Paper:
Extracting low-dimensional dynamics from multiple large-scale neural population recordings by learning to predict correlations
A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data are limited to single population recordings, and can not identify dynamics embedded across multiple measurements. We propose an approach for extracting low-dimensional dynamics from multiple, sequential recordings. Our algorithm scales to data comprising millions of observed dimensions, making it possible to access dynamics distributed across large populations or multiple brain areas. Building on subspace-identification approaches for dynamical systems, we perform parameter estimation by minimizing a moment-matching objective using a scalable stochastic gradient descent algorithm: The model is optimized to predict temporal covariations across neurons and across time. We show how this approach naturally handles missing data and multiple partial recordings, and can identify dynamics and predict correlations even in the presence of severe subsampling and small overlap between recordings. We demonstrate the effectiveness of the approach both on simulated data and a whole-brain larval zebrafish imaging dataset.

Review:
The authors suggest a method to estimate latent low dimensional dynamics from sequential partial observations of a population. Using estimates of lagged covariances, the method is able to reconstruct unobserved covariances quite well. The extra constraints introduced by looking at several lags allow for very small overlaps between the observed subsets.
This is an important work, as many imaging techniques have an inherent tradeoff between their sampling rate and the size of the population. A recent relevant work considered this from the perspective of inferring connectivity in a recurrent neural network (parameters of a specific nonlinear model with observations of the entire subset) [1].
The results seem impressive, with an ability to infer the dynamics even for very low overlaps, and the spiking network and zebrafish data indicate that the method works for certain nonlinear dynamics as well.
A few comments:
1.	In Figure 3b the error increases eventually, but this is not mentioned.
2.	Spiking simulation – the paper assumes a uniform sampling across clusters. How sensitive is it to under-sampling of some clusters?
3.	The zebrafish reconstruction of covariance. What is the estimated dimensionality of the data? The overlap is small in terms of percentage (1/41), but large in number of voxels (200K). Is this a case where the overlap is much larger than the dimensionality, and the constraints from lagged covariances do not add much? This example clearly shows the computational scaling of the algorithm, but I’m not sure how challenging it is in terms of the actual data.
[1] Soudry, Daniel, et al. "Efficient" shotgun" inference of neural connectivity from highly sub-sampled activity data." PLoS computational biology 11.10 (2015): e1004464.