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J Neurophysiol. 2017 Mar 1;117(3):919-936. doi: 10.1152/jn.00698.2016. Epub 2016 Dec 7.

Revealing unobserved factors underlying cortical activity with a rectified latent variable model applied to neural population recordings.

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Applied Mathematics and Statistics and Scientific Computation Program, University of Maryland, College Park, Maryland; and
Applied Mathematics and Statistics and Scientific Computation Program, University of Maryland, College Park, Maryland; and.
Department of Biology and Program in Neuroscience and Cognitive Science, University of Maryland, College Park, Maryland.


The activity of sensory cortical neurons is not only driven by external stimuli but also shaped by other sources of input to the cortex. Unlike external stimuli, these other sources of input are challenging to experimentally control, or even observe, and as a result contribute to variability of neural responses to sensory stimuli. However, such sources of input are likely not "noise" and may play an integral role in sensory cortex function. Here we introduce the rectified latent variable model (RLVM) in order to identify these sources of input using simultaneously recorded cortical neuron populations. The RLVM is novel in that it employs nonnegative (rectified) latent variables and is much less restrictive in the mathematical constraints on solutions because of the use of an autoencoder neural network to initialize model parameters. We show that the RLVM outperforms principal component analysis, factor analysis, and independent component analysis, using simulated data across a range of conditions. We then apply this model to two-photon imaging of hundreds of simultaneously recorded neurons in mouse primary somatosensory cortex during a tactile discrimination task. Across many experiments, the RLVM identifies latent variables related to both the tactile stimulation as well as nonstimulus aspects of the behavioral task, with a majority of activity explained by the latter. These results suggest that properly identifying such latent variables is necessary for a full understanding of sensory cortical function and demonstrate novel methods for leveraging large population recordings to this end.NEW & NOTEWORTHY The rapid development of neural recording technologies presents new opportunities for understanding patterns of activity across neural populations. Here we show how a latent variable model with appropriate nonlinear form can be used to identify sources of input to a neural population and infer their time courses. Furthermore, we demonstrate how these sources are related to behavioral contexts outside of direct experimental control.


barrel cortex; dimensionality reduction; latent variable models; two-photon imaging

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