much slower than
ours which for them is reasonable since their experiments take place on
larger time scales. Nonetheless, thank you for bringing this paper to our
attention; it should definitely be referenced here.
“Second, the
treatment of X is wrong... state that what you are doing is at most an
approximation.” You are correct: the text has been updated to clarify
the treatment of X and the approximation made here.
“An
alternative to the ranking... where one component after the other in x_n
is selected.” We tried this, but this procedure takes much too long to
compute due most importantly to an increase in runtime/convergence rate of
VB. Inference is slowed down by a large factor which grows with R due to
the iterative nature of VB. While it is hard to quantify the convergence
rate in terms of R, we can say empirically that it is not tractable to
score this way even when R=4.
 