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Last week, I co-organized the NIPS workshop titled: Large scale optical physiology: From data-acquisition to models of neural coding with Ferran Diego Andilla, Jeremy Freeman, Eftychios Pnevmatikakis and Jakob Macke. Optical neurophysiology promises larger population recordings, but we are also facing with technical challenges in hardware, software, signal processing, and statistical tools to analyze high-dimensional data. Here are highlights of some of the non-optical physiology talks:

Surya Ganguli presented exciting new results improving from his last NIPS workshop and last COSYNE workshop talks. Our experimental limitations put us to analyze severely subsampled data, and we often find correlations and low-dimensional dynamics. Surya asks “How would dynamical portraits change if we record from more neurons?” This time he had detailed results for single-trial experiments. Using matrix perturbation, random matrix, and non-commutative probability theory, they show a sharp phase transition in recoverability of the manifold. Their model was linear Gaussian, namely $R = U X + Z$, where X is a low-rank neural trajectories over time, U is a sparse subsampling matrix, and Z is additive Gaussian noise. The bound for recovery had a form of $\mathrm{SNR} \sqrt{MP} \geq K$, where K is the dimension of the latent dynamics, P is the temporal duration (samples), M is the number of subsampled neurons, and SNR denotes the signal-to-noise ratio of a single neuron.

Vladimir Itskov gave a talk about inferring structural properties of the network from the estimated covariance matrix (We originally invited his collaborator Eva Pastalkova, but she couldn’t make it due to a job interview). An undirected graph which has weights that corresponds to an embedding in an Euclidean space shows a characteristic Betti curve: curve of Betti numbers as a function of threshold for the graph’s weights which is varied to construct the topological objects. For certain random graphs, the characteristics are very different, hence they used it to quantify how ‘random’ or ‘low-dimensional’ the covariances they observed were. Unfortunately, these curves are very computationally expensive so only up to 3rd Betti number can be estimated, and the Betti curves are too noisy to be used for estimating dimensionality directly. But, they found that hippocampal data were far from ‘random’. A similar talk was given at CNS 2013.

William Bishop, a 5th year graduate student working with Byron Yu and Rob Kass, talked about stitching partially overlapping covariance matrices, a problem first discussed in NIPS 2013 by Srini Turaga and coworkers: Can we estimate the full noise correlation matrix of a large population given smaller overlapping observations? He provided sufficient conditions for stitching, the most important of which is to make the covariance matrix of the overlap at least the rank of the entire covariance matrix. Furthermore, he analyzed theoretical bounds on perturbations which can be used for designing strategies for choosing the overlaps carefully. For details see the corresponding main conference paper, Deterministic Symmetric Positive Semidefinite Matrix Completion.

Unfortunately, due to weather conditions Rob Kass couldn’t make it to the workshop.

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