
Submitted by
Assigned_Reviewer_4
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 paper contributes a statistical method to “stitch”
together sequentially imaged sets of neurons. Such a method expands the
population sizes for which population dynamics can be characterized beyond
the number of simultaneously imaged neurons and provide a better image of
the circuit which cannot be imaged as a whole for experimental and
technical limitations. The method is then applied on simulated data as
well as on experimental calcium imaging data in mice. Authors show that
they can estimate correlations in variability across two populations which
were not imaged simultaneously. The Authors model the problem as
fitting a latent dynamical system with missing observations. In this case
they used simple linear Gaussian system. Four parameters were defined in
the model: a functional coupling matrix, a stimuli receptive fields’
matrix which models the stimulus dependence of the population activity and
two covariance matrices for neural and measurement noise. The parameters
were estimated from experimental data using a variant of standard EM
algorithm.
Quality The model works nicely on the simulated
data with two nonoverlapping populations of neurons but when applying on
real data populations must have a certain level of overlap to get
reasonable results. It is clear why the greater the overlap the better the
results are, the question is why wasn’t overlap necessary in the simulated
data example? Also, the authors do not address the source for the
great difference in correlation shown when applying the model on simulated
data as in fig 2c and on real data as in fig 3b The beauty of the
model is the recovery of pairwise correlations between nonsimultaneously
measured neuron pairs.
Clarity The paper is well written,
although all figure legends are not descriptive enough and the text
related to the figures in the body of the paper does not elaborate enough
on the figures.
Originality The authors list several works
which have addressed the question of inferring functional connectivity
from 2photon imaging data or electrophysiological measurements. However,
these works do not infer functional connections of nonsimultaneously
imaged neurons.
Significance There are many fundamental limits
to the number of neurons which can be simultaneously imaged. That of
course, limits our capabilities to reveal the nature of the neural
computation at the level of the circuit (or more than a few hundreds of
cells). This paper suggests a method for expanding these limited
capabilities.
Q2: Please summarize your review in
12 sentences
Overall, this is a good model paper, which uses a
relatively simple linear dynamics model and captures measures which are
not easy to retrieve otherwise. 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)
This paper shows that you can infer network properties
of a large network by sequentially recording from subnetworks and then
stitching the resulting submodels. Extended to pointprocess data, this
could be applied to a lot of datasets where the typically a few of the
channels are moved every day. I am not really aware of any similar work
(J. W. Pillow and P. Latham, “Neural characterization in partially
observed populations of spiking neurons” seems to come the closest), and
it seems like a powerful idea.
In practice it's not clear how much
this method is limited to data that is close to linearGaussian, and I
don't get a good intuition from the paper how the fitting might break down
from various deviations to the assumption. In the extreme case, where the
full model can be estimated from one subset (up to a linear transformation
of the latent dimensions, as the authors state), it's not clear how much
additional information about the coupling matrix is gained from adding on
other subsets, as opposed to, say, just using more data from one of the
subsets.
Another point that raises some questions is, why does the
model on real data only work if there is some overlap between the two
population? Obviously this suggests that the linearGaussian simulated
data does not tell the full story, but it would be nice to have at least
some intuition what the overlap does to better constrain the model.
In the experiments on real data, where the linearity assumption
probably breaks, one must also wonder how much of the explained noise
correlations (which are fit well, the couplings themselves hardly
correlate to the true couplings at all in 3b) are due to common input and
not direct, pairwise couplings. I would assume that the noise
correlations could be better modeled with latent variables than pairwise
couplings.
The authors devote a lot of space to intro and
discussion, but are awefully light on the details of the estimation. The
equation for the M step on the bottom of page 3 is presented as the main
contribution, but not really explained or derived. Maybe it's a trivial
result to LDS experts, but that would erode a lot of the novelty of the
paper. I think the authors had a very good idea, but it just needs to be
explained better to properly convey the significance of the result.
Q2: Please summarize your review in 12
sentences
A neat idea tested against real data, but some details
aren't clear.
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 the reviewers for their thoughtful comments
and are pleased that they find it wellwritten, original and timely, and
unanimously recommend our paper for acceptance.
In our paper, we
demonstrated a rather simple but consequential idea  that it is possible
to "stitch" the dynamics of large neural populations, while only ever
simultaneously recording from a few neurons at a time. In particular, we
demonstrate for the first time that it is possible to successfully predict
noisecorrelations even for nonsimultaneously recorded neuronpairs. Our
contribution is an algorithmic approach for overcoming the limitations of
current experimental methods for recording neural activity. Our approach
based on linear gaussian dynamical systems, while simple, convincingly
demonstrates our main claim with surprising accuracy on real data. We
performed GCaMPbased 2photon calcium imaging in layer 2/3 neurons of the
mouse somatosensory cortex and showed that we were able to predict
correlations between nonsimultaneously imaged neurons in both awake and
anesthetized conditions.
We thank the reviewers for pointing out
ways in which to improve our presentation: 1) As R4 suggests, we will
improve our figure legends and descriptions. 2) R5 suggests defining
noise correlations more clearly. Indeed, we use the definition of Averbeck
et al 2007, as in linear dynamical systems, noise correlations depend both
on the system noise and the connectivity matrix. 3) As R6 suggests, we
will improve our description of the estimation algorithm.
The
reviewers were puzzled by the differences in performance between the toy
simulation and the real data. This is because we did not attempt to
carefully match the statistics of our simulated network to the real data.
Our goal with the simulations was to demonstrate that  in the best of
all worlds  it is possible to "stitch" together the population model,
even with no overlap. Of course we do not expect this idealized scenario
to hold, but rather than making our simulations more realistic, we decided
to directly test our model on real data. Thus all our main results are
based on real calcium imaging datasets.
In line with previous work
(Yu et al., 2009; Briggman et al., 2006) and in contrast to our
simulations, we find that the neural activity in layer 2/3 neurons are
driven largely by lowdimensional common input. This means that only a
small subspace of the activity is actually excited by the lowdimensional
input, and hence in our model only the corresponding entries of the
Amatrix will be constrained to meaningful values. The remaining part of
the Amatrix is nonidentifiable and unimportant to the neural dynamics.
This explains why Fig 3b has a larger scatter than Fig 2c.
Further, we find in Fig 4c that the parameter correlation
decreases with increasing population size. This can be interpreted as
evidence that the dimensionality of common input (and hence the
dimensionality of the constrained parameter space) grows more slowly than
the unconstrained noise parameter space. The common input could also be
part of the explanation for why some amount of overlap is required for
good prediction on the layer 2/3 data.
We agree with the reviewers
that improving the simple LDS model to better model common input, the
dynamics of the calcium signal and spiking activity will be important
directions for future research.
 