Paper:
Learning a latent manifold of odor representations from neural responses in piriform cortex
A major difficulty in studying the neural mechanisms underlying olfactory perception is the lack of obvious structure in the relationship between odorants and the neural activity patterns they elicit. Here we use odor-evoked responses in piriform cortex to identify a latent manifold specifying latent distance relationships between olfactory stimuli. Our approach is based on the Gaussian process latent variable model, and seeks to map odorants to points in a low-dimensional embedding space, where distances between points in the embedding space relate to the similarity of population responses they elicit. The model is specified by an explicit continuous mapping from a latent embedding space to the space of high-dimensional neural population firing rates via nonlinear tuning curves, each parametrized by a Gaussian process. Population responses are then generated by the addition of correlated, odor-dependent Gaussian noise. We fit this model to large-scale calcium fluorescence imaging measurements of population activity in layers 2 and 3 of mouse piriform cortex following the presentation of a diverse set of odorants. The model identifies a low-dimensional embedding of each odor, and a smooth tuning curve over the latent embedding space that accurately captures each neuron's response to different odorants. The model captures both signal and noise correlations across more than 500 neurons. We validate the model using a cross-validation analysis known as co-smoothing to show that the model can accurately predict the responses of a population of held-out neurons to test odorants.

Review:
The authors describe the application of a Gaussian Process Latent Variable Model to neural population recordings in the Piriform cortex, obtained from mice, using a fluorescent calcium reporter. The goal of the study is to model the relations between different odorants, which presumably are encoded by the brain to lie in some smooth and continuous latent space, although the Piriform cortex itself has never been shown to have the same obvious topography as e.g. the visual or auditory cortices. The central claim of the paper is that although odorants can be "described by thousands of features in a high-dimensional chemical feature space", the "dimension of olfactory perceptual space" is unknown, and the authors propose a model that identifies a "low-dimensional space governing odor perception" learned from the neural activity caused by presenting an odor to a mouse undergoing brain imaging. Discovering a true or even merely useful latent embedding of monomolecular odors is indeed an open problem, and there is a question of whether there even exists a continuous latent space for odorants. There is a body of prior work on this topic that unfortunately was not cited, such as Koulakov 2011, Mamlouk et al 2003, Haddad et al 2008 and Iurilli et al 2017.   The model of choice here is a GPLVM augmented to account for specific covariance structure among trial-to-trial noise variability per neuron, as well as covariance between neural population responses to odorant stimuli. This is modeled efficiently using a Kronecker-factored full covariance matrix. Although interesting, it is my understanding that the specific model structure and optimization procedure are not methodological innovations. Regardless, if the goal of the work is to discover useful representations of odors, comparison to alternate model formulations for building the embeddings is crucial. For instance, how well does this modeling approach compare to using logistic regression on the Dragon molecular descriptors as input?  Along those lines, I particularly appreciated the study of alternate treatments of the covariance structure in the model on synthetic data, but would have preferred this to be run on the real data. Further, applying this kind of test to the choice of the RBF kernel, which likely has dramatic effects on the structure of the embedding, would provide further evidence on whether the particular modeling choices made here serve the purpose of the work. For instance, if the authors hypothesized that odors are naturally organized in a smooth embedding space, the choice of the RBF kernel artificially inflates the likelihood of finding such an embedding after fitting the model.  The experimental set up was described well, but some details were missing. It would be useful to know if there is a mouse driver line, or if a non-targeted viral transfection was used, how exactly 'neuropil contamination' was removed (this is often a very ad hoc computer vision processing step that can dramatically affect data quality).   Overall, I found the paper clearly written, although dense in places. Unfortunately, I do not believe that this submission contains new knowledge of interest to the NIPS community, and the scientific findings are not tested thoroughly enough in the current state of the paper to be of significance.  Some specific comments:  - The use of the term 'topography' is a bit confusing, as it is usually used in the neuroscience context to refer to a physical correspondence to stimulus space and the layout of a cortical area. E.g., retinotopy refers to the layout of the retina mapping physically onto visual cortex.  - The prior for embedding locations is set to be an uninformative prior, due to the lack of inclusion of chemical features per odorant. However, that information is available, and would be very useful to incorporate.  - No axes or labels on 2B  - An existing hypothesis about how odors are encoded in the piriform cortex is that it is performing random projections through the anatomy of connections from the mitral cells to pyramidal cells in the piriform. Random projections would thus be a natural baseline to compare against.   - Typo: "captures each neuron?s response"    ---------------------------------------------------------------- After author's response and reviewer discussion: I was surprised to see how out-of-range this review was, and after discussion with other reviewers, have revised my score upwards. My main critical thoughts on the paper were: - If this is a methods paper, it relies heavily on a single application, doesn't present clear technical superiority over competitive alternative methods, and doesn't present sufficient technical novelty, with a small exception. The GPLVM model proposed is technically interesting and challenging, but the main features used are not new, which the authors acknowledge. The exception here, as the authors point out, is modeling multi-trial covariance structure, which is indeed a tough problem to tackle in neuroscience data. I weighted the work down because of limited technical novelty, mostly ignoring the fact that this modeling approach has not been applied widely for modeling neural spiking data. Fusing an old technique with a new application is indeed an interesting endeavor, and thoroughly useful -- if we generate new knowledge in the application space.  - If this is an applications paper, we did not learn anything new about the application. The stated goal of the work is to find a smooth olfactory embedding, which practitioners in the field do hope exist and have been searching for for quite some time. Properties of a putative embedding have huge potential impact in olfactory neuroscience, and in understanding how sensory circuits in general process information from the outside world. However, the authors unfairly stack the deck in their favor -- they build a GPLVM model with a smooth priors, and do not provide the reader a way to evaluate if their embedding is superior along any other axis besides smoothness. I weighted the work down because their results in this application were presented without sufficient context and comparison, and because of the circular nature of how they defined success -- smoothness is good, so we fit a model that can likely only produce smooth embeddings.  However, it was brought to my attention by fellow reviewers that non-novel but cutting-edge methods (which this paper uses) cleanly applied to interesting domains (which this paper does), even if no new knowledge is generated, is of interest to the NIPS community.